Arduino Elderly Care System

Patients, Primary Care, and Policy: Simulation Modeling for

Health Care Decision Support

Martin Comis · Catherine Cleophas · Christina B¨using

Creasing Due To The Ongoing Demographic Change,

while at the same time health service providers face difficulties in finding skilled personnel. This cre-

Ates Pressure On Health Care Systems Around The

world, such that the efficient, nationwide provision of primary health care has become one of society’s greatest challenges. Due to the complexity of health care systems, unforeseen future events, and a fre-

Performance Of Health Care Systems Means Tackling

a wicked problem. To support this task for primary care, this paper introduces the hybrid agent-based

Simulation Model Sim-Care. Sim-Care Models The

interactions of patients and primary care physicians on an individual level. By tracking agent interac- tions, it enables modelers to assess multiple key in- dicators such as patient waiting times and physician utilization. Based on these indicators, primary care

Systems Can Be Assessed And Compared. Moreover,

changes in the infrastructure, patient behavior, and service design can be directly evaluated. To show- case the opportunities offered by SiM-Care and aid model validation, we present a case study for a pri-

Mary Care System In Germany. Specifically, We In-

This work is supported by the Freigeist-Fellowship of the Volkswagen Stiftung. This work is supported by the German research council (DFG) Research Training Group 2236 UnRAVeL.

Catherine Cleophas

Working Group Service Analytics, Christian-Albrechts- Universit¨at zu Kiel, Westring 425, 24118 Kiel, Germany vestigate the effects of an aging population, a de- crease in the number of physicians, as well as the combined effects.

1 Introduction

Health is one of the most important factors for the prosperity and well-being of a society. Therefore,

Eryone’S Access To Health Services . The Foun-

dation of universally accessible health services is

Physicians , Primary Care Systems “Serve As The

patient’s first point of entry into the health care sys-

Tem And The Continuing Focal Point For All Needed

health services”. To that end, they feature a set of

Mary Care Services To A Defined Population Of Pa-

tients”. Such primary care services include “health promotion, disease prevention, health maintenance, counseling, patient education, diagnosis and treat- ment of acute and chronic illnesses”.

Progress Paired With Improved Living Conditions

and reduced birth rates lead to a rise in the share of elderly citizens. In the United States, the percent- age of individuals aged 65 and older is predicted to exceed 21% of the total population by 2030 .

2

Martin Comis et al.

Age, Their Demand For Primary Care Services Tends

to increase. This is primarily due to the prevalence of chronic illnesses which disproportionately affect

Older Adults . On The Supply Side, Primary

care physicians are also aging, e.g., 34.1% of all

Or Older By The End Of 2017 And Thus About To

retire. Moreover, fewer medical students are will-

Private Primary Care Practice . This Leads To Re-

duced treatment capacities and exacerbates the risk for supply disruptions. In the United States, the “confluence of a rising de-

Mand For Primary Care Services And A Decreasing

supply of professionals providing these services” is

Considered A “Crisis In Primary Care” . In Order

to manage this crisis, existing primary care systems

Have To Be Fundamentally Adjusted . Various

new concepts and policies to maintain the standard of health care provision are discussed by the statu-

Cians . However, All Such Concepts Call For

validation and evaluation prior to their potentially

Costly Implementation . Naturally, This Leads To

the pressing question: How can the quality of pri- mary care systems and the effect of changes to them

Which Defines Adequate Health Care Supply On The

basis of profession-specific ratios. The law subdi-

Ical Specialization. For Example, The Predefined

nominal ratio of primary care physicians is one PCP per 1,671 inhabitants [24, §11(4)]. This base indi-

Dividual Demographic And Geographic Characteris-

tics [24, §2]. If the actual ratio of a zone is signif- icantly higher than the nominal ratio, closing prac- tices will not be replaced. If it is significantly lower, new practices are permitted to be opened.

Services Administration (Hrsa) Defines Adequate

health care supply based on profession- and region- specific population-to-provider ratios. If the pre-

Needs ) Of A Geographic Area Is Exceeded, Hrsa

designates it a health professional shortage area to

Which National Health Service Corps Personnel Is

directed with priority. Obviously all ratio-based assessments have several

Justment Rules Are Highly Dependent On The Defini-

tion of the underlying zones or geographic areas. Factors such as the accessibility of practices and

The Pcp’S Individual Workload Are Completely Ne-

glected. Finally, ratio-based assessments cannot ac-

Count For New Health Care Concepts Such As Tele-

medicine, mobile medical units, or centralized ap- pointment scheduling.

Model Dynamic Effects In Primary Care Systems Is

required. However, analyzing and evaluating health

Due To The Large Number Of Involved Individuals

and uncertain nature of health care processes, e.g., fluctuating demand, arrival time of patients, emer-

Modeling (Abm), Which Account For Individual

agents and their interactions on the micro-level. A general introduction to the concept of ABM is pro-

Numerous Applications Of Abm In Field Of Health

care , e.g., for accountable care organizations [5,

44], For Medical Workforce Forecasting , And In

epidemiology .

Care Systems. Sim-Care Models Patients And Pcps

on an individual level as illustrated by Figure 1:

On Their State Of Health And Pcps Handle Appoint-

ment requests, manage patient admission, and treat patients. By tracking the resulting interactions in Patients, Primary Care, and Policy: Simulation Modeling for Health Care Decision Support

Patients

Fig. 1 Geo-social system of patients and physicians.1

Different Subproblems, Evaluate New Planning Ap-

proaches, and quantify the effects of interventions

Measurements. From Empirical Data, We Develop Re-

alistic test scenarios including a controllable degree of uncertainty realized via stochastic simulation ex- periments.

Model Sim-Care, Which Provides Decision Makers

with a versatile decision support tool for primary

Be Easily Modified And Extended To Meet Each Mod-

eler’s needs. Patients and physicians are modeled as individuals who follow their own objectives, learn, and adapt. To ensure computational tractability, the model incorporates a global event queue at its core.

From Agent-Based Modeling And Discrete Event Sim-

ulation. Based on empirical data for a German pri-

Mary Care System, We Illustrate How Scenarios For

the simulation model can be generated. Finally, we

Showcase The Opportunities Of Sim-Care Through A

case study. To the best of our knowledge, SiM-Care is the first model of its kind that captures entire pri-

Mary Care System With All Physicians And Patients

as individual agents and allows for the simultane-

Ous Consideration Of Microsystem Improvements As

well as macrosystem reforms. 1 Map tiles by Stamen Design, under CC BY 3.0. Data by OpenStreetMap, under ODbL.

Based Simulations With A Focus On Health Care Ap-

plications. Section 3 introduces SiM-Care based on

Aid Model Validation And Showcase How Sim-Care

can be applied to support health care planning. Sec- tion 5 discusses the potential applications and entry

Requirements Of Sim-Care. Finally, Section 6 Con-

cludes and provides directions for future work.

2 Related Work

Decision support for health care planning is an area

Care Systems, Decision Support Tools Have To Deal

with the detail complexity that is inherent to the

Health Care Sector : Patients Schedule Appoint-

ments based on their preferences and state of health, while PCPs offer appointments and treat patients. Thereby, micro-interactions affect macro-level in- dicators as agents observe, learn and adapt, decide and act, and - as a group - determine the system’s

Behavior . When A System’S Status Depends On

such micro-interactions, its behavior becomes diffi- cult to predict and a “wide range of possible out- comes may arise from any policy change” .

Simulation Modeling Can Deal With This Kind Of

complexity by “simulating the life histories of in- dividuals and then estimating the population effect

Such, Simulation Models Represent A Powerful Tool

to inform policy makers: They can provide valuable

Insights Into The Dependencies Within Health Care

systems and allow for the prediction of the outcome of a change in strategy ahead of a potentially costly and risky real-world intervention .

Given these potentials, the use of computer simula- tion to study health care delivery systems has sig-

Nificantly Increased Over The Recent Years . The

resulting body of literature on applications of simu- lation in health care is rich and can, from a method- ological point of view, be classified into four main

More Of The Former Paradigms . To Catego-

rize related work on the study of primary care sys- tems even further, we distinguish in the following

Models That Focus On Microsystem Improvements

and models that aim at macrosystem reforms.

4

Martin Comis et al.

Improvements In Primary Care Systems Mostly In-

clude a detailed model of a single (specific) outpa-

Potential Improvements. Zong Et Al. Present A

discrete event simulation for a pediatric clinic at includes a very detailed representation of the se- quential stages during a patient’s visit. In a set of

The Overall Performance Of The Clinic Is Impacted

by different scheduling templates, a change in the medical assistant to physician ratio, and the pairing of resident doctors with clinicians. Shi et al.

Developed A Discrete Event Simulation Model For

eran Affairs. Within the model, the different patient flow routes for appointment patients, walk-ins, and nurse-only patients are distinguished. In a scenario analysis, the authors investigate how the clinic’s performance is affected by six distinct factors that

Include Walk-In And No-Show Rates As Well As The

double booking of appointments. Cayirli et al.

Used Empirical Data Collected At A Primary Care

clinic in New York to devise a discrete event simu- lation of a generic single-server primary care prac- tice. The model distinguishes new and returning pa- tients and accounts for walk-ins, no-shows, patient punctuality, and service time variations. In a sim- ulation study, the authors evaluate 42 appointment

Systems That Vary In The Implemented Sequencing-

and appointment rules. A similar discrete event sim- ulation of a generic single-server primary care prac-

Tice Is Introduced By Schacht . In His Model,

all arriving patients have a stochastic willingness

To Wait And Always Request An Appointment. If The

indirect waiting time for this appointment exceeds a patient’s willingness to wait, they become walk- ins. The arrival rate of patients depends on the ses-

Sion, Day, And Month To Model Seasonality. In A

case study, the author evaluates a class of appoint-

Make Up A Primary Care System. Moreover, All Of

these models adopt a different approach to the rep-

Resentation Of Patients: While Sim-Care Models A

persistent patient population that is shared by all providers, the previous models perceive patients as non-persistent, i.e., patients are generated as they arrive at the practice and cease to exist as soon as they are discharged. As a result, the previous mod- els cannot account for the effects of individual mi-

Crosytem Improvements On The Entire Primary Care

system itself. Simulation models aimed at investigating macrosys- tem reforms of primary care systems mostly include

An Entire Primary Care System, However They Are

usually much more high level. Matchar et al.

Use The Methodology Of System Dynamics To De-

velop a simulation model to aid primary care plan-

Work. The Authors Evaluate Three Policy Changes

that constitute in reducing the service gap, reduc- ing the out-of-pocket costs, and increasing the num-

Sim-Care And Does Not Model Patients Or Physi-

cians as individuals. Consequently, the model can- not account for the objectives and satisfaction of in- dividual stakeholders which limits the possibilities

Based Model To Investigate The Paradox Of Primary

care. Their model features patients, PCPs, and spe- cialists as individual agents. Every patient has a health status that changes over time: The contrac- tion of illnesses leads to a (temporary) decrease in the patients’ health; the treatment of acute illnesses

By Pcps And Specialists As Well As Regular Check-

ups (performed exclusively by PCPs) lead to an in- crease in the patients’ health. Tracking the evolu- tion of the patients’ average health status over time, the authors investigate how public health is posi- tively affected by the interplay of different mecha-

Nisms In Primary Care. As Such, The Model Of Homa

et. al has a different objective than SiM-Care: While Homa et al. investigate the external effects of treat- ments in primary care on the entire health care sys- tem, SiM-Care focuses on the processes within pri-

Mary Care Systems. To That End, Sim-Care Models

the scheduling of appointments, the patients’ actual practice visits that result in waiting times through the interaction of patients, and the physicians’ treat- ments of patients with variable service times which are not part of the model by Homa et al.

