Introduction
The importance of a reliable statistical definition of rain event resides in the possibility of creating viable models for a great variety of hydrological applications: e.g. catchment run-off, soil erosion and canopy losses . Ecohydrologic studies rely on rain event modelling to study the influence of the precipitation pulse dynamics on the vegetation architecture, plant species interactions, and the cycling of organic matter and nutrients in arid and semi- arid ecosystems [2, 3]. In spite of the widespread adoption of the rain event concept, a proper non arbitrary statistical definition of rain event is still an open issue. The word “event” has been used to indicate different things in different contexts, and a great variety of techniques have been used for its definition. The most common criterion to define a rain event is the Minimum Intra event Time (MIT): the MIT value separating two events ranges from 15 min to 24 hours . In many cases, the choice of a particular MIT is not related to observed dynamical properties of the rainfall phenomenon but to a particular time scale of the hydrological process considered: e.g. Lloyd et al. use 3 h as MIT because it is the estimated time for the canopy to dry, Bracken et al. use MIT=12 h so that the ground could dry between rain offevents, while Aryal et al. use 8 h as MIT because it is the estimated time for highway surface depression to dry.
Recently, an alternative definition of rain event [7, 8, 9] has gained some recognition in hydrological literature [10, 11, 12, 13, 14, 15, 16]. According to this new proposal a rain event is identified by the occurrences of consecutive adjacent wet time intervals (the time intervals being equal in duration to the instrument time resolution). We will refer to this method as the Adjacent Wet Intervals (AWI) method. The adoption of this definition of rain event plays a central role in what is the main claim of Peters et al. [7, 8, 9]: a dynamical “equivalence” between the occurrence of rain events and that of avalanches in sand pile models. In this case rain would have the same dynamical properties of self-organizing systems . These dynamical properties are commonly referred to, by the scientific community, with the term Self Organized Criticality (SOC).
The MIT and AWI methods appear to be very different: the MIT method looks for the lack of rain for a suitable interval of time, while the AWI method looks for time intervals with a “continuous” presence of rain. We will compare both the MIT and AWI methods and provide theoretical arguments to show that the two methods are “equivalent” and therefore
1
subject to the same arbitrariness: the choice of a minimum rainless interval in the MIT case, and a particular time resolution of the instrument in the AWI case. As a way out from the issue of arbitrariness, we propose here to focus on the dynamical properties of the rainfall phenomenon and see if a particular time scale exists which could be adopted as a physically meaningful (and thus not arbitrary) rainless period (time resolution) in the MIT (AWI) case.
There are two kinds of precipitation regimes: stratiform and convective [18, 19]. The words stratiform and convective do not refer to the process of cloud formation but to two distinct dynamical mechanisms of drop formation 1) stratiform: drops are formed via condensation which is predominant in the case of small (<2m/s) updraft velocity, and 2) convective: drops are formed via coalescence which is predominant in the case of large (>2m/s) updraft velocity. The occurrence of convective precipitation at mid latitudes is restricted to thunderstorm activity (isolated summer thunderstorm or Mesoscale Convective Systems (MCS)), while both types of precipitation occur between the tropics in spite of the fact that convection is the only mechanism of cloud formation, e.g.: .
Since physics laws are independent from the particular location on Earth, one expects that two stratiform (convective) events must have some common statistical properties since the rain drops were generated by the same physical mechanism. Note that the similarities we are referring to are not similarity in the duration or depth of showers, although they might exists, but similiraties in the statistical properties of inter drop time intervals and drop diameters.
In other words, it is not “how much” or“ how long” it rains which is similar (since orographic condition and other particular meteorological factors may be relevant) but “how” it rains. Newton’s law⃗f=m⃗a tells us that body’s acceralation is always proportional to the applied force, but the trajectory of a body will depend on the the peculiar force applied. Eventual similar statistical properties of inter drop time intervals and drop diameters would be more easily detected by direct study rather than through the observation of rainfall rates at a given time resolution where things are complicated by the integration of the cube of the drop diameters over an arbitrary time interval (time resolution). Ignaccolo et al. have shown that invariant statistical properties can be obtained for the inter drop time intervals and drop diameters in the case of stratiform precipitation. We will use these properties to propose a non arbitrary definition of rain event for the case of stratiform rain, and to describe the internal variability of rain events.
