Cadence Stratus HLS

Abstract

High-level synthesis (HLS) is a process that automatically translates a software program in a high-level language into a low-level hardware description. However, the hardware designs produced by HLS tools still suffer from a significant performance gap compared to manual implementations. This is because the input HLS programs must still be written using hardware design principles.

Existing techniques either leave the program source un- changed or perform a fixed sequence of source transformation passes, potentially missing opportunities to find the optimal design. We propose a super-optimization approach for HLS that automatically rewrites an arbitrary software program into efficient HLS code that can be used to generate an optimized hardware design. We developed a toolflow named SEER, based on the e-graph data structure, to efficiently explore equivalent implementations of a program at scale. SEER provides an ex- tensible framework, orchestrating existing software compiler passes and hardware synthesis optimizers.

Our work is the first attempt to exploit e-graph rewriting for large software compiler frameworks, such as MLIR. Across a set of open-source benchmarks, we show that SEER achieves up to 38× the performance within 1.4× the area of the origi- nal program. Via an Intel-provided case study, SEER demon- strates the potential to outperform manually optimized designs produced by hardware experts.

Ntroduction

High-level synthesis (HLS) is a process that automatically translates a software program in a high-level language such as C/C++ into a hardware description in a low-level language such as Verilog/VHDL. This allows software engineers with- out any hardware background to customize their hardware accelerators. Today, HLS tools have been widely used and actively developed in both academia and industry, for example,

Ynamatic From Epfl, Bambu From The Politecnico

di Milano, Stratus HLS from Cadence, Catapult HLS

From Siemens, Intel Hls From Intel And Vitis Hls

from AMD Xilinx. Still, it remains the case that automatically synthesizing efficient hardware designs from arbitrary high-level software programs is challenging. A major reason is that each HLS tool only applies a fixed sequence of general source transfor- mations for all input programs, as shown in Figure 1. This significantly restricts the optimization space for a particular

Seer

Figure 1: pi denotes an optimization pass, and si denotes a repre- sentation of a program. HLS Tools 1 and 2 take the same input program s0 and apply different sequences of optimization passes,

Pi And P′

i respectively. The transformed programs sk and s′

K May

result in different hardware designs because of the difference in pass sequences. SEER efficiently explores all these possibilities in parallel using e-graphs, ei.

program. This is known as the ‘phase-ordering problem’ in compilers . The phase-ordering problem for HLS tools is more chal- lenging for two reasons. First, an HLS tool contains optimiza- tions at different granularities, such as higher-level control path optimizations and lower-level data path optimizations.

These optimizations may interfere, resulting in a larger, more complex space of optimization orderings than in software com- pilers. Second, evaluating hardware metrics from an input software program is challenging in existing frameworks. This means that the optimizer needs to repeatedly call the down- stream synthesis tool to evaluate which source representation is efficient when mapping into hardware.

Existing works on HLS source rewriting build an optimiza- tion sequence based on heuristics. This misses opportunities to perform program-specific optimizations for a given input program, potentially making the optimal hardware design un- reachable. In practice, significant manual effort is spent on rewriting the program source for HLS tools to resolve the

Problem Above. Both Stratus Hls And Vitis Hls ,

provide recommended coding styles in their user manual to restrict users to a subset of C programs for better performance. A designer must write the HLS program following these guide- lines and using hardware design principles in order to produce efficient hardware.

In order to tackle the problems above, our work aims to

Isting 3: Transform 2

Figure 2: A motivating example of loop fusion. loop_1 and loop_3 cannot be fused because of the memory dependence on array x. It is challenging to determine which representation is better, fusing loop_1 and loop_2 or fusing loop_2 and loop_3? of optimizations that can be mapped into efficient hardware

Based On The Program Source?

We propose an approach named SEER (Super-optimization Explorer using E-graph Rewriting) to resolve the challenges above. Given a software program, SEER automatically deter- mines a sequence of optimizations for efficient hardware syn- thesis. SEER is the first approach to HLS ‘super-optimization’, since it explores different source-level optimization orderings in parallel, then customizes the sequence to the input program.