Ous Work On Simulation Models For The Evaluation

of primary care systems that allow for the simulta-

Neous Consideration Of Microsystem Improvements

and macrosystem reforms as in SiM-Care. Patients, Primary Care, and Policy: Simulation Modeling for Health Care Decision Support

Sim-Care Models The Interaction Of Patients And

primary care physicians in a restricted geographical area over a given period of time; compare Figure 1.

The Model Features Two Types Of Agents: A Popu-

lation of potential patients P and a population of

Primary Care Physicians G. Every Patient Ρ ∈P Re-

sides at a specific location, belongs to a certain age group, has an individual health status, as well as in- dividual treatment preferences; compare Figure 2.

Patients continuously develop acute illnesses that

Depend On Their Age And Health Status And Require

treatment until they subside. Additionally, patients

Need To Be Monitored By A Physician On A Regular

basis. To receive medical attention, patients either

Schedule An Appointment Or Visit A Pcp’S Practice

without prior notice. Thereby, the patients’ decision making process depends on their individual prefer- ences and health status which determine the choice of physician, the type of the visit (walk-in/ appoint- ment), as well as the time of the visit. Physicians φ ∈G practice at a certain location and have weekly opening hours during which they admit patients for treatment; see Figure 2. Moreover, every physician φ ∈G follows individual strategies that govern how they manage appointments, admit patients, and per- form treatments. As patients and physicians inter- act, they influence each other and adapt by adjust- ing their preferences and strategies.

And Policy Makers. These Objectives Are Assumed

by the model as follows: While PCPs strive to effi- ciently utilize their time, patients strive for a quick

Cost Of Health Care To Maximizing The Degree Of

patient-centered care. Policy makers are not repre-

Sented By Agents Within Sim-Care. Instead, Policy

decisions set relevant model parameters such as the

Number Of Physicians In The Area, Treatment Stan-

dards, and the financial reimbursement system.

Scribed By Grimm Et Al. . To Concisely High-

light the interaction of relevant components in that

Scales Within Sim-Care. Second, Section 3.2 De-

scribes the representation of the relevant entities and state variables, including patients and physi- cians with their sensing, predicting, adapting, in- teracting, and learning actions. Third, Section 3.3

Of Health Care Systems Through Stochastic Parame-

ters. Fifth, Section 3.5 briefly reviews the indica- tors that result from running the simulation and ex- plains their emergent properties. Sixth, Section 3.6 discusses the initialization of a simulation experi-

Ment. Seventh, Section 3.7 Documents The Submod-

els that implement, e.g., the PCP’s strategies to han- dle appointments. Finally, Section 3.8 describes our structural validation as well as our approach to ver- ification taken when implementing the model.

Sim-Care’S Environment Entails The Geographical

and temporal structure as well as policy effects.

Coordinates Latitude And Longitude Indicating The

north-south and east-west position, respectively.

The Modeled Time Period Is Considered As A Con-

tinuum structured by points in time and durations. For any time object (point in time or duration) t =

Same Encoding For Points In Time And Durations As

context uniquely defines which of the former a time object refers to. For example, (38,0.55) ∈T corre- sponds to day 38 and 24 · 60 · 0.55 = 792 minutes, i.e., 1:12 p.m. as a point in time or, analogously, to a duration of 38 days, 13 hours, and 12 minutes.

To ease notation, we associate every point in time

R≥0.

In addition to the continuous representation of time, we structure each day into a morning and an after-

Is Uniquely Defined By A Day Δ ∈N And A Binary

indicator γ ∈{0,1}. Thereby, the binary indicator γ

6

Martin Comis et al.

Illnesses

Fig. 2 Concept of SiM-Care showing both types of agents with their main attributes as well as interactions between agents. defines whether it is the morning (γ = 0) or the after- noon (γ = 1) session. Sessions reoccur on a weekly basis which yields an equivalence relation ∼on the

Set Of Sessions Λ Via

(δ1,γ1) ∼(δ2,γ2) :⇔δ1 ≡δ2 mod7 ∧γ1 = γ2. The resulting equivalence class for a session λ ∈Λ defined as [λ] := {λ′ ∈Λ : λ′ ∼λ} contains all ses-

Sions Sharing The Same Day Of The Week And Time

of the day, e.g., all Thursday afternoon sessions.

Classes Λ/∼:= {[Λ] : Λ ∈Λ} With The 14 Sessions

of the week, i.e., Monday to Sunday with a respec- tive morning and afternoon session.

Pcps Φ ∈G Are The Active Entities In The Simula-

tion. Their interaction is motivated by patients’ suf- fering from illnesses and therefore seeking treat-

Its. Both Patients And Pcps Are Complex Individu-

als featuring characteristics that represent entities

Themselves. Going From Simple To More Elaborated,

we begin by describing the self-containing entities

Of Sim-Care And End With The Description Of The

agents representing patients and physicians.

When Patients Suffer From An Acute Illness, They

want to be treated as soon as possible, ideally by their preferred physician. For the continuous treat-

Ment Of Chronic Illnesses And The Follow-Up Care

of acute illnesses, patients prefer treatment by the same physician through appointments in regular in- tervals. Physicians, on the other hand, aim at effi- ciently utilizing their available time while minimiz- ing overtime. Thus, patients’ and physicians’ objec- tives are in conflict as it is ineffective for physicians

Ments In Strict Intervals Would Prevent Pcps From

reacting to demand fluctuations.

One Hand, They Need To Ensure A Certain Minimum

standard in health care quality to guarantee patients are treated when necessary. On the other hand, they

Cannot Afford To Subsidize An Excessive Number Of

physicians. Thus, policy makers necessarily aim at a trade-off: A purely patient-based system that dis- regards efficiency is likely to turn out to be unaf-

Cess Times. Sim-Care Represents Policy Decisions

through their resulting parameter values, e.g., the number of physicians and their distribution.

3.2.2 Illnesses And Families Of Illnesses

Illnesses are health concerns that cause discomfort to patients and require treatment. They belong to a certain illness family (e.g. cold or heartburn), have a certain seriousness (e.g. mild or severe), persist over a certain period of time, and require an initial

Treatment Within An Acceptable Time Frame As Well

as subsequent follow-up visits in regular time inter- vals. In SiM-Care, we formalize illnesses as tuples Patients, Primary Care, and Policy: Simulation Modeling for Health Care Decision Support

7

i = (si, fi,di,ωi,νi) ∈I with attributes as shown in

Table 1. Thereby, Si ∈ Defines The Seriousness

of the illness, fi ∈F defines the illness family of

Illness. The Parameter Ωi ∈T Defines The Illness’

willingness to wait, which is the patient’s maximum accepted waiting time for the initial treatment. The

Parameter Νi ∈T Defines The Illness’ Follow-Up In-

terval, which specifies the frequency of the required aftercare that follows the initial treatment. When we use this representation to model health concerns that are not strictly illnesses like the need for vac- cination, the characteristics duration and follow-up interval may not apply. In such cases, setting pa- rameter values di = /0 and νi = /0 indicates that the respective characteristic is not applicable for i ∈I .

Families of illnesses serve as the classification sys-

Tem Of Illnesses Within Sim-Care. While Emerg-

ing illnesses vary in their manifestation, families of

Illnesses Define The Common Constant Traits Of All

illnesses belonging to the same illness family. In

Ing To Illness Family Fi ∈F Are The Expected Du-

ration D fi(si) ∈T , the expected willingness to wait Wfi(si) ∈T , and the follow-up interval Nfi(si) ∈T . The expected duration D fi(si) and expected willing- ness to wait Wfi(si) are exclusively used during the

The Means For Distributions From Which We Sample

each illness’ stochastic duration di and stochastic

Willingness To Wait Ωi. Thus For All Emerged Ill-

nesses i ∈I , it generally holds that di̸ = D fi(si)

Emerged Illnesses I ∈I Derives From The Illness

family in a deterministic way, i.e., νi = Nfi(si).

In Order To Define The Common Traits Of Emerg-

ing illnesses, families of illnesses f ∈F are for-

Tion D F : →T That Defines The Expected Dura-

tion D f (s) in days for all emerging illnesses with

And Nf : →T That Analogously Define The Ex-

pected willingness to wait in days and follow-up in- terval in days; see Table 2. As above, we indicate the inapplicability of the characteristics duration or follow-up interval to families of illnesses by setting D f = /0 and Nf = /0, respectively.

To illustrate the concept of illnesses and families

Cold” With Expected Illness Duration Defined By

Table 1 Attributes of illnesses i ∈I .

[Days]

Table 2 Attributes of families of illnesses f ∈F .

Κf ∈{0,1}

D f (s) = 10s + 3, expected willingness to wait de-

Ness Family “Common Cold” Defines The Expected

duration, expected willingness to wait, and follow- up interval of the mild cold as D f (si) = 5 days, Wf (si) = 2.4 days, and Nf (si) = 6.6 days. The ac- tual duration and willingness to wait of the devel-

Oped Mild “Common Cold” Are Stochastic And Vary

around their expected counterparts, e.g., di = 5.5 days and ωi = 2.7 days. The illness’ follow-up in- terval is deterministic and derives from the illness family via νi = Nfi(si) = 6.6 days.

Chronic Attribute Κf ∈{0,1} Identifies Families Of

chronic illnesses. Thereby, κf partitions F into the set of acute families of illnesses F act := { f ∈F : κf = 0} and the set of chronic families of illnesses

F Chro := { F ∈F : Κf = 1}. This Directly Induces

a partition of the set of illnesses I into the set of acute I act and the set of chronic illnesses I chro.

Time And Patients Can Simultaneously Suffer From

an arbitrary number of acute illnesses I act ⊆I act. Chronic illnesses ς ∈I chro are conceived as static

By The Model – They Neither Develop Nor Heal In

the modeled time period. Instead, each patient ρ ∈

From A Chronic Illness From Those Who Do Not, We

refer to the former as chronic patients.

8

Martin Comis et al. Table 3 Attributes of age classes a ∈A.

3.2.3 Appointments

Appointments specify the point in time at which the treatment of a specific patient is scheduled to take

Place. To That End, Appointments B ∈B Are Defined

by the time of the appointment tb ∈T , the attend-

Non-Chronic Patients Can Have At Most One Sched-

uled appointment bact ∈B, called the acute appoint- ment. Acute appointments are intended for the ini- tial treatment of acute illnesses, the follow-up treat- ment of acute illnesses, or both. Chronic patients,

May Have A Regular Appointment Breg ∈B To Treat

their chronic illness in addition to the acute appoint- ment to treat their acute illnesses. While chronic illnesses are only treated during regular appoint- ments, acute illness are treated during any appoint- ment. Thus, all of a patients’ acute illnesses I act are treated during every appointment.

Serve The Purpose Of Defining The Common Charac-

teristics of patients within the respective classes. For patients of age class a ∈A, these characteristics are the deviation from the expected illness duration

∆D

a > 0, the deviation from the expected willingness

Number Of Annual Acute Illnesses Defined Through

the linear function Ia : →R≥0; see Table 3. The deviation from the expected illness duration ∆d

A

is a multiplicative factor, that determines whether

The Expected Willingness To Wait Wfi(Si) ∈T Of An

illnesses changes for patients of age class a ∈A.

The Linear Function Ia : →R≥0 Defines The Ex-

pected number of annual acute illnesses Ia(c) ∈R≥0

Which Can Range From Perfectly Healthy (C = 0) To

extremely delicate (c = 1).