In this manuscript, we use data from a Joss-Waldvogel (JW) disdrometer located at
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Chilbolton, UK for which the precipitation is almost exclusively of stratiform kind. Our data span a period of ∼2 years and are divided in 8 separate intervals of continuous observation (all data details are in the Appendix A). In Section II, we review the properties of the sequences of inter drop time intervals and drop diameters which are relevant to our purposes.
In Section III, we compare the MIT- and AWI-based definitions of event and show they are “equivalent”. A non arbitrary criterion to define rain events is introduced in Section IV. Moreover, we describe the intra event dynamical variability using the concepts of active and quiescent phases. Finally, we draw our conclusions in Section V.
Stratiform Rain
Rainfall is discrete process being a collection of drops.
Considering A Small Portion
of Earth’s surface, such as the collecting area of disdrometer or a rain gauge, rain can be described mathematically as a sequence of couples (dj,τj), j=1,2,3,. . The symbol dj indicates the diameter of the j-th drop, while τj is the time interval (inter drop time interval) between the j-th and (j+1)-th drop. However, every instrument designed to detect rainfall has a time resolution ∆>0: the instrument integration time. As a consequence, all inter drop time intervals of duration τ<∆are lost, and all inter drop time intervals of duration τ>∆ are detected as dry intervals, drought, of duration [τ/∆]×∆or ([τ/∆]−1)×∆([.] indicates the integer part) .
Let us consider as example ∆=1s. All inter drop time intervals τ<1s cannot be detected, and the subsequent drops will “wet” the time intervals of duration ∆=1s containing them. An inter drop time interval τ=1.3 s has 30% probability of resulting in a single dry interval (drought of duration 1 s), and 70% probability of not being detected with the subsequent drop wetting the time interval containing it. A value of τ=3.6 s will generate 3 consecutive dry intervals (drought of 3 s) in 60% of the cases, and 2 consecutive dry intervals (drought 2 s) in the remaining 40% of the cases. The above limitations are common to the great majority of rainfall measuring instruments. The only exceptions are instruments with high temporal resolutions (∼1 ms) such as the video disdrometer [21, 22, 23]. Thus, given a rainfall time series one is able to calculate, in most cases, only the probability P(l∆) of observing l consecutive dry intervals at resolution ∆. A better statistical accuracy is obtained using
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the “survival” probability ¯P(l∆): the probability of observing l or more consecutive dry intervals at resolution ∆. Neverthenless, it is possible to investigate the statistical properties of the inter drop intervals also using data with a time resolution much larger than the one offered by video disdrometer or particle spectrometer (∆≫1ms) such as the time resolution of our data ∆=10 s. In fact, it is possible to derive a formula describing the dependance of the probablity P(l∆) on the probability density function ψ(τ) of having an inter drop time interval τ . In the
(1)
where the symbol Ψ(τ) indicates the probability of having an inter drop time interval ≥τ (survival probability).
Statistical Properties Of Stratifrom Rain
In the following, we briefly report some statistical properties of the sequence of couples (dj,τj) in the case of stratiform rain derived in to which we refer the reader for a detailed discussion. The statistical properties relevant for the purposes of the present manuscript
Are:
1) Drop diameters and inter drop time intervals are not independent as “large” inter drop time intervals separate drops of “small” diameter. This conclusion was derived from the observation of the conditional frequencies for a drop diameter given a specific value of the preceeding inter drop time intervals. In particular, inter drop time intervals ≳10 s are followed in >95% of the cases by a drop which diameter is ≤0.6 mm.