SEER enables super-optimization using an efficient data structure, known as an e(quivalence)-graph , which pre- serves a set of program representations to resolve the phase- ordering problem. As shown in Figure 1, SEER can explore alternative optimization sequences in a single e-graph at the same time. Our main research contributions include: • a technique to determine an optimization order for efficient hardware synthesis by exploring equivalent representations

Of A Program In An E-Graph;

• an orchestration technique that explores an e-graph with ex- isting optimization passes from large software frameworks, such as MLIR , and hardware synthesis optimizers, such

As Rover , To Explore Rewriting At Scale;

• a hardware-aware evaluation model at the source level to evaluate the quality of hardware synthesized from a repre-

Sentation Of A Software Program; And

• over a set of benchmarks, SEER achieves up to 38× the performance within 1.4× the area of the original program, and demonstrates the potential to outperform manually opti- mized designs by hardware experts.

The rest of the paper is organized as follows. Section 2 presents a motivating example to illustrate the challenge in automated source rewriting for HLS. Section 3 provides the necessary background and related work. Section 4 explains the theoretical details of our work. Section 5 evaluates the effectiveness of our work by comparing it with vanilla Stratus HLS and manual design by experts.

Table 1: The performance of hardware generated from the represen- tations in Figure 2 depends on the operation latencies. These could be affected by other transformation passes and are not evaluated in the existing flow. The best performance in each case is highlighted.

Otivating Example

Using an example, we present the challenge to conventional, fixed pass-order HLS flows and how our approach can over- come these challenges. Listing 1 presents a program with three sequential loops. Loop fusion is an optimization technique that combines multiple sequential loops into a single loop. In HLS, loop fusion avoids the area overhead of the loop control logic for separate loop instances and could exploit more data parallelism in the fused loop body. However, the throughput of a loop is restricted by the slowest data path in the loop body.

Loop fusion can exhibit an area-performance tradeoff. A pre-condition for loop fusion being valid is that the se- quential loops must have no data dependence. For the example in Listing 1, loop_1 and loop_3 access array x at overlap- ping indices, preventing loop fusion. However, loop_2 has no data dependence with either loop_1 or loop_3, since it only accesses array y. This means that we can safely fuse loop_1 and loop_2 (Listing 2) or fuse loop_2 and loop_3 (Listing 3). Note that the user or automated tool must choose between these fusion passes, since Listing 2 is not reachable from Listing 3, and vice versa.

Without evaluating downstream hardware optimization passes, it is difficult to determine whether Listing 2 or 3 will generate better hardware. Table 1 shows the performance of the hardware generated from these representations for different latencies of the functions f and h. Such latency information is unpredictable at the source rewriting stage because later passes

Hardware Design

Figure 3: HLS development flow for hardware production. The right side provides examples of optimizations for each step. SEER aims to solve the challenge in efficient source rewriting for arbitrary programs (shown as Manual) for better hardware performance.

might alter these functions. This correlation could make a locally sub-optimal transformation globally optimal. SEER models hardware scheduling information in software and effi- ciently explores transformations of these representations in an e-graph instead of manipulating a single representation.

Problem Formalization

A key novelty of our work is that SEER explores the corre- lation among transformation passes, which opens up a larger design space. Let P be a set of available transformation passes, PN be all possible sequences of the elements in P and let R be the set of functionally equivalent representations of a given program. As shown in Figure 1, an HLS tool uses a fixed sequence of passes t = (p0, p1,..., pk) ∈PN. The transfor- mation steps in t result in a set of representations R′, where R′ ⊆R. SEER searches the space of pass sequences PN and ex- tracts a customized t′ ∈PN for each input program. SEER can explore a potentially larger set of representations R′′, where R′ ⊆R′′ ⊆R. This is because SEER searches for t′ by ex- ploring PN in parallel. In the rest of the paper, we show how to construct R′′ using an e-graph and how to determine t′ for mapping an arbitrary program to efficient hardware.

Background

3.1. Phase-Ordering Challenges in High-Level Synthesis HLS tools automatically map a high-level software program into a custom hardware design in a low-level hardware de- scription, e.g.

A Production Hls Development

flow comprises three steps, as shown in Figure 3. First, a high-level specification of an algorithm is manually rewrit- ten following the recommended coding guidelines producing code that is amenable to optimization by the HLS tool. Sec- ond, the rewritten HLS program usually contains design con- straints expressed via inline directives or pragmas to exploit hardware parallelism and resource sharing. The process of exploring these constraints is known as design-space explo-

E-Class

Figure 4: An e-graph grown from two rewriting steps to represent three equivalent expressions. Each green node is an e-node, and each red box is an e-class. Edges connect e-nodes to child e-classes.

ration (DSE) and is already semi-automated [16, 24, 33]. Finally, the optimized design constraints are sent with the HLS program to the HLS tool, which synthesizes a hardware design. The HLS tool automatically performs low-level hard- ware optimizations, such as hardware scheduling and binding, which maps the start times of operations into clock cycles with efficient hardware resource sharing [4, 19, 25, 56]. The HLS tool also performs register retiming to achieve a high clock frequency [19, 25].