3.2.5 Age Class-Illness Distribution

The age class-illness distribution πact : A ×F act →

Builds The Connection Between The Set Of Age

classes A and the set of acute families of illnesses F act. To that end, πact defines the expected distri- bution of acute illness families for each age class, i.e., among all developed acute illnesses by patients

Of Age Class A ∈A, A Fraction Πact(A, Fi) ∈ Is

expected to belong to illness family fi ∈F act. As a result, πact defines a discrete probability distribu- tion on the set of acute families of illnesses F act for fixed age class a ∈A, i.e., ∑fi∈F act πact(a, fi) = 1.

3.2.6 Patients

Patients are the driving force of the simulation, as their health concerns trigger the events that underly most of the simulation’s processes. All non-chronic patients ρ ∈P are characterized by their geograph-

Pointment Bact ∈B, And Preferences. While The Lo-

cation, health condition, and age class of each pa-

Tient Remain Constant Throughout A Simulation Ex-

periment, a patient’s acute illnesses, acute appoint-

Ment And Preferences Are Variable And Change Over

time. Chronic patients possess all the characteristics of non-chronic patients, but are additionally identi-

Fied By A Constant Chronic Illness Σ ∈I Chro And A

variable regular appointment breg ∈B.

Seeks Treatment With Pcps Outside The Considera-

tion set. Since continuity in the treatment of chronic illnesses is particularly important, chronic patients select a distinguished family physician φfam ∈Gcon

With Whom All Regular Appointments Breg ∈B Are

exclusively arranged. While every patients’ consid-

Modeled Time Period, Patients Reevaluate And Vary

their family physician. Naturally, patients have per-

Availabilities Given By Α: Λ/∼→{0,1}, Where 0

Patients, Primary Care, and Policy: Simulation Modeling for Health Care Decision Support

9

encodes unavailability. Finally, patients maintain

For Every Weekly Session [Λ] ∈Λ/∼And Every Con-

sidered physician φ ∈Gcon.

Ratings Are The Means By Which Patients Express

their satisfaction with a physician’s services. When-

Physician Is Determined By The Patient’S Current

ratings. To that end, ratings incorporate patients’

Sense Of Geographic Distance, Matching Of Opening

hours with availabilities, and previous positive and negative experiences. As patients adjust their rat- ings over time, they adjust their choice of PCP. If

A Physician Is Unable To Meet An Appointment Re-

quest, incurs excessive waiting time, or rejects pa- tients due to capacity overruns, patients reduce their rating. Positive experiences such as successful ap-

Pointment Arrangements Or Short Waiting Times In-

crease ratings. In other terms, through their sens- ing of the quality of treatment and the adaptation of their ratings, patients learn about the quality of PCPs throughout the simulation cycle.

Sidered Pcps Gcon. Appointment Requests Are One

of the ways in which patients and PCPs interact. Patients attempt up to two appointment requests in

Assign To The Considered Primary Care Physicians

φ ∈Gcon. If both requested PCPs fail to offer a fea- sible appointment within the patient’s willingness to wait, patients resort to their second way of in-

Teracting With Physicians: They Forgo An Appoint-

ment and visit a PCP as a walk-in patient. The se- lection of the PCP for the walk-in visit is based on

(Φ,[Λ]) Of The

targeted session λ ∈Λ.

Upon Arrival, Patients May Be Rejected By Physi-

cians due to, e.g., capacity overloads. Following a rejection, patients update their rating of the reject- ing PCP and attempt a new visit as walk-in patient at the then-highest-rated PCP. Rejected patients are

Unsuccessfully Continue To Seek Treatment. In Our

model, this emergency state does not enforce a par-

Ticular Pcp Behavior. Instead, Pcps May Include

the emergency state in their decision making. Until an illness i ∈I act subsides, patients continu- ously try to arrange follow-up appointments to the initial treatment with the attending physician in the Table 4 Attributes of (chronic) patients ρ ∈P.

Variable

follow-up interval νi ∈T . Analogously, chronic pa- tients continuously try to arrange regular appoint- ments with their family physician φfam ∈Gcon in the

Illness Σ ∈I Chro. Only If The Arrangement Of A

follow-up or regular appointment fails and the after- care of the patients is endangered, do patients seek follow-up treatment as walk-in patients. As a result, a chronic patient’s chronic illness ς ∈I chro can be treated by a physician other than the family physi-

Cian Φfam ∈Gcon, But Only Through A Walk-In Visit

triggered by the unavailability of a regular appoint- ment. In SiM-Care, patients do not directly interact with other patients. However, an indirect form interac-

Tion Emerges As Patients Compete With Each Other

for timely treatment by their preferred PCP. The attributes shared by all patients as well as the

Attributes Specific To Chronic Patients Are Summa-

rized in Table 4.

Primary Care Physicians Operate Practices Featur-

ing an uncapacitated waiting room to offer medical services to patients in need. The model character-

Izes Physicians Φ ∈G By Their Geographic Location

ℓ∈L, opening hours, as well as an individual set of strategies to schedule appointments, manage patient admission, and organize treatments.

Sim-Care Assumes That All Physicians Operate In

clinical sessions. Opening hours for these sessions

The Session Of The Week Via O: Λ/∼→H × H

where H denotes the set of decimal times defined in

10

Martin Comis et al. Section 3.1. Opening hours specify for each session λ ∈Λ the time window o([λ]) := [o([λ]),o([λ])] dur- ing which a physician generally admits patients for

Is Defined As O(Λ) := (Δ,O([Λ]) ∈T , The Session’S

end as o(λ) := (δ,o([λ]) ∈T . To encode that a PCP

Is Closed For A Weekly Session [Λ] ∈Λ/∼, We Set

o([λ]) = /0. Physicians utilize the first hour after the

End Of Each Session As Time Buffer To Compensate

for possible delays and walk-in patients. Buffers are

Considered Anticipated Working Time So That Only

service time that extends beyond the buffer consti- tutes overtime. Figure 3 provides a schematic visu- alization of a PCP’s working day.

Primary care physicians implement a set of strate-

Gies To Schedule Appointments, Decide On Patient

admissions, and organize the treatment of patients. These strategies govern the physicians’ interactions with patients and incorporate all of their sensing, predicting, adapting, and learning.

Appointment Slots And How The Resulting Slots Are

assigned to requesting patients. The feasible set of

Via The Interface Shown In Figure 4. That Is, Ev-

ery appointment scheduling strategy S ∈Sapp has to provide the functionality to answer appointment re- quests with an appointment suggestion (that can be

Empty). Thereby, Every Appointment Request Speci-

fies the requesting patient, earliest possible appoint- ment time, willingness to wait, whether the request is for a regular appointment, and whether patient’s availabilities have to be respected. Furthermore, ev- ery appointment scheduling strategy S ∈Sapp has to provide the functionality to schedule previously of- fered appointments as well as the functionality to cancel previously scheduled appointments. Finally,

Pointments Within A Session That Are Scheduled To

take place after specified point in time.

Order Of Treatment Among Patients From The Wait-

ing room. Physicians sense their patients’ waiting times as input for their strategy. To account for the

Cians Adjust Their Consultation Speed And Thereby

service times. The feasible set of treatment strate- gies Stmt is defined via the interface shown in Fig- Table 5 Attributes of PCPs φ ∈G.

S ∈S Tmt

ure 4. That is, every treatment strategy S ∈Stmt has to keep track of admitted patients, count the number

Of Waiting Patients With And Without Appointment,

and define how the treatment strategy is affected by the beginning of a session. Moreover, every treat- ment strategy S ∈Stmt has to determine the next pa- tient to be treated (that might not exist) as well as the PCP’s current consultation speed which is thor- oughly discussed in Section 3.7.4.

Waiting Room. In Sim-Care, Pcps Are Required To

treat all admitted patients. Thus, physicians under- estimating their workload due to faulty predictions

Overestimate Their Workload Reject Too Many Pa-

tients and fail to fully utilize their available time.

At The End Of Every Session’S Buffer, Physicians

learn by reevaluating their predictions and adapt- ing their admission policy. The feasible set of ad- mission strategies Sadm is defined via the interface shown in Figure 4. That is, every admission strategy S ∈Sadm has to be able to decide whether an arriv- ing patient is admitted or not given the PCP’s treat-

Over, Every Admission Strategy S ∈Sadm Has To De-

fine the adaptive traits that are performed at the end

Of Every Session’S Buffer And Depend On The Pcp’S

treatment strategy. Physicians do not directly interact with other physi-

Emerges As Pcps Compete For The Patients’ Favor

while striving for optimal utilization. The attributes of PCP’s are summarized in Table 5.

Within Sim-Care, The Progression Of Time Is Mod-

eled via the discrete event paradigm. That is time Patients, Primary Care, and Policy: Simulation Modeling for Health Care Decision Support

Overtime

Fig. 3 Schematic representation of a PCP’s morning (λ0) and afternoon (λ1) session visualizing service-, idle- and overtime.

Iadmissionstrategy

boolean acceptPatient(IAppointmentSchedulingStrategy as,

Itreatmentstrategy Ts, Arrivalevent Ae)

void adaptStrategy(Session session, ITreatmentStrategy ts) Fig. 4 Interfaces implemented by strategies. is a continuum which is traversed between discrete

Events At Which The System State Is Updated. The

model stores events of the form (t,e) in a sequential

Queue Q Where T ∈T Is The Point In Time An Event

of type e ∈E occurs.

Events In Q Happen Chronologically, I.E., Q =

{(t1,e1),...,(tn,en)} with ti ≤ti+1 for 1 ≤i ≤n−1.

As Soon As An Event (Ti,Ei) ∈Q Occurs, The Simu-

lation advances from time ti−1 to time ti, compare

Point In Time T ∈T , I.E., When The First Element

(ti,ei) ∈Q with ti ≥T occurs.

Any Event (T,E) ∈Q Can Generate New Events Or

delete existing ones. To be introduced or affected

By Event (T,E) ∈Q , Events (T′,E′) ∈Q Must Hap-

pen after time t, i.e., we require t′ > t, so that time progresses in a consistent fashion. By construction, event queue Q never runs empty.

Every simulation run follows the structure depicted in Figure 6, chronologically processing the events in Q until time T ∈T is reached. In this, the spe-

Cific Process Depends On The Event Type E ∈E. We

now describe the different event types. Arrival events are indicated by earv(φ,ρ). As illus- trated in Figure 7(a), they mark the event of patient ρ arriving at physician φ’s practice, either for an ap- pointment or as a walk-in. The physician’s decision to admit or reject arriving patients depends on φ’s admission strategy. Every admitted patient is guar-

Anteed To Receive Treatment And Enters The Physi-

cian’s waiting room. If the physician is currently idle, this triggers the physician’s treatment strategy and treatment commences.

Follow-up events are indicated by efol(φ,ρ,i). Some families of illnesses fi ∈F cannot be treated via a single visit. Instead, the related illnesses i ∈I re-

Quire Follow-Up Treatments In Intervals Defined By

the parameter νi̸ = /0. Ensuring continuous follow-

Up Treatments, Patients Always Try To Arrange A

follow-up appointment immediately after the treat- ment of illnesses requiring follow-up consultation. To account for the fact that no feasible follow-up

Appointment Might Be Available, Sim-Care Gener-

ates a follow-up event efol(φ,ρ,i) at time ttreat + νi every time illness i ∈I with νi̸ = /0 suffered by pa-

Tient Ρ ∈P Is Treated By Physician Φ ∈G At Time

ttreat ∈T . Follow-up events serve as the patient’s reminder to actively re-pursue follow-up consulta- tion for illness i after the duration of the follow-up interval. Triggered by a follow-up event efol(φ,ρ,i), patient ρ reattempts to arrange a follow-up appoint-

Unable To Provide A Suitable Appointment, Ρ Seeks

follow-up consultation as a walk-in patient. Every follow-up treatment of an illness i ∈I invalidates all associated existing follow-up events, as the follow- up interval is reset. Therefore, SiM-Care deletes all

Ated With Illnesses I ∈I That Were Treated During

a visit before the new follow-up events are gener- ated. As a result, follow-up events only trigger if an illness has not been treated for the duration of its follow-up interval νi ∈T .