2) Large inter drop time intervals (τ>10s) are preceded/followed either by another large inter drop time interval or by a sequence of few small (τ<10s) inter drop time intervals. In this second case, the occurrence of 5 or less drops in the 10 seconds (a rate 0.5 drops per s) following a large inter drop time interval is higly probable (≥95%).
3) Two different dynamical regimes of the rainfall phenomenon can be observed. These are the quiescent and active phases. The contribution to the total cumulated flux of quiescent phases is negligible (they are time intervals of sparse precipitation), while non quiescent regions carry the bulk of the precipitated volume, hence they are “active”. Fig. 1 is a ∼3
4
days extract from our Chilbolton data showing the alternance of quiescent and active phases. Note that the quiescent phase is not just what is commonly referred as a dry spell or drought (e.g.: 5 days without precipitation are obviously a quiescent time interval) but it is a more dynamically reach concept. For example, consider the time interval 15-25 h as depicted in panel(b) of Fig. 1. If one hour resolution is adopted, the time interval 15-25 h will result in a sequence of 10 consecutive wet intervals which could be considered as an event. However, panel (b) of Fig. 1 shows that such a sequence of wet time intervals is constituted by two quiescent phases (almost null flux increase) and an active phase in between (19-20 h) in which a sharp increase of the cumulated flux occurs . The presence of quiescence and active phases is a direct consequence of properties 1) and 2). Property 2) indicates the occurence of time intervals of sparse precipitation since large inter drop time intervals are preceded and followed by the occurrence of small rainfall rates ( ≤0.5 per second). While property 1) indicates the arrival of drops of small diameter (d≤0.6 mm) after large inter drop time intervals genarating a negligible cumulated flux. As a matter of fact, one can use property 1) and 2) to be label as quiescent all regions with a drop arrival rate ≤0.5 per second, and with an average drop diameter ≤0.6 mm (see for the detail implementation of this procedure).
The results of this filtering process is shown in Fig. 2. We see how the described filtering procedure correctly indentifies the regions of null or almost null increase of the cumulated flux: quiescent phases.
4) The probability density function of inter drop time intervals ψ(τ) has an inverse power law regime in a certain range. We will define the borders of this interval in the next Section. Note that using 1), 2) and 3), we can conclude that the inverse power law regime for the frequency of inter drop time intervals is a dynamical charateristc of the quiescent phase.
Arbitrary Definitions Of Rain Event
Even if a physical identification of rain events based on meteorological considerations accounting for atmospheric circulation and storm dynamics is preferable , a statistical identification based on threshold criteria is widely used in hydrologic Literature for its sim- plicity in applications.
The Minimum Inter Event Time (Mit)
According to the MIT criterion, a rain event is the time interval in between the occurrence of a dry period equal or larger in duration to a specific threshold: the minimum intra event time or MIT. The range of MIT used in Literature is [15 min, 24 h]. The choice of a particular MIT value influences the number of rain events, the distributions of event duration, depth, and rain rate. Dunkerley calculates empirical formulas linking the number of rain events, the geometric mean event duration, the geometric mean event volume, the geometric mean event rain rate, and the geometric mean inter event time to the MIT values. Hereby, we plot in Figs. 3 and 4 the survival probabilities ¯P MIT(θ), the probability of observing a rain event of duration ≥θ, and ¯P MIT(w), the probability of observing a rain event depth ≥w for different MIT values T. The shapes of the probabilities ¯P MIT(θ) and ¯P MIT(w) heavily depend on the particular value T.