The phase-ordering problem refers to the challenge of de- termining the optimal order of optimization passes at compile time. It is challenging due to the destructive interaction of optimization passes, as discussed in Section 2. Existing works address the phase-ordering problem for compilers using two approaches. First, there are works that use machine learn- ing [2, 3, 20, 27, 38] for inferring a productive sequence of optimization steps. These approaches only work for domain- specific programs, while our approach works for arbitrary or iterative approaches for efficient searching for the optimiza- tion steps [26, 39, 55]. The intermediate traces during the iterations are not efficiently preserved, while our work carries it in the e-graph during the exploration. All these approaches only target software optimization, while our approach targets hardware optimization.

In HLS, the phase-order problem is more complex, because the benefit of software transformation passes, such as loop fu- sion and if conversion, can only be evaluated by analyzing the generated hardware. In this work, SEER orchestrates software transformations for hardware optimization using hardware modeling. To the best of our knowledge, SEER is the first attempt to resolve the general phase-ordering problem in HLS.

E-Graph Representation

An e(quivalence)-graph, is a data structure used to represent a set of equivalent expressions [37, 47, 51] as shown in Figure 4. The e-graph organizes functionally equivalent expressions into equivalence classes, known as e-classes, drawn as red boxes in the figure. Nodes in an e-graph, known as e-nodes, represent either values or operators with edges connecting

Equivalence Check

Figure 5: An overview of the SEER toolflow. Our contributions are highlighted. e-class children, illustrated as green nodes in the figure. E- classes are represented as groups of e-nodes. The e-graph is grown via constructive rewriting, meaning that the left-hand side of the rewrite is retained in the data structure. A minimal cost expression is typically extracted from the e-graph, based on a user-defined cost model.

A main benefit of the e-graph data structure is that it ef- ficiently represents equivalent expressions by sharing and reusing common sub-expressions, such as sharing x in Fig- ure 4. Operator e-nodes have edges connected to child e- classes. This captures the intuition that, for a given sub- expression, we can choose from a set of equivalent sub- expressions. The reduced redundancy in the e-graph enables more efficient analysis and optimization of a program.

E-graphs can be found in modern SMT solvers, such as Z3 [14, 15]. The recently developed egg library , pro- vides an extensible e-graph implementation that has fueled a new wave of e-graph research. Since its release, e-graphs have been applied to hardware design automation [10, 48], nu- merical stability improvement , compiler design and much more [36, 43, 49]. One relevant work , identified improvements to program analysis capabilities by using the e-graph representation. We describe how SEER exploits this in Section 4.5. SEER is the first approach to apply e-graphs to program optimization using compiler frameworks such as

R.

In this work, we incorporate and extend an existing egg based data path optimization engine, named ROVER [10, 11]. ROVER takes a combinational hardware design and op- timizes the data paths using optimizations for circuit area minimization. The existing ROVER implementation leaves the control path untouched, such as loops. SEER generalizes ROVER to a higher-level software abstraction for HLS tools and combines it with control path optimizations for pipelined designs.

Ulti-Level Intermediate Representation

Multi-Level Intermediate Representation (MLIR) is a compiler infrastructure framework developed within the Low- Level Virtual Machine (LLVM) project . It aims to ad- dress the challenges of representing and optimizing programs at different levels of abstraction. Dialects can be seen as a namespace for operations, types and attributes modelling spe- cific abstractions (i.e. control flow or affine loops). Primarily, SEER uses the affine and scf dialects. The affine dialect provides a program abstraction for affine operations, and the scf dialect provides a program abstraction for structured con- trol flows. MLIR offers a comprehensive set of transformation and analysis passes that can be directly reused and explored in

Rct Is An Mlir-Based Hardware Compiler Frame-

work under LLVM, which lowers MLIR to RTL code as an open-sourced HLS tool. Xu et al. propose a specific MLIR di- alect named HECTOR for hardware synthesis , which can be translated into RTL code. There are also source transfor- mation tools that transform MLIR into optimized HLS code in C [28, 54] or LLVM IR [1, 57]. Both these works and SEER have an end-to-end HLS flow in MLIR. Prior work suffers from the phase-ordering problem illustrated in Figure 1 because they use a fixed sequence of transformation passes.