12

Martin Comis et al.

E4

Q = {(t1,e1),(t2,e2),(t3,e3),(t4,e4),(t5,e5),(t6,e6),(t7,e7)}

T4 −T3

Fig. 5 Progression of time induced by the processing of event queue Q via the discrete event paradigm.

T < T

Fig. 6 Structure of simulation run with time horizon T.

Begins, The Sampled Service Time Determines The

time of the subsequent release event erel(φ,ρ). All treated illnesses i ∈I act without duration (di = /0) are cured through a one-time treatment and thus re- moved from I act. Subsequently, all existing follow-

In The Previously Described Manner. The Success-

ful treatment revokes existing emergency flags, i.e., we set ε = 0. If the patient’s chronic illness ς ∈I was treated, the next recurrent regular appointment

Breg ∈B With Physician Φfam Is Requested At Time

ttreat + νς. Then, patients request an acute appoint-

Up Treatment Of The Persisting Acute Illness I∗=

argmini∈I act:νi̸=/0 νi with smallest follow-up interval.

The Requested Appointments Ensure The Follow-Up

treatment of all illnesses suffered by patient ρ and

Will Preempt The Previously Generated Follow-Up

events. Finally, physicians implement their treat-

Ment Strategy To Select The Next Patient From The

waiting room if the latter is non-empty. Otherwise, physicians remains idle until the next arrival event triggers the treatment strategy. As a result of this behavior, physicians are never intentionally idle.

Illness events are indicated by eill(ρ). As illustrated in Figure 7(c), they describe that patient ρ starts to suffer from a new acute illness. This means that the

Model Generates A New Acute Illness I ∈I Act With

stochastic qualities that depend on the patient’s age and health condition and adds it to their set of ill- nesses I. To treat the emerged illness, patients re-

Quest An Appointment From Their Preferred Physi-

cians or, in case this does not succeed, directly visit the preferred physician as a walk-in. As a result, each illness event generates a corresponding arrival event earv(φ,ρ) and adds it to the queue Q . Finally, each illness event generates a future illness event eill(ρ) for patient ρ and adds it to the queue Q to

Mark The Next Point In Time Patient Ρ Develops An

acute illness.

Illness I ∈I Act. Whenever The Model Generates A

new acute illness i ∈I act with di̸ = /0, it also gen- erates a corresponding recovery event erec(ρ,i) at time till + di, where till ∈T is the point in time illness i is developed. Illnesses without duration (di = /0) do not require a recovery event as they are immediately cured through their initial treatment. A recovery event removes illness i from I and deletes any associated follow-up event efol(φ,ρ,i) ∈Q . If patient ρ does not suffer from acute illnesses fol- lowing the removal of illness i, i.e., I act = /0, the

(C)

Fig. 7 Processing of (a) arrival events earv(φ,ρ), (b) release events erel(φ,ρ), and (c) illness events eill(ρ); ρ ∈P and φ ∈G. cur with the patient’s age-class-specific probability

Pa ∈ And Consequently Delete The Associated

arrival event earv(φ,ρ). As a result, some patients

Debriefing. Should Patient Ρ Be Currently Seeking

walk-in treatment due to persisting chronic illness ς ∈I, this effort is continued. Otherwise, current walk-in attempts are canceled and the associated ar- rival event earv(φ,ρ) is deleted.

Open- And Close Events Are Indicated By Eopn(Φ)

and eclo(φ), respectively. They mark the beginning and ending (including buffer) of a session λ ∈Λ op-

Strategies Become Aware Of A Session’S Beginning,

e.g., to allow for strategies that do not treat early- arriving patients before o(λ), and that overtime is

Incurred For All Treatments Performed Beyond The

anticipated buffer time of λ.

Frequency Of Events. This Applies To Aspects Of

illnesses as well as to patient arrivals, appoint-

Quence, Every Simulation Experiment Includes Mul-

tiple stochastic repetitions of the modeled time pe-

Riod, Termed Simulation Runs. When Examining Sim-

ulation output, we account for the resulting variabil- ity through confidence intervals.

In The Following, We Highlight The Aspects Of The

model that are probabilistic rather than determinis- tic and discuss how the distributions underlying the random values are parameterized.

Frequency Of Acute Illnesses. The Occurrence Of

acute illnesses in SiM-Care is modeled via a Pois- sion process. Patients develop acute illnesses at a frequency that depends on their age and health con-

Health Condition C ∈, The Expected Number Of

acute illnesses per year is given by the parameter Ia(c). The intensity (or rate) of the Poission proc- cess is thus Ia(c)/364 per day. Moreover, the dura- tion between two consecutive illness events eill(ρ)

For Patient Ρ Can Be Sampled From An Exponential

distribution with rate Ia(c)/364; see [20, chapter 2]. Type of Acute Illnesses. Whenever an illness event eill(ρ) occurs and patient ρ ∈P falls ill, the model

C ∈. The Model Assumes A Probabilistic Link

between illness family fi ∈F act and the patient’s age class a that is expressed via the age class-illness distribution πact; see Section 3.2.5. To that end, any emerging acute illness of patient ρ is randomly as- signed to an illness family according to the discrete probability distribution f 7→πact(a, f) for f ∈F act.

Care, Its Seriousness Si ∈ Depends On A Tri-

angular distribution defined on the closed interval

14

Martin Comis et al.

A (Fi,Si) = 2

Fig. 8 Weibull distributions of ωi ∈T for different values of patient’s age adjusted expected willingness to wait Eω a (fi,si).

i. Thus, patients with a bad health condition tend to develop more serious illnesses.

The Duration Di ∈T Of Illness I Depends On A Log-

normal distribution. Given i’s family of illnesses

A(Fi,Si) := ∆D

a · D fi(si).

Therefore, Sim-Care Samples The Illness’ Duration

di from a log-normal distribution with sdlog σ = 0.3

And Meanlog Μ = Log(Ed

a(fi,si))−σ2/2. Patient ρ’s willingness to wait for the initial treat-

Ment Of Illness I As Specified By Ωi ∈T Depends

on a Weibull distribution. Given i’s family of ill-

Oping Patient’S Age Class A ∈A, The Age-Adjusted

expected willingness to wait of illness i is defined

Et. Al , We Sample Ωi From A Weibull Distribu-

tion with shape parameter p = 2 and derive the scale

Γ Denotes The Gamma Function. Figure 8 Visualizes

the resulting density functions for various choices of the age-adjusted expected willingness to wait. Patient Punctuality. Patients do not always arrive on time for their scheduled appointments b ∈B. In- stead, SiM-Care allows for patient arrivals to vary

And Standard Deviation Of Σ = 6 Minutes Such That

roughly 20% of all patients are expected to arrive late for their appointments which is consistent with the observations reported in .

Beta(1.93,2.94)

Fig. 9 Histogram and beta distributed maximum-likelihood fit for empirical walk-in arrival rates from .

Walk-In Arrivals. Walk-In Patients Have No Pre-

specified time at which they are expected to arrive. Instead, SiM-Care defines for every walk-in patient

Arrival Time B ∈T Which Are Both Situational And

thoroughly discussed in Section 3.7.3. The walk-in patients’ actual arrival within the given feasible ar- rival interval [a,b] depends on a beta distribution.

Specifically, we fit a beta distribution using maxi- mum likelihood estimation to the empirical arrival

Rates Reported By Shan Et Al. . As A Result, We

sample the arrival times of walk-in patients from the interval [a,b] of feasible arrival times according to a beta distribution with shape parameters p = 1.93 and q = 2.94; cf. Figure 9.

Service Time. SiM-Care treats the service time per patient, i.e., the duration of treatments, as a random

Practice. As Suggested In Literature , We Di-

vide the sample into patients with and without ap-

Hood Fit. Histograms Of Our Empirical Samples And

the resulting distributions for walk-ins and patients with appointment are depicted in Figures 10 and 11. Based on the fitted distributions, we sample the ser- vice times of patients with appointment from a log-

Normal Distribution With Meanlog Μ = 1.82 And Sd-

log σ = 0.692 and the service times for walk-in pa- tients from a log-normal distribution with a mean- log µ = 1.254 and sdlog σ = 0.723. As our collected data set does not incorporate transition times, we prolong all sampled service times by one minute.

Appointment Cancellations. Patients That Recover

from all their current acute illnesses, i.e., I act = /0,

6.174

Fig. 10 Histogram and log-normal maximum-likelihood fit for empirical service times of patients with appointment.

3.505

Fig. 11 Histogram and log-normal maximum-likelihood fit for empirical service times of walk-in patients.

Compare Section 3.2.4. As Long As Patients Suffer

from acute illnesses, they only cancel their acute ap- pointment if they require earlier treatment due to a newly emerged acute illness. All patients that have not canceled their appointment will arrive for it. As chronic illnesses are static within the model, regular appointments are never canceled.

Sim-Care Tracks Key Performance Indicators From

the point of view of patients, primary care physi- cians, and policy makers. Thereby, it aims to illus- trate the trade-offs between the stakeholders’ objec- tives. As these indicators emerge from agent inter- actions based on patients’ evolving preferences and physicians’ evolving strategies, they are difficult to predict in general.

From The Patients’ Point Of View, Key Performance

indicators include access time, travel distance, and

Waiting Time. Access Time Measures The Time A Pa-

tient has to wait for an appointment, i.e, given the

Time Of The Arranged Appointment Tb ∈T It Is De-

fined as ac-time := tb −t. The travel distance mea-

Sures The One-Way Distance Patient Ρ ∈P Has To

travel when visiting physician φ ∈G, i.e., tr-dist := dist(ℓρ,ℓφ), where dist(ℓ1,ℓ2) denotes the driving

Distance Between Locations ℓ1 ∈L And ℓ2 ∈L In

kilometers. The patient’s waiting time measures the time spent on-site before the actual treatment com- mences. For walk-in patients, we define the waiting time for given walk-in arrival tarr ∈T and treatment commencement ttreat ∈T as wait-time :=ttreat−tarr.

Ing Time For Given Time Of The Appointment Tb ∈

T , patient’s arrival at the practice tarr ∈T , and

Treatment Commencement Ttreat ∈T As Wait-Time :=

max{ttreat −max{tb,tarr}, 0}. To evaluate patient’s indicators, SiM-Care keeps track of the total access

Time Of Arranging Acute And Regular Appointments,

the total number of arranged acute and regular ap-

Pointments, The Total Number Of Attended Appoint-

ments, the total number of walk-in patients, the total distance traveled by patients to access physicians, and the total waiting time for both patients with ap- pointment and walk-ins.