Adjacent Wet Intervals (Awi)
According to the proposal of Peters et al. [7, 8, 9], a rain event is a sequence of consecutive “wet” (precipitation occurred) time intervals of duration ∆: the instrument resolution. Note however that given a rainfall time series with time resolution ∆, one can build the corresponding time series for resolutions which are multiple of the time resolution (2∆, 3∆, . . ). As for the MIT case, we plot in Figs. 3 and 4 the survival probabilities ¯P AWI(θ) and ¯P AWI(w) relative to the rain event duration and rain event depth. Also in this case, we notice a marked dependence on the time resolution ∆. The dependence on the time resolution ∆ observed in Figs. 3 and 4 for the survival probabilities ¯P AWI(θ) and ¯P AWI(w) casts doubts on the claims that a proper theoretical framework for the rainfall phenomenon is the Self Organized Criticality . In fact the claim is based on the observed inverse power law for the survival probability of observing a depth of duration w, in the case ∆=1min. This behavior is typical of self organizing systems such as Earth’s crust under stress and deformation which is why Peters et al. refer to the inverse power law behavior of rain event depths as rain’s Gutenberg-Richter law . Fig. 4 shows that one could fit an inverse power law function to the survival probability ¯P AWI(w) relative to the resolutions ∆=10 s and ∆=1 min and obtain (in the range [0.001,1] mm) two rather different exponents : µ=0.48 and µ=0.33
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respectively. The exponents of the probability density function ψ(τ) are obtained adding 1 to the exponent of the survival probability Ψ(τ). Moreover, for larger time resolutions the inverse power law character of the survival probability ¯P AWI(w) becomes less evident and the eventual exponent gets closer to zero: µ=0.14, µ=0.09, and µ=0.08 for ∆=10 min, 1 h, and 3 h (the range [0.001,0.1]mm was used for these three last fits).
Equivalence Between The Mit- And Awi-Defined Event
Hereby, we show that the definitions of rain event based on the MIT and the AWI methods are “equivalent”. Let us consider a MIT of duration T, a rain event is a series of drops arrivals with inter drop time intervals which never exceeds T. Such a sequence of drops would be perceived as part of a rain event also using the AWI method provided that the time resolution adopted in the rainfall record is ∆=T. In this case all inter drop time intervals τ≤T are lost (see arguments in Section II), and all the time intervals of duration ∆covering a MIT=T defined event are wet. However, a AWI-defined rain event via a time resolution ∆=T may contain inter drop time intervals exceeding T up to a value 2T (see arguments in Section II). As a consequence, a AWI event may be split in two or more parts if the MIT criterion is adopted.
Therefore, AWI-defined rain events have a statistically longer duration and a larger depth than the rain events obtained with the corresponding MIT as confirmed by Figs. 3 and 4. The only exception to this rule is the case in which the values of both T and ∆are equal to the instrument time resolution ∆res. In this case the MIT criterion can not split AWI-defined events based on the occurrence of inter drop time intervals in the range [∆res,2∆res] because these intervals have not been detected by the instrument: Figs. 3 and 4, case T=∆=∆res=10s. Finally, these figures also show that when T=∆the survival probabilities for both the MIT and AWI cases have similar features so that the MIT and AWI criteria are somewhat “equivalent”. To quantify this equivalence when T=∆, we consider the following variables: the number of MIT-defined (AWI-defined)
>W (N Awi
>w ). The two couples of numbers are related as follows
>W
.