SEER overcomes the phase-ordering challenge using e-graphs, customizing the MLIR pass order for each input program and optimization objective.

Ethodology

In this section, we describe the proposed source-to-source super-optimization tool for HLS. First, we provide an overview of the proposed SEER toolflow. We then introduce a new intermediate language, named SeerLang, that provides the first interface between MLIR and the egg e-graph library. Next, we explain the rewriting rules included in SEER and how to explore these rewriting rules in the e-graph, to construct R′′ in Section 2. Finally, we describe the cost functions used for representation extraction for determining t′ in Section 2.

Seer Overview

To maximize generality and avoid targeting a particular HLS tool, SEER performs source-to-source transformation on the input software program and generates an efficient represen- tation for HLS tools. SEER accepts C, C++, SystemC code, and other software programming languages that can be trans- lated to MLIR. Figure 5 illustrates a high-level overview of the SEER tool flow for HLS super-optimization.

⃝The Input Program In C/C++/Systemc Is Parsed By

Polygeist , a C (and C++) front end for MLIR, trans- lating the program into the MLIR affine or scf dialects. We implemented MLIR transformation passes for convert- ing a subset of SystemC.

2⃝The SEER front end translates the MLIR into a new inter- mediate language, SeerLang, which provides an interface

Between Mlir And The E-Graph Library, Egg . Seer-

Lang is described in Section 4.2. 3⃝From SeerLang an initial e-graph is constructed in egg, where each e-class contains a single e-node.

4⃝SEER provides a set of patterns to egg, which are used to search for rewriting opportunities in the e-graph, a process known as e-matching.

5⃝Once a pattern in the e-graph is matched, a validity condi- tion is checked and a new equivalent SeerLang expression is constructed. Section 4.3 describes SEER’s rewrites.

6⃝If the rewrite is valid, the new SeerLang expression is unioned into the e-graph, as shown in Figure 4. The e- graph continues to grow until reaching a user defined limit, or until no new equivalent representations can be found.

Rewriting in SEER is explained in Section 4.4. 7⃝From the final e-graph, an extraction is performed to ob- tain an efficient implementation based on control path and data path hardware cost functions. The details of these cost functions are explained in Section 4.6.

8⃝The extracted SeerLang expression is translated back to the MLIR affine or scf dialects by the SEER back end, such that we can exploit existing MLIR back ends.

9⃝The generated MLIR is converted back to SystemC us- ing emitC , such that the optimized program can be parsed by HLS tools. We extended the C back end to emit ⃝The equivalence between the original and transformed programs is proven by a formal equivalence checking tool,

Formal From Synopsys , At Systemc Level. The

equivalence check steps are explained in Section 4.7

Seer Intermediate Representation

A key challenge for enabling MLIR exploration via e-graph rewriting in egg is that these two frameworks do not share a common representation language, and re-implementing either would require significant engineering effort. We identified three potential solutions for orchestrating them in the same toolflow. First, we could keep each MLIR representation in memory but removing redundancy among these versions is challenging, making the memory size unscalable. Second, we could keep a single representation and pass traces for obtain- ing each new MLIR representation. This leads to unscalable compilation time for reproducing the required representation.

Finally, we decided to propose a new language named Seer- Lang in egg for translation to and from MLIR. In egg, users define an S-expression based language similar to Common Lisp to represent expressions.

Term ::= (Operator [Term] [Term]...[Term])

This language format allows users to concisely express rewrites. We defined a domain-specific representation, called

Isting 5: Mlir Code

1 (affine.for "affine.for_0" %i 0 8 1 none none none

Isting 6: Seerlang Expression

Figure 6: Example of SeerLang for expressing a for loop and mem- ory operations. SeerLang, that provides an interface between MLIR and egg.

The semantics of SeerLang are similar to MLIR as the repre- sentation is for translation only. SeerLang supports a subset of MLIR operations including operations in the affine, scf, memref and arith dialects, but can be extended to support other MLIR operations. In addition, SeerLang supports a seq operator to encode the original program ordering between two operations.

Here we introduce two key constructs in SeerLang, opera- tion and block, inspired by MLIR. An operation takes a set of inputs and produces a set of results. An operation could be a data path operation like an add operation or a mul operation, or a control path operation like a function, a loop or an if statement. A block contains a set of operations. In each block, the SeerLang front end analyses the data dependence between operations in the same block and reconstructs expression trees.