From The Physicians’ Point Of View, Key Perfor-

mance indicators include the utilization, overtime,

Number Of Treatments, And Number Of Rejected Pa-

tients with and without appointment. A physician’s utilization describes the percentage of the available working time spent treating patients, i.e., for a ses-

24). Note That

our definition of utilization clearly underestimates a physician’s actual utilization as we do not account for additional tasks such as reporting, accounting,

In Sim-Care. Overtime Describes The Physician’S

working time beyond the anticipated buffer, i.e., if the last patient in session λ ∈Λ is released at time

1

24, 0}; see Figure 3. To evaluate the physician’s in- dicators, SiM-Care collects on physician level the total service time spent treating patients, the total number of performed treatments, the total overtime, and the total number of rejected patients with and

Can Be Derived From The Opening Hours O And The

modeled time horizon T.

Authors:

Peder EZ Larson 1, 2,* , Jenna ML Bernard1, James A Bankson 3, Nikolaj Bøgh 4, Robert A Bok1, Albert P. Chen 5, Charles H Cunningham 6,7, Jeremy Gordon1, Jan-Bernd Hövener 8, Christoffer Laustsen 4, Dirk Mayer 9,10, Mary A McLean11 12, Franz Schilling13, James Slater1, Jean-Luc Vanderheyden5, 14, Cornelius von Morze 15, Daniel B Vigneron1, 2, Duan Xu1, 2, and the HP 13C

94143, Usa.

Denmark. 5 GE Healthcare, Menlo Park, California, USA. 6 Physical Sciences, Sunnybrook Research Institute, Toronto, Ontario, Canada.

8 Section Biomedical Imaging, Molecular Imaging North Competence Center (MOIN CC), Medicine, Baltimore, MD, USA. Cambridge, United Kingdom.

14Jlvmi Consulting Llc, Dousman, Wi, Usa

#See Acknowledgements for a list of all HP 13C MRI Consensus Group Members This work was supported by the ISMRM Hyperpolarized Media MR Study Group, the ISMRM Hyperpolarization Methods & Equipment Study Group, and the Hyperpolarized MRI Technology Resource Center (NIH/NIBIB grant P41EB013598).

Abstract

MRI with hyperpolarized (HP) 13C agents, also known as HP 13C MRI, can measure processes such as localized metabolism that is altered in numerous cancers, liver, heart, kidney diseases, and more. It has been translated into human studies during the past 10 years, with recent rapid growth in studies largely based on increasing availability of hyperpolarized agent preparation methods suitable for use in humans. This paper aims to capture the current successful practices for HP MRI human studies with [1-13C]pyruvate - by far the most commonly used agent, which sits at a key metabolic junction in glycolysis. The paper is divided into four major topic areas: (1) HP 13C-pyruvate preparation, (2) MRI system setup and calibrations, (3) data acquisition and image reconstruction, and (4) data analysis and quantification. In each area, we identified the key components for a successful study, summarized both published studies and current practices, and discuss evidence gaps, strengths, and limitations. This paper is the output of the “HP 13C MRI Consensus Group” as well as the ISMRM Hyperpolarized Media MR and Hyperpolarized Methods & Equipment study groups. It further aims to provide a comprehensive reference for future consensus building as the field continues to advance human studies with this metabolic imaging modality.

Keywords: Hyperpolarized MRI, metabolic imaging, carbon-13, pyruvate, dissolution dynamic

Introduction

MRI with hyperpolarized 13C agents, also known as hyperpolarized (HP) 13C MRI, has shown great potential as a novel imaging modality, particularly for its ability to probe metabolic processes in real time. The first human studies with HP [1-13C]pyruvate were performed in 2011 in prostate cancer patients (1).

Since then, there have been over 60 papers published with imaging results of human subjects from 13 different sites, with applications including prostate cancer, brain tumors, breast cancer, kidney cancer, pancreatic cancer, metastatic disease, liver disease, ischemic heart disease, diabetes and cardiomyopathies. The vast majority of these studies used [1-13C]pyruvate (1–63), where [2-13C]pyruvate (64) and 13C-urea (56) have been demonstrated too.

As clinical HP 13C MRI advances, there is a growing need to build consensus for best practices, which are critical for comparing data across sites, performing multi-site trials,deploying methods to new sites, partnering with vendors, and potentially for obtaining broader regulatory approvals.

In March 2022, we initiated an effort to build consensus within the HP 13C MRI community with this opportunity in mind, and it was greeted with strong enthusiasm. The “HP 13C MRI Consensus Group”, containing over 55 members from 27 sites, identified the area of greatest need and opportunity for consensus building to be HP [1-13C]pyruvate human

●

Pyruvate is the most mature and widely used HP agent and has the most significant translational evidence emphasizing the potential clinical impact.

●

Clinical trials, particularly multi-site trials, have the strongest need for consensus methods to ensure that data can be combined across sites. This work is a Position Paper for which the goal is to describe current successful practices and study methods for HP [1-13C]pyruvate human studies along with justification to support those practices. This is divided into four major topic areas: (1) HP 13C-pyruvate preparation, (2) MRI system setup and calibrations, (3) data acquisition and image reconstruction, and (4) data analysis and quantification (Fig. 1). The current successful practices and study methods include a literature review of published peer-reviewed journal papers showing human HP [1-13C]pyruvate study data, up to September 2022 (1–63), as well as new unpublished information from surveys of HP 13C study sites. Based on this information, we also highlight the evidence gaps, strengths, and limitations of current practices which are summarized at the end of each section.

Figure 1: Illustration of the HP 13C MRI human study process, including the 4 major areas covered in this paper: Hyperpolarized 13C-pyruvate preparation, MRI system setup and calibration, Acquisition and Reconstruction, and Data Analysis and Quantification.

Figure 2: Anatomical targets of HP [1-13C]pyruvate MRI human studies published up to September 2022.

Hyperpolarized 13C-Pyruvate Preparation

This section covers the processes for creating the HP agent, 13C pyruvate, and will include many aspects and considerations that are needed to safely and effectively prepare doses for metabolic imaging studies in human subjects. These include material, personnel, equipment and facility, fluid path preparation, quality control, and release.

It is helpful to understand that the specifications of a dose of 13C pyruvate suitable for in vivo MR HP metabolic imaging were shaped in part by early preclinical studies performed by GE HealthCare summarized in Ref. (65). In short, the safety of the two novel drug components, 13C pyruvate and the electron paramagnetic agent (EPA) AH111501, were demonstrated in those studies. The more precise formulation of the dose suitable for human use was then determined from clinical studies (66) that included two Phase 1 clinical trials in young and elderly healthy volunteers without hyperpolarization of the 13C nuclei and another Phase 1/2a dose escalation and imaging feasibility study with HP 13C pyruvate in 31 prostate cancer patients at the With the exception of the first HP 13C imaging clinical trial, which utilized a prototype device in a cleanroom (1), all HP 13C studies performed in humans to date have utilized the SPINlab polarizer (manufactured by GE HealthCare). Consequently all doses of the HP 13C pyruvate delivered by SPINlab have been produced using the “SPINlab Pharmacy Kit” that serves as the container-closure system for the various drug components (13C pyruvic acid and EPA mixture, dissolution medium, and neutralization and dilution medium) during sample polarization, dissolution and quality control (QC) processes. Thus many aspects of the HP sample preparation considerations discussed below are related to the SPINlab instrument and the consumables designed to be used with it (67).

General Considerations

While more than 860 patients or healthy subjects having been injected with HP 13C pyruvate as of January 2022 without reports of any serious adverse events (68), HP 13C pyruvate injection remains an investigational MR contrast agent and can only be administered by those with Investigational New Drug (IND) exemption from the Food and Drug Administration (FDA) in the USA, a Clinical Trial Application (CTA) in Canada, approval from National Research Ethics Committee Services in the UK, or approval from the relevant local regulatory body. Thus, methods and processes involved to produce a dose should have patient safety as the first priority. Since utilizing dissolution dynamic nuclear polarization (dissolution-DNP) for human use is still a relatively new development, there are no existing published regulatory guidelines specifically for this method.

There are two major production styles that determine how various sites approach the agent preparation. In the US, the most common approach is to rely on a sterilizing filter (“Terminal Sterilization”) to ensure sterility of the final product, akin to PET tracer production, where a starting molecule with a radioisotope is processed using various other ingredients to make the final, desired and injectable contrast agent within a necessarily short amount of time (69). For these sites, sterilization of the components and accessories upstream of this filter are not required, although many of them were manufactured and tested following Good Manufacturing Practice (GMP) or Good Laboratory Practice (GLP) requirements. The filling process is usually performed under an ISO 5 laminar flow hood, but a clean room or an isolator is not required.

This approach is typically accompanied by testing the integrity of the sterilizing filter prior to release of the dose for injection. Typically, post release endotoxin and sterility tests are performed using an aliquot reserved from each released dose.

In the UK and EU, the most common approach is to more-closely follow sterile pharmaceutical compounding guidelines (70), where all components and ingredients are required to be sterile or manufactured under GMP guidelines and are assembled and filled within a clean room environment or an isolator system (“Sterile Preparation”). Typically a batch of Pharmacy Kits for HP 13C pyruvate injection are prepared together. The sterility of the final dose is also ensured by batch validation testing, in addition to the sterility of the ingredients and the sterile compounding process. The endotoxin and sterility testing are performed for the process validation but are not performed for each injected dose.

Some institutions fill and assemble the Pharmacy Kit required for a specific study on the same day or the day prior to polarization, dissolution, and patient administration, but others have also demonstrated the feasibility of preparing a batch of kits, keeping them in a -20ºC freezer and using them over a period of a few months.

Beyond the obvious requirements that the process and the facility has to ultimately produce a dose that is safe to inject into a human, regulatory authorities will also focus on the question “Are you in control of your processes?”. To be in control of your process requires an in-depth and broad understanding of all processes involved in pre, post, and during the production process.

Personnel

It is typical and may be required to have licensed personnel involved in the production process depending on local regulations.Typically a pharmacist, radiopharmacist or other similarly qualified person (QP), in charge of the facility where the Pharmacy Kit filling and preparation is taking place, is responsible for the overall process and the release of the injectable dose.

Qualified cleanroom technicians are often involved in the Pharmacy Kit filling under the supervision of the pharmacist or QP. As is required for pharmaceutical compounding or PET tracer production, training requirements and training records for all personnel need to be maintained and available for audit by the FDA or equivalent.

Equipment And Facility

The facility and all equipment need to have standard operating procedures (SOPs) that describe how equipment is used, maintained, and calibrated to comply with relevant legislation. Currently, almost all the filling of the Pharmacy Kit takes place within a compounding laminar flow hood or isolator (typically ISO 5). At some sites, the filling is conducted within a cleanroom, while at others, it is conducted in a dedicated non-cleanroom space, reflecting differences in cleanroom approach and specifications between regulators worldwide (71). Some equipment or facilities, such as the compounding hood or cleanroom, may require external certified laboratories for testing.

Material Handling

Material handling guidelines (69,70) require SOPs detailing a system to track all of the materials involved in the HP production process for a particular patient dose, similar to current good manufacturing practice (cGMP) requirements for material handling for drug compounding. This includes acceptance standards, storage conditions, amount used in the patient dose for each ingredient and materials used in the assembly of the fluid path and Pharmacy Kit. Currently some users choose to open and inspect and sometimes modify the Pharmacy Kits upon arrival, but some users keep them in the sealed packaging until they are required for dose preparation.