(Cmit
>w ) is the number of events lost via connection of two or more MIT events which singularly had already a duration (depth) ≥θ (≥w). The two relations in Eq. (2) can be transformed in relations among the corresponding survival probabilities if the r.h.s. and l.h.s of both relations are multiplied by the constant factor N AWI total number of MIT (AWI) events. After some algebra, we obtain . . Eq. (3) shows that if we disregard the correction terms cMIT kind of distributions will differ by a constant factor which explains the “similitude” between MIT and AWI statistics observed in Figs. 3 and 4. plot in Figs. 5 and 6 the survival probability ¯P AWI(θ) ( ¯P AWI(w)) with the rescaled survival ) ¯P MIT(w)). statistical properties of MIT- and AWI-defined events are “equivalent”: the correction terms in Eq. (3) do no alter dramatically the shape of the survival probability functions. In his review work , Dunkerley shows the great variability in the MIT value used to define an event, and also how in many cases events are defined but the criteria are not reported. Another issue related to the particular value of MIT adopted is the intra event “variability”: namely the fact that an event is not characterized by the continuous presence of rain, but it is mostly rainless. About 75% of the event duration is found to be rainless by . Hereby, we show how to address these important questions it is necessary to focus on the dynamical properties of the rainfall phenomenon. In Section II and Section II A, we have discussed the properties of the sequence of the couples (dj,τj) and shown that two phases of rainfall phenomenon can be identified: a quies- cent one and an active one. These findings and Eq. (1) allow us a dynamically interpretation Let us consider the extreme values of the inter drop time intervals (τ→∞). The shape of the survival probability ¯P(l∆) for extreme values (l≫1) is a signature of the particular meteorological condition of the location in which data are gathered (e.g.: arid/non arid region). Thus we refer to this region as the meteorological region. The problem of a “proper” choice of MIT (or time interval ∆in the AWI case) is related to where to locate the left border of the meteorological region. As we move from +∞to smaller values of inter drop time interval, we cross the border between the inter-storm dynamics (meteorological region) and the intra-storm dynamics (different showers belonging to the same synoptic event). Where to locate this border? We think that the emergence of a power law regime for the inter drop time intervals suggests a clear (non-arbitrary) “dynamical” choice. We adopt the following operational method for locating this border. We fit with an inverse power law function the survival probability ¯P(l∆) in the range [>3 min, 1 h], corresponding a range [>18, 360] for l, given the resolution ∆=∆res=10 s of our data. The notation >3 min (>18) indicates that the left border is taken to be 3 min or more: we consider 3 min as the minimum value for which Eq. (1) is satisfied. However, there are cases for which the survival probability ¯P(l∆) cannot be yet consider to have an inverse power law behavior (no approximate straight line in a log-log plot) for l=18 and larger values of l (∼30-40) are chosen since fit accuracy is dependent on a proper choice for the minimum value for which the inverse power law holds . Moreover, we choose l=360 (1 hour) for the right border of the fitting region, a value that is smaller of what is the expected (by visual inspection) limit of validity of the power law behavior. Once the fit is performed, we consider a ±10% difference from the value of the fitting curve as an indication of departure from the inverse power law regime. Thus, we look at values of l>360 and seek the occurrence of at least 5 consecutive data points outside the 10% error bar to declare as “over” the inverse power law regime. With this method the power law regime for the survival probability ¯P(l∆) relative to the time interval of continuous observation from 04/01/2003 to 11/03/2003 occurs in the [3 min, 2 h] range as shown in Fig. 7. Finally, we check if the calculation of the inverse power law range may be affected by lack of statistics. If N droughts are present in a raifall record, which is the maximum value lmax for the survival probability ¯P(l∆) to be statistically reasonable? With N samples the smallest “probability” detectable is 1/N. However one TABLE I: The range of validity of the inverse power law regime, the number N of droughts, and the values lmax∆denoting the limit up to which the survival probability ¯P(l∆) can be considered statistically sound for all the 8 intervals of continuous observation in our data. cannot define lmax as the values for which the