A seq operation is purely an annotation, preserving the origi- nal program order by keeping memory operations in the block and associating them using seq operations. This facilitates memory dependence analysis for the transformation pass.

An example of SeerLang is shown in Figure 6. Listing 4 shows a for loop that contains two memory operations. This is translated into Listing 5 in the MLIR affine dialect. The for loop in C is translated into an affine.for operation because the loop contains only affine memory accesses. The memory operations are translated into affine memory operations as the array index is a simple loop iterator and is in affine form.

The arithmetic operations are translated to operations in the MLIR arith dialect. The equivalent SeerLang of Listing 5 is shown in Listing 6.

Translating into SeerLang from MLIR is nearly lossless since each operation in SeerLang keeps the type and operand Table 2: Example SEER rewriting rules implemented directly in egg. SEER contains 106 data path and gate-level rewrites . All datapath rewrites are signage and bitwidth dependent.

A∥B

information, except for the program order of independent data path operations. Independent operations are parallelized in hardware and its original program does not affect correctness.

The data dependence is analyzed by the front end of SeerLang when translating from MLIR. For example, in Listing 6, the arithmetic operations for %b0 and %b1 are converted into a nested expression at line 6. This recovers the data flow graph of the block for data path optimization. The operations with a potential data dependence are connected using seq operations.

In SEER, we assume there exists a data dependence between every two memory operations for simplicity. The memory operations are connected using seq operations, such as the load and store operations in Listing 6. This preserves the program order of memory access and ensures the correctness of memory transformation.

Rewriting Rules

The rewriting rules in SEER enable the exploration of equiv- alent implementations of a program. SEER supports both internal rewrites, expressed directly in SeerLang, and exter- nal rewrites, expressed as MLIR passes. For internal rules, egg can directly apply them to add equivalent sub-expressions to the e-graph. A subset of these rules is shown in Table 2.

External rules are implemented as dynamic rewrites in egg, where we match against a SeerLang pattern and then construct an equivalent implementation using an external pass. In this construction, SeerLang must be translated into a compatible representation, modified by the external pass, and translated back to SeerLang. At this point egg can union this new sub- expression into the appropriate e-class. Such an approach makes it simple to implement new rules and enables the reuse of existing rules from other toolflows. SEER rewrites at differ- ent granularities, allowing it to simultaneously optimize at the control path level, data path level and gate level.

First, the control path-level rewrites modify the control flow graph (CFG) of the original program. Particularly, we focus on the transformation of for loops and if statements. This includes ten MLIR passes for loop re-ordering, loop merging and if conversions. We maximize the reuse of available MLIR passes in upstream in SEER.

Most of the loop transformation passes are directly adopted from the MLIR/LLVM upstream and applied to SEER. The loop unroll pass performs complete unroll of a loop. This enables potential loop body reduction by other passes such as the memory forward pass. We disable exploring loop un- rolling with different unrolling factors by default to improve scalability. It is provided as a user option. The loop fusion, loop interchange and loop flatten passes are existing compiler transformations which are directly mapped to SEER. The loop perfection pass converts a loop nest that contains code in its outer loop body and outside its inner loop body to a perfect loop nest. This is done by moving the code outside the inner loop body into the inner loop body with predicates. Loop per- fection opens up opportunities for more loop transformation, such as loop interchanging and loop flattening.

The if conversion pass is used to convert if statements to select operations, reducing the control flow complexity. This has been widely used in the HLS code transformation for maximizing a data path region for pipelining. The memory forward pass removes redundant load and store operations in the code to reduce memory accesses. The upstream pass only removes store operations. We extend it to remove redundant load operations as well.

Customized MLIR passes can also be easily extended to SEER with the same interface. For instance, the if correlation pass is a customized pass which detects correlation among conditions of several sequential if statements and merges them if the conditions are identical or disjoint. An example of if correlation is described in Section 4.5. The memory reuse pass moves a read-only memory access outside the loop. The control flow mux pass moves an operation in both branches of an if statement outside the if statement and select its args in the branches for resource sharing at the source level.

The data path-level rewrites modify the program at a finer grain and are mostly re-used from the e-graph based ROVER tool [10, 11]. They include expression balancing, constant folding and manipulation, and strength reduction. Data path optimization is currently under-explored in existing commer- cial synthesis tools and recent synthesis-aware data path rewrit- ing has been shown to reduce circuit area [10, 11]. Two rewrites from Table 2 are applied to the e-graph in Figure 4