Pharmacy Kit Filling And Assembling

As required by an IND or its equivalent, the preparation of the doses of HP 13C agent are detailed in the Chemistry, Manufacturing, and Control (CMC) section of an applicable regulatory submission; an example of this has been made available (72). It describes the processes of filling the Pharmacy Kit with the different components that make up the final drug product, and of assembling the final kit for either storage or immediate use in the polarizer. Special attention should be given to the laser welding process in order to satisfy installation qualification (IQ) and operational qualification (OQ). Typically, the final developed process is validated by process qualification (PQ) runs, during which 3 or more Pharmacy Kits are filled and used and the final HP 13C products are tested for endotoxin and sterility and to confirm that they meet the dose specifications for injections (usually including pyruvate concentration, residual EPA concentration, pH, liquid state polarization level and dose temperature). The data from 3 consecutive PQ runs are submitted as part of the IND submission (or its equivalent), and are often also reviewed by the Institutional Review Board (IRB) where the studies are conducted.

Quality Control And Dose Release

The quality control (QC) and dose release can be separated into two aspects: one is the QC and release of the filled Pharmacy Kit, and second is the QC and release of the HP 13C agent for injection, after polarization and dissolution. For institutions filling a batch of kits and storing them to use over a period of time, typically the batch can be released based on initial validation, environmental monitoring data from the day of kit production, and if filters are used during preparation of any of the components, filter integrity testing. But in some cases one or more kits are used for validation before the batch of kits are released for future use. For institutions that fill only the kits required for specific studies shortly before the experiment, the filled kits often do not go through separate release tests before they are used.

The quality control of the HP 13C pyruvate solution post dissolution is primarily performed to ensure that the agent meets the dose specifications (Table 1) before it is administered to the subject. These specifications target both safety (pH, residual EPA, temperature) and efficacy (pyruvate concentration, polarization, volume). Typically, the pyruvate concentration, residual EPA concentration, pH, dose temperature, dose volume, and liquid state polarization are measured by the QC accessory associated with the SPINlab polarizer. Some users perform a secondary measurement for one of the parameters, such as pH, using a different instrument or pH paper. For sites that do not go through a separate release testing process for batch filled kits, the integrity of the sterilization assurance filter, a part of the Pharmacy Kit, is typically tested as a part of the dose release. It is also common for these users to preserve an aliquot of the final HP 13C pyruvate solution for post-release endotoxin and sterility testing. This testing cannot be completed fast enough to test an individual dose prior to injection, but this is why other processes such as PQ runs and validation testing are done to minimize the chance a subject could be injected with a contaminated dose.

The Final Dose Release And Injection

should be done under the supervision of a licensed professional, based on local regulations.

Some Key Challenges

Many of the challenges associated with HP 13C pyruvate preparation can be attributed to the conditions required for the dissolution-DNP method of high magnetic field (~3-7 T) and very low temperature (~1 K) during polarization, with pressurized and superheated water necessary for the rapid dissolution event. These extreme conditions are quite challenging for the design of the container-closure and fluid path system. In particular, the cryogenic temperature in the polarizer requires special attention to any moisture or ambient (moist) air introduced into that portion of the fluid path, which can form an ice block at ~1 K. This ice can lead to flow restriction during the dissolution event and reduce the strength of the laser welded bond between the cryovial and its cap. This can ultimately produce failures in the dissolution step, including variations in final pyruvate concentration and pH that may fail to meet QC release criteria as well as fluid path ruptures that provide no available dose and result in polarizer down-time.

The polarization of the HP 13C pyruvate sample decays quickly over the span of a few minutes after dissolution, and thus the process of dissolution, QC for release, and injection should be completed as fast as possible to preserve the high polarization level achieved. Any delays in the preparation process, such as transportation time or equipment malfunction, can significantly reduce the final polarization and result in lower quality imaging data.

Current Practices

A summary of data collected from all sites performing clinical trials with HP 13C-pyruvate is shown in Fig. 3 and Table 1, including the specification of the final dose and how the quality control and release of the final dose are performed. There is a split in the Production Style, described in the General Considerations section above, with 8/13 sites using Sterile Preparation versus 5/13 using Terminal Sterilization. While many of the dose specifications show notable differences in acceptable ranges, all of these variations listed in tables have been successfully and safely been used to perform HP 13C pyruvate studies in humans. Their differences depend on the institutions’ preferences, resources and their particular regulatory situation. There is high similarity in pyruvate ranges, temperature ranges, EPA limits, and volume limits. There is modest variability in pH ranges and large variability in the endotoxin test limit. There is a 3-fold difference in acceptable polarization levels, which are measured to ensure a futile dose is not injected since the polarization is directly proportional to SNR. This reflects the decision by several sites to believe that useful data can be still be obtained with suboptimal polarizations.

Figure 3: Hyperpolarized agent preparation methods reported by sites currently performing HP

In House

Table 1: HP 13C-pyruvate preparation parameters, methods, and dose specifications used for quality control testing and release as well as validation. These were obtained from a survey of all sites performing clinical trials with HP [1-13C]pyruvate. The parameters used for product release are noted in bold text, otherwise these parameters are measured for batch validation or other QC measurements. The endotoxin and sterility testing are performed during process validation of the batch and/or post-injection, and largely depends on the agent production approach.

Summary

The overall safety record of HP 13C-pyruvate has been very strong, and the SPINlab hyperpolarizer has proven to provide high polarizations at human sized doses while meeting numerous QC and release criteria. A weakness remains the failure modes of the SPINlab Phamacy Kits (e.g. ice blocks, path ruptures), which are placed under extreme requirements particularly during dissolution. The preparation process still requires a high degree of expertise.

Therefore, there is a significant need to improve the reliability, robustness, and ease of operation for generating HP 13C-pyruvate doses for human studies. Furthermore, there is a divide between manufacturing and sterile compounding style preparation as well as other site-specific practices, resulting in variations in SOPs and justification required to relevant regulatory bodies. There have also been no comparisons between these approaches. It is also unclear what release criteria and QC parameters are truly required to ensure patient safety.

However, all of the reported methods are acceptable and approved by the appropriate regulatory authorities, and have led to the rapid expansion of successful human studies in recent years.

Mri System Setup And Calibrations

This section covers the MRI system setup, including the imaging system, RF coils, phantoms, and prescan calibration methods.

Imaging System

The main prerequisite for a given MRI scanner to be capable of supporting studies with HP 13C is its “broadband” capability to transmit and receive radiofrequency (RF) signal at the frequency of 13C, which is around 4 times lower than 1H. This does not come as a default on clinical MR devices. The transmit power of the broadband amplifier should also be sufficient to support the intended flip angle and RF pulse shape with the employed transmission RF coil(s) for 13C. Most studies to date use relatively low flip angles (< 90 degrees) for HP 13C in order to preserve polarization for time-resolved imaging. The capability to receive 13C signal on multiple channels is also desirable to increase SNR, as discussed further in the “RF coils” section.

The choice of magnetic field strength is primarily dependent on the metabolites’ frequency separation due to chemical shift dispersion and 1H imaging. High field strengths do not enhance hyperpolarized 13C signal as they do for 1H because the signal strength in a HP experiment relies on manipulating the population of quantum energy states outside of the MRI scanner.

However, the injected HP 13C-pyruvate and its metabolic products have greater frequency separation at higher fields, and it may thus be easier to separate and quantify these resonances at higher fields. This comes at the cost of a reduction in the achievable T2* and often reduced T1. As the initial polarization is independent of the imaging field strength it has been proposed that the increased T2* at 1.5T can potentially be exploited to increase SNR by adapting the acquisition bandwidth or reduce off-resonance imaging effects in cases when the decay of the transverse magnetization is dominated by T2* (73). In practice, 3T has been used in all published human 13C-pyruvate studies surveyed (Supporting Table S1), and comprises the majority of scanners currently in use for human studies (Table 3). A field strength of 3T is well-suited for 1H MRI anatomical reference and correlative imaging.

Stronger and more rapidly slewing magnetic field gradients support more rapid spatial encoding, particularly for metabolite-specific single-shot imaging using echo-planar imaging (EPI) or spiral imaging (See “Acquisition and Reconstruction”). Although the spatial resolution acquired for HP 13C imaging is typically much coarser than for 1H MRI, the factor of ~4 in gyromagnetic ratio leads to the same reduction factor in performance of the gradient system, so 13C experiments are potentially more limited by gradient hardware performance. To date, all human studies have used the commercially-available integrated gradient systems provided in clinical MRI scanners.

Optimization of scanner design has understandably focused on minimization of artifacts in 1H MRI, where devices such as room lights, the gradient amplifiers, and the motors driving the patient bed are checked to ensure that they do not produce RF interference at the 1H frequency, but artifacts may arise at other frequencies. Eddy current compensation is also not always appropriately adjusted for nuclei at other frequencies (74). In order to optimize for 13C, many sites have performed checks on phantoms for RF interference, gradient artifacts, and eddy currents (74), including the use of post-hoc gradient impulse response function characterisation and correction, and some vendors have fixed these issues as well.

Rf Coils

For HP 13C imaging studies in humans, RF coils for both 1H and 13C nuclei are needed, with 1H MRI providing an anatomical reference for registration and optional additional multiparametric MRI readouts. At the Larmor frequency of 13C nuclei, the relative contributions from coil noise compared to sample noise increase compared to 1H (73,75), although sample noise still is likely the dominant contributor for human-sized coils at 32.1MHz - the resonance frequency of 13C nuclei at 3T.

The key requirement for human 13C-pyruvate RF coils are that the coil geometry and sensitive volume must cover the volume of interest in the subject. Table 2 and Figure 4 shows coil configurations that have been used and optimized for applications in different anatomic regions.

Volume resonators are most commonly used for transmit, as they surround the subject to

Provide B1 Transmit Across The Fov (B1

+). While 1H relies on a large birdcage (“body”) coil built into the scanner, 13C transmit coils must be placed inside the bore. This takes up valuable space within the magnet, and also has led to the use of designs with relatively inhomogeneous

B1

+. Many human studies have used Helmholz pair resonators for transmit, including the “clamshell coil”, which has a notably inhomogeneous B1

+ Profile But Has Been Used Because Of

relatively easy integration into the scanner bore. B1

+ Variation Results In Variations In The Flip

angles that control the use of the hyperpolarized magnetization and creates errors in common HP metrics (9,76). The exception are head coils, where birdcage designs with highly

Homogeneous B1

+ can be placed around the head while easily fitting inside the bore. As with 1H MRI, higher SNR can typically be achieved by smaller receive coil elements, such as surface coils or phased arrays, and the majority of 13C receive coils used have layouts similar to 1H phased arrays.

RF coil quality control is important to ensure proper functioning of the coils to provide consistent imaging quality, especially with limited natural abundance 13C signal in vivo. It typically involves 1) a physical integrity check of the coil cables and connectors and 2) phantom SNR tests to check the coil’s performance and to monitor it over time (see Phantoms below). An useful reference for RF coil quality control is outlined in the MRI accreditation program of the American College of Radiology (77) and can be adapted for 13C coils.

Notably, configurations for brain and prostate studies used dual-tuned 1H/13C coil designs, which greatly simplify workflow and registration of 1H and 13C images, as no switching of coils is needed.

(1)

Table 2: RF coil configurations reported for human HP [1-13C]pyruvate studies.

Tx = Transmit

coil, RX = receive coil. The commonly used “clamshell” TX coil is a Helmholz pair design. For 1H RF configurations, all used the Body coil for TX unless otherwise noted, and “repositioned” indicates the 13C coil was removed for 1H imaging. One representative reference is listed for each configuration. The RF coil configurations reported in the reviewed papers are shown in Supporting Table S1.

Figure 4: Examples of RF coil configurations used for human HP [1-13C]pyruvate brain studies. (A,B) 13C Clamshell TX (Helmholz pair) and 2× 4-channel paddle RX arrays. (C) 13C Birdcage volume TX and 32-channel RX array (RX array slides into TX coil). (D) 13C Birdcage volume TX and 24-channel RX array, combined with a 1H 8-channel RX array. Image reproduced with permission from Ref (16).