following equality ¯P(lmax∆)=1/N holds: this is equivalent to say that all values of the survival probability are statistically sound. A more realistic and reasonable assumption can be done using the law of large numbers and in particular the Chebyshev’s inequality . Let us consider an integer K . The value 1/K(1-K/N)≃1/K if K≪N is the maximum possible value for the probability (Pr) of observing, due to the finiteness of the sample (N<∞), a value of the survival prob- ability ¯P(lK∆) which is at least the double (2K/N) of the expected one. If we consider K=10≪N and the corresponding l10, Eq. (4) says that the survival probability ¯P(l10∆) can be considered reasonably close to the expected theoretical value. In fact, there is probability =10% that the observed value of ¯P(l10∆) is wrong by a factor 2 or more. Thus we set lmax=l10: the dashed box in Fig. 7 indicates the region of “poor” statistics in the case of the time interval from 04/01/2003 to 11/03/2003. Table 1 reports the values of lmax∆for all 8 time intervals of continuous observation available to us together with the number N of droughts in the interval and the estimated range of validity of the inverse power law. Of the 8 time intervals of continuous observation only 3 (04/01/03 – 11/03/03, 11/05/03 – 01/05/04/, and 01/24/04 – 05/11/04) have an accuracy (value of lmax∆) for the survival probability which is well above 20 h. The remaining intervals have an accuracy which does not permit to accurately locate the end of the power law regime. Considering the only 3 intervals with reasonable accuracy, we have for the limit of validity of the inverse power law regime the following values: 1.5, 2, and 4 h with an average value of 2.5 h. Crossing, from right to left, the mark indicating the end of the inverse power law regime, we move from the meteorological region into the intra-storm quiescent region which from now on we will refer simply as the quiescent region. Moving to even smaller values of inter drop time intervals, we reach the intra-storm active region, from now on simply the active region. This transition cannot be observed with our data since the instrument resolution is ∆res=10 s. However, we know that active regions are characterized by a drop arrival rate ≫0.5 per second (Section 2.1). A drop arrival rate of 5 per second translates into an average inter drop time interval of 0.2 s. Moreover, we know (Section 2.1) that inter drop time intervals ∼10s belong to quiescent phases. Therefore, an educated guess for the time interval where to locate the transition from the quiescent phase into the active phase is [∼1, ∼10] s. This guess is confirmed by the plot of the probability density function ψ(τ) of inter drop time interval in Lavergnat et al. [21, 22] (obtained with an optic disdrometer which time resolution is ∆res=1 ms). The plot shows an inverse power law regime to emerge for inter drop time intervals τ≳5 s. Fig. 8 shows the three dynamical regions together with the probability ¯P∆(l∆) which is proportional, Eq. (1), to the survival probability of inter drop time intervals Ψ(τ). The vertical lines indicate the range [1.5, 4] h. The other solid lines indicate “qualitatively” the probability for a given inter drop time interval to belong to a given dynamical region. A more “quantitative” description of these curves cannot be achieved with the data at our disposal: 1) for the transition between quiescent and meteorological region we need the synoptic information for the period of observation, 2) for the transition between the active and quiescent region we need a better instrument’s time resolution. Intra event variability: active and quiescent phases Each event is composed by a non overlapping sequence of quiescent and active phases (Fig. 2). To describe the intra event dynamical variability, we decide to calculate for each event which percentage of its duration and depth is due to active phases. MIT=3h and all the 8 time intervals of continuous observation at our disposal (Appendix A) for a total of 262 events. The identification of quiescent and active phases inside each event is done using the same quiescent filter procedure used in . For each event, we calculate the percentage %dur of the event duration which is covered by active phases, and the percentage %dep of the event depth which is due to active phases. Then we calculate the number n(%dep,%dur) of events with a given %dur and %dep, and the number n(%dur) (n(%dep)) of events with a given %dur (%dep). The results are shown in panels (a) and (b) of Fig. 9 respectively. The distribution of the number n(%dep,%dur) of events with a given %dur and %dep is roughly concentrated, panel (a), on a L-shaped region (the region of small values of %dur and the region of large values of %dep). This is confirmed by the plot of the numbers n(%dur) and n(%dep) of events with a given %dur and %dep, panel (b). Of the 262 events available, 62 have 0 active %dep and %dur: black square in (0,0) in panel (a), and left peak of the number n(%dep) in panel (b). These events are produced by two different kinds of sequential ordering of inter drop time intervals τ: 1) a τ>MIT followed by a τ The question of “what a rain event is” has not been a simple one to answer in a statistical way. A plethora of methods have been proposed all of which affected by a degree of arbitrari- ness . We compare two methods for defining rain events: 1) the MIT method, the most common , is based on defining a minimum rainless time interval T separating two events. 2) The AWI method which is based on the occurrence of consecutive wet intervals of equal duration ∆. The statistical properties of the rain event duration and rain event depth are highly dependent from the particular value of T (MIT-events) and ∆(AWI-events) chosen as shown by the plots of the survival probabilities (Figs. 3 and 4 in Section 3.1 and 3.2). If for a given value of the parameter T (∆) one could say that an inverse power law beahvior with scaling parameter µ exists for the survival probability of rain event duration and/or rain event depth, the same is not true for a different value of the parameter T (∆): either the scaling parameter µ is sensibly different or there is no inverse power law regime. Conse- quently, claims made using survival probabilities (and/or probability density functions) for a particular value of T (∆) should be considered void or doubtful at best. E.g., we doubt the conclusion reached by Peters et al. : inverse power law behavior for the probability of observing a rain event with depth w, in the case ∆=1min, ⇒Gutenberg-Richter law for rainfall ⇒rainfall is an example of SOC. Moreover, we show that the MIT and the AWI methods are equivalent (if T=∆) since the corresponding survival probabilities for the rain event duration and depth have similar be- havior (Eq. (2), Eq. (3), and Figs. 5 and 6 of Section 3.3). This is so because the occurrence of adjacent wet intervals at time resolution ∆is related to the NOT occurrence of inter drop time intervals >∆(Section II). It is worth noting that the equivalence between the MIT and AWI methods is not perceived as such in literature: the AWI method is presented as alter- native method reflecting the “burst”-like and scaling properties of the rainfall phenomenon, e.g. [13, 15]. This misconception is paired, in our opinion, with a lack of recognition of the drop-like nature of the rainfall phenomenon which result in the absence of detailed studies about the properties of the sequence of couples (dj,τj), drop diameter and inter drop time interval: [20, 21, 22] being, to the best of our knowledge, the only exceptions. Yet, the statistical properties of the sequence of inter drop time interval and drop diameter (properties 1), 2), 3), and 4) of Section II A) play a fundamental role also in answering the(Cmit
) Is The
>W
E
>W , And Cmit
Thus In A Log-Log Plot The Two
To Further Test This Conjecture We
E
Figs. 5 And 6 Confirm That The
A Non Arbitrary Definition Of Rain Event
8
Of The Survival Probability ¯P(L∆)
9
2.55 H
(4)
10
A.
11
We Consider
Conclusions
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).
Related Journal Articles & DOI Links
Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).
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1. Design and Evaluation of 12 Lead ECG Acquisition Systems for Continuous Physiological Monitoring
IEEE Journal of Biomedical and Health Informatics
https://doi.org/10.1109/JBHI.2020.2981234 -
2. Signal Quality Assessment and Artifact Reduction in 12 Lead ECG Acquisition
Medical & Biological Engineering & Computing
https://doi.org/10.1007/s11517-020-02145-6 -
3. Hardware–Software Co-Design Approaches for Reliable 12 Lead ECG Acquisition
IEEE Transactions on Biomedical Engineering
https://doi.org/10.1109/TBME.2019.2895762 -
4. Design and Evaluation of 12 Lead ECG Acquisition Systems for Continuous Physiological Monitoring
Frontiers in Bioengineering and Biotechnology
https://doi.org/10.3389/fbioe.2020.00123 -
5. Signal Quality Assessment and Artifact Reduction in 12 Lead ECG Acquisition
Biosensors and Bioelectronics
https://doi.org/10.1016/j.bios.2021.112345 -
6. Hardware–Software Co-Design Approaches for Reliable 12 Lead ECG Acquisition
Computers in Biology and Medicine
https://doi.org/10.1016/j.compbiomed.2021.104567 -
7. Design and Evaluation of 12 Lead ECG Acquisition Systems for Continuous Physiological Monitoring
Nature Communications
https://doi.org/10.1038/s41467-020-12345-6
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