Phantoms

Since hyperpolarized magnetization is non-renewable, phantoms containing 13C nuclei are important to: 1) test the multi-nuclear capabilities of the imaging system, including all parts of the signal excitation and receive chain; 2) perform calibration measurements before a scan with hyperpolarized nuclei; and 3) perform necessary pre-scan adjustments (see “Prescan Calibration” section). The phantoms currently in use are listed in Table 3. Their composition must provide sufficient 13C signal, with additional considerations of conductivity, stability, chemical shift(s) present, potential for dynamic imaging, and cost. The phantom geometries are typically either compact, in order to be used alongside the subject during a HP scan, or large enough to mimic the inner volume of a RF coil for system testing.

One popular compact design contains enriched 13C-urea at high concentration, typically 8 M, which provides a single resonance, placed inside a small container ~1 mL. The most common recipe mixes 13C-urea in a 90% water/10% glycerol solution, with glycerol used to increase the urea solubility and doping with a Gd-based contrast agent to shorten T1 which increases the potential SNR per unit time. For example, when Dotarem is added at a 3:1000 volume ratio the 13C-urea T1 is around 500 ms and T2 is around 100 ms. However, when testing pulse sequences influenced by T1 and T2, doping should be used carefully. This phantom is suitable for frequency calibration, transmit gain calibration, sequence testing, and as a fiducial marker when placed next to a patient. However, enriched 13C-urea has a relatively high cost compared to natural abundance compounds.

For larger volumes (>100 ml), the phantoms most often used contain undiluted ethylene glycol, glycerol, or dimethyl silicone. These compounds have sufficiently high carbon concentrations to provide sufficient 13C signal even with the 1.1% natural abundance of 13C. These larger phantoms matching the inner volume of an RF coil are useful for coil testing, including transmit

+) And Receive (B1

-) coil profile mapping, as well as to mimic acquisitions using in vivo FOV requirements. In this case, size and conductivity should match the expected subject size in order to mimic coil loading and get a realistic estimation of B1+. Large-volume natural abundance urea phantoms have also been used by some sites, but suffer from higher conductivity compared to biological tissues. Typically, it is easier to increase the conductivity and hence coil loading of the non-conductive phantom by adding NaCl to match physiological loading (16,78).

Dynamic phantoms that aim to mimic metabolite kinetics have also been developed (79–81), and have the potential to more closely mimic the HP experiment, but so far these are not widely used.

Prescan Calibration

Prior to performing an MRI acquisition, the so-called prescan procedure is used to set the shim parameters to maximize B0 homogeneity over the field of view (FOV) or a specific region of interest (ROI), the scanner center frequency (CF), the RF transmit gain, and the receiver gain.

While this calibration procedure is usually automated for 1H, the lack of sufficient natural abundance 13C signal prevents use of automated methods. (Although natural abundance 13C lipid signal has been detected, there are so far no reports on using this signal for prescan.) Table 3 shows current practices across sites.

Maximizing B0 homogeneity is independent of the nucleus and is therefore performed prior to 13C imaging using the 1H water signal and existing shimming tools, such as by a standard automated process (“Auto Shimming”) or using high order shimming routines. Similarly, the 13C CF can be calculated from the 1H CF using a predetermined scaling factor that depends on the target chemical shift (82). Another common approach used is to have a small, high-concentration 13C phantom, e.g. 8M 13C-urea, integrated in the RF coil or placed next to the scan subject (1). The reference frequency can also be based on real-time measurements after the HP injection but prior to imaging (83). Both the CF and B0 shimming are critical when using spectrally-selective RF pulses, as inmetabolite-specific imaging methods, where the desired excitation bandwidths are typically very narrow and frequency offsets can lead to a failure mode that is only apparent after injection.

The calibration of the RF transmit power is typically performed on a small, high-concentration 13C phantom placed near the region of interest during the scan or on a large 13C phantom of similar size and coil loading as the subject, prior to the subject scan. Reference power is often done by sweeping the power in a pulse-acquire sequence (53,62), or the Bloch-Siegert method (52,84). When using a small phantom, the location of the phantom, B1

+ Inhomogeneity As Well

as any shielding effects, e.g., when the phantom is integrated into a coil (1), may degrade the accuracy. Other methods include real-time Bloch-Siegert method measurements after the HP injection (83), and using the stronger natural abundance 23Na signal that is close enough to the 13C resonance frequency to be detected by 13C coils (82).

The receiver gain is predetermined, either systematically based on independent phantom measurements and assuming the dose and polarization of the HP compound is known prior to injection, or based on past HP imaging studies.

Power [Kw]

Phantom(s) - during study Phantom(s) - before study 13C Frequency

8

13C-bicarbonate doped with dimethyl silicone, various

Maximum Values

Table 3: Summary of the imaging systems, phantoms, and prescan procedures used at sites currently performing HP 13C-pyruvate human studies. These were obtained from a survey of all sites performing clinical trials with HP [1-13C]pyruvate. *Previously performed studies with a Siemens 3T Tim Trio. The imaging systems, phantoms, and prescan procedures reported in the reviewed papers are shown in Supporting Table S1.

Summary

Commercially available 3T MRI systems are by far the most commonly used for human HP 13C-pyruvate studies, although a systematic investigation of the impact of B0 has only recently been investigated (73). The multi-nuclear RF transmit and receive chain has proven sufficient for current acquisition strategies, although many sites have observed artifacts due to RF interference, gradient interference, and residual eddy currents when operating at the 13C frequency. A variety of 13C RF coils, tailored for numerous anatomical targets, have been successfully demonstrated, with the main limitation that most transmit coils take up a lot of additional space inside the bore and provide relatively inhomogeneous B1

+ Profiles. The

phantoms used have converged into generally 2 categories - small phantoms containing 13C-enriched compounds that can be used during the study and human-sized phantoms containing compounds with high carbon concentrations but without 13C enrichment that are used to test and calibrate the coils. There are no standardized compositions or geometry, and dynamic phantoms that recapitulate in vivo kinetics would be desirable but are still an emerging area. Prescan calibration procedures were not well defined in most publications, so we surveyed individual sites to determine current practices. Calibration procedures for the B0 field (13C CF and shimming) for most sites take advantage of 1H signal and methods, while methods

For Calibration Of B1

+ is more variable across sites, likely a reflection of remaining challenges in how to perform this calibration. Standardization of both phantoms and calibration procedures would synergistically improve the robustness and reproducibility of HP 13C studies.

Acquisition And Reconstruction

Data acquisition strategies in human HP [1-13C]pyruvate MRI studies must account for multiple chemical shifts, efficiently utilize the non-renewable HP magnetization, and acquire data quickly relative to metabolism and relaxation decay processes. These studies require spectral encoding to separate metabolites, necessitating pulse sequences that efficiently encode up to 5D data (3 spatial + 1 spectral + 1 temporal dimension). RF pulses must efficiently sample without immediately saturating the non-renewable HP magnetization, and sequences must acquire data quickly and be robust to both experimental and physiologic variation (e.g. B1

+ Inhomogeneity,

variation in perfusion) to ensure reproducibility and minimize scan-to-scan variability. This section covers current successful practices for data acquisition in human [1-13C]pyruvate studies, and accompanying 1H imaging, from different anatomic regions, including scan parameters and image reconstruction.

Acquisition And Reconstruction Methods

The acquisition methods used in human [1-13C]pyruvate studies can be classified into 3 categories: 1) MR spectroscopy or MR spectroscopic imaging (“MRS/I”), 2) chemical shift encoding methods, and 3) metabolite-specific imaging (Fig. 5).

Mrs/I Methods Specifically

resolve a spectrum that can be analyzed to extract expected as well as unexpected resonances, making this approach very robust. It was used in many initial studies (1).

Chemical Shift

encoding methods, most commonly the Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL) method, use imaging sequences acquired with multiple TEs and rely on a model-based separation of expected chemical shifts (85).

Metabolite-specific imaging methods use specialized RF pulses that are spatially and spectrally selective to excite individual metabolites which are then typically imaged with fast k-space trajectories such as echo planar imaging (EPI) or spirals (86).

Their Application To Different

organ systems is described below. The image reconstruction methods used in human [1-13C]pyruvate studies have typically been conventional methods (e.g. FFT, non-uniform FFT, or equivalent). The incorporation of accelerated imaging and advanced reconstruction methods including parallel imaging (4,57,87) and compressed sensing (7) has also been applied in human studies for improved spatial resolution, temporal resolution and coverage, but have the potential for additional artifacts as well as SNR losses due to ill-conditioning of the reconstruction (e.g. g-factor).

The Majority Of

published studies do not use accelerated imaging indicating the resolution and coverage achievable without acceleration is currently adequate for successful data collection. Performing coil combination, even with fully sampled data has also been shown to have specific challenges for HP human images: using naive sum-of-squares methods suffer from high noise amplification in the relatively low SNR regime of HP [1-13C]pyruvate (compared to 1H), motivating several HP 13C-specific methods that include data-driven coil sensitivity estimation which have shown obvious improvements over sum-of-squares (11).

More recently denoising techniques have been applied as post-processing of human HP data(41,42,44). The techniques applied are based on spatial-temporal singular value decomposition for unsupervised estimation of signal and noise components. They have shown improvements in apparent SNR in the brain and liver, while care must be taken to choose parameters such as the rank threshold to avoid oversmoothing and overfitting to the estimated signal components.

Prostate Studies

Prostate cancer was the first human application of HP [1-13C]pyruvate (1), and data was acquired with MRS/I methods: 1D dynamic MRS, single-slice 2D dynamic echo-planar spectroscopic imaging (EPSI), and single time point 3D EPSI. Advances in imaging strategies led to the development and application of new acquisition schemes, including undersampled 3D EPSI with compressed-sensing (7), model-based chemical shift encoding methods that use a priori information (47,59), and metabolite-specific EPI (10), all of which can provide volumetric whole-organ coverage and dynamic acquisitions.

The pyruvate bolus arrival in the prostate can vary by ± 10 s between patients, necessitating dynamic imaging to reliably and consistently capture the pyruvate bolus (18). For this reason, all currently ongoing studies acquire dynamic data. While MRS/I, chemical shift encoding, and metabolite-specific imaging can all achieve dynamic imaging, chemical shift encoding and metabolite-specific imaging provide greater dynamic and volumetric coverage (85). For scan prescriptions, the FOV is designed to provide full prostate coverage and typically to match the orientation of the anatomic imaging used for registration. Flip angles used in current studies are constant through time, as quantification with a variable-through-time flip scheme is highly sensitive to bolus timing (8) and errors in the RF transmit (B1 +) field (76).

Heart Studies

Data acquisition methods for 13C imaging in the heart must be designed to meet the demands of significant cardiac motion and blood flow. To cope with the periodic cardiac motion, most human heart studies to date used gating to the diastolic window, the longest cardiac cycle interval, which has reduced motion (2,22,28,30,35,36,38,45,52). The duration of the diastolic window limits the available data sampling time, making cardiac acquisitions the most time-constrained of the HP 13C MRI applications. The most common acquisition approach is metabolite-specific imaging with spiral k-space trajectories (2). Their single-shot imaging capability makes these methods particularly robust to motion effects. Furthermore, spiral k-space trajectories provide rapid k-space coverage and relatively benign flow and motion artifacts. The majority of studies have used 2D multi-slice acquisitions, but 3D encoding has also been used successfully (35).

Brain Studies

For HP 13C MRI of the human brain, the majority of studies have also used 2D (slice selective) acquisitions (10–12,14,16,28,33,40,41,44,51,53,60), with a trend toward volumetric coverage using 2D multi-slice metabolite-specific imaging. 3D metabolite-specific imaging of the whole brain, with phase encoding of the slice direction (34,57), has been shown to provide similar SNR efficiency (88) compared with multislice imaging. A number of studies have employed MRS/I (5,6,29,31–33,50,55) resulting in a spectrum from each voxel, which has the advantage of not requiring a priori information about which peaks to encode. This was important in early brain studies when it was not known which peaks would be detectable. Chemical shift encoding, using a set of images with different echo times and an iterative reconstruction of the individual resonances (i.e. the IDEAL approach (85)), has also been used (12,49,54), with the drawback that coverage in the slice direction was limited due to the time required to acquire multiple echo time images.

Abdomen And Breast Studies

The fundamental approaches to data acquisition and reconstruction in the abdomen and breast are largely similar to the aforementioned applications, but demand attention to particular challenges associated with these anatomic regions, especially relating to respiratory motion.

Although it has been shown that a basic 2D MRSI approach based on phase encoding and FID readout can be successfully applied for HP 13C imaging in breast (15) and kidney (13), major advantages in terms of spatiotemporal resolution and coverage have been realized using tailored approaches based on metabolite-specific imaging (43,62) and chemical shift encoding (43), which have facilitated multi-slice or 3D dynamic acquisitions over large FOVs in the abdomen (4,37,46).

The significant respiratory motion encountered in these regions can directly blur 13C images, and has further favored these rapid acquisition strategies. Motion also degrades B0 homogeneity, which can shift frequency-selective excitation profiles and introduce artifacts into rapid imaging readouts. This makes accurate determination of the acquisition center frequency and shimming essential in these regions which often cover large FOVs. (See “Prescan Calibration” section for more information). In some studies, breath-holding was used to minimize motion effects and enforce frame-to-frame data consistency (42). A pragmatic and reasonably effective approach for dealing with respiratory motion during 13C data acquisition is an initial breath-hold (as long as can be tolerated), followed by free-breathing (46,62).

1H Imaging

Collection of 1H imaging data is essential both for prescribing the 13C acquisition and for interpretation of the resulting 13C data. Multi-planar 1H scouts are acquired prior to 13C acquisition to enable graphical prescription of the 13C imaging region. All human HP 13C-pyruvate imaging studies acquire conventional MRI scans (e.g. T1- and T2-weighted volumes) for anatomic reference, aiming to cover at least the full 13C FOV. Acquiring these anatomic scans as close as possible to the time of 13C imaging (immediately before or after) minimizes potential misregistration between the data sets. Depending on the application, other advanced 1H sequences are also acquired (e.g. diffusion-weighted imaging for cancer imaging).

When contrast-enhanced data is acquired, it is done after 13C imaging, as paramagnetic contrast agents will accelerate 13C relaxation.

Reported Study Parameters

Figures 5 and 6, and Supporting Table S2 shows the reported acquisition study parameters for human HP [1-13C]pyruvate studies published as of September 2022. Figure 5 shows a mixture of MRS/I, metabolite-specific imaging, and chemical shift encoding methods have been successfully used, where spectroscopy-based methods have become less prevalent in recent studies. Figure 6 shows the acquisition timing, including the important start time and interval/temporal resolution, is quite variable across studies.

Figure 5: Acquisition methods used in published HP [1-13C]pyruvate human studies published up to September 2022, classified into: MR spectroscopy and spectroscopy imaging (MRS/I); chemical shift encoding methods, such as IDEAL, that use multiple TEs and model-based reconstructions; and metabolite-specific imaging methods that use spectrally-selective excitation to image a single resonance at a time.

Figure 6: Temporal acquisition characteristics reported in HP [1-13C]pyruvate human studies published up to September 2022. (a) Reported referencing of acquisition start times.

(B)

Acquisition start times reported when using dynamic imaging and when timing was reported relative to the end of the injection. (c) Temporal resolutions. “Not Applicable” indicates dynamic imaging was not used.

Summary

Three general categories of acquisition strategies have been used successfully for human HP 13C-pyruvate studies: MRS/I, model-based chemical shift encoding (e.g. IDEAL) methods, and metabolite-specific imaging methods. These have enabled successful studies in the prostate, heart, brain, abdomen, and breast. Recent studies increasingly have used the imaging-based strategies of metabolite-specific imaging and chemical shift encoding which are the fastest methods, although a heads-to–head comparison between techniques has not been performed.

Metabolite-specific imaging is quite popular because of its speed and compatibility with single-shot imaging, but is sensitive to B0 field variations and thus requires careful calibrations. Nearly all studies surveyed acquired data dynamically, allowing measurement of the bolus and metabolite kinetics. The exact timings and associated flip angles vary quite widely across reported studies, with no consensus yet as to how to choose these parameters. Image reconstruction is typically done directly using Fourier Transform methods, and accelerated imaging strategies are uncommon.

Data Analysis And Quantification

This section covers the analysis of data from human HP [1-13C]pyruvate studies, including modeling and metrics, visualization, as well as considerations for how to store data and metadata. Depending on study design, the analysis may need to give quantitative or semi-quantitative output reflecting a biological process or may just reflect a contrast between different regions of interest for quantitative evaluation.

Metrics

Figure 7: HP [1-13C]pyruvate raw data (A) have typically been quantified using four categories of metrics depending on the acquisition. Data acquired as a single time point are often quantified using normalized metabolite images or metabolite ratios (B). Dynamic data can be quantified using normalized metabolite images or metabolite ratios (B), or with metabolite timings such as time-to-peak (TTP) or pharmacokinetic (PK) models (C). The latter two require the data to be time-resolved. [1-13C]alanine and 13C-bicarbonate are analyzed similarly to [1-13C]lactate but omitted here for display.

Metabolite images are commonly used as summary metrics for HP MRI data, often including some form of normalization as well as summed over time as an area under the time curve (AUC) (17). These are analogous to the visual evaluation that is most used for routine clinical work (89,90). In these metabolite images, we expect that the [1-13C]pyruvate AUC signal is predominantly weighted towards perfusion and uptake, while [1-13C]lactate, [1-13C]alanine and 13C-bicarbonate AUCs represent metabolic conversion. The strength of this approach lies in its simplicity and relatively few underlying assumptions. Limitations to the use of single-metabolite images or AUCs include sensitivity to inhomogeneous coil profiles (57,87,91), the acquisition strategy and acquisition parameters, pyruvate polarization and concentration level, and signal relaxation rates (92). Further, the reader must be careful to interpret all the images in conjunction to better understand the underlying biology; for example, increased [1-13C]lactate in the presence of decreased [1-13C]pyruvate delivery can have a very different meaning compared to increased [1-13C]lactate with increased [1-13C]pyruvate delivery.

In an attempt to address variations in coil sensitivity, polarization level, and pyruvate delivery, AUC images are often computed by normalizing to a specified parameter, such as the maximum pyruvate or average lactate signals, or presented as a ratio such as lactate/pyruvate or divided by “total Carbon” - the sum total of HP 13C signal observed across all metabolites. The AUC ratios between metabolites and pyruvate are proportional to the corresponding forward kinetic rates (81,93), but are not directly comparable to rate constants when magnetization loss rates (e.g. relaxation and losses due to signal excitation) differ between studies. Similarly, the ratios between the produced metabolites (e.g. bicarbonate/lactate) can reflect the balance between downstream metabolic pathways (12,55). Care must be taken to consider how AUC images are calculated and normalized before comparing values between studies.

To further quantify the interpretation, pharmacokinetic (PK) modeling approaches were developed to compute the apparent kinetics of pyruvate-to-metabolite exchange (92,94–99). These yield semi-quantitative to quantitative apparent rate constants, given in s-1. Some models require a vascular input function, while others avoid this requirement (95). PK models can explicitly account for acquisition-specific details such as excitation angle and repetition time, and thus may reduce the effects of these details on quantification. An input-less model, provided in the Hyperpolarized-MRI-Toolbox (https://github.com/LarsonLab/hyperpolarized-mri-toolbox) (100) and thus frequently employed for human data, has been shown to fit well and robustly to prostate and brain data (8,20). PK models are quantitative in nature, arguably provide more relevant biological information (8,20), and appear to be reproducible across sites (51). However, rate constants derived from PK models are still apparent rates, and likely do not reflect a single biological characteristic.

Some additional considerations include whether complex or magnitude data is used, as the noise behaviors will impact the analysis differently. Additionally, cut-off thresholds or other criteria may be used to identify and avoid voxels with insufficient SNR before analysis to improve robustness (20,41).

Regardless of the analysis approach, the underlying biology is not always clearly represented by the data; instead, the metrics may be influenced by perfusion, barrier permeability, intercellular shuttles, enzyme activities, co-substrate concentrations, or combinations thereof, depending on the organ and disease of interest (19,43,94,101–103). This may be addressed by incorporating complementary information. As an example, HP 13C pyruvate data is influenced by perfusion, and thus addition of perfusion MRI could be important for interpretation (98,104,105).

All the methods outlined above have been explored in clinical studies, described in Supporting Table 3 and summarized in Figure 8. As of September 2022, approximately 52% of studies involving human subjects report rate constants derived from a PK model with a few different models reported. A nearly equal fraction (51%) of the studies report AUC ratio values.

Approximately 66% of these studies report metabolite-specific images or AUC values. About 40% report SNR values; this metric is particularly frequent in manuscripts that describe technical developments for clinical HP MRI. Approximately 16% of these studies summarize model-free metrics, and 10% report measurements from a single timepoint. Most studies report a combination of quantities.

Figure 8: Reported metrics used for analysis in HP [1-13C]pyruvate human studies published up to September 2022.

Visualization

A wide variety of approaches have been used for visualizing data from human HP 13C-MRI studies. The challenges and practical considerations are: 1) choosing the appropriate metrics to display, 2) how to encode the parameters (e.g. the colormap), and 3) choosing how to provide anatomical context and other multi-parametric data. The choice of visualization also depends on the goal which could be for diagnostic interpretation, but also quality control, reproducibility among readers and publication.

Metrics

The choice of HP 13C metrics is described in detail above. At this stage in HP 13C development where there is no standardized metric, often a combination of metabolite images and ratios or PK model parameters are shown.

Parameter Encoding

The mapping function chosen should provide an adequate, often quantitative, impression of the parameter mapped. There is a consensus in the visualization field that perceptually uniform maps are best suited to visualize continuous parameters, like the greyscale typically used by radiologists as well as other monochrome (black to blue) and color ranges (fire-type, rainbow-type) (106,107). Multi-color heatmaps have been the most frequently employed method for HP 13C data, while greyscale has infrequently been used but it ensures there is no coloring-based bias as well as facilitating later reuse (Fig. 9a). Among the color schemes employed in the clinical HP 13C literature, fire-type scheme seems to be the most common [similar to “Plasma” or “Inferno” in matplotlib.org]. Next most commonly employed is the rainbow-type scheme [similar to “Rainbow” in matplotlib.org].

Anatomical Context

HP MRI faces the challenge that it does not necessarily depict the anatomical features, similar to PET, and thus requires an anatomical reference. Most often, a grayscale anatomical image is overlaid with a HP colormap (Fig. 9c,d). This approach is very intuitive, but can skew perception as the grey-scale anatomical reference may affect the brightness of the HP data (e.g. signal in the skull). This bias does not occur when showing adjacent maps (Fig. 9a, b). Here, anatomical outlines may help to provide reference (Fig. 9b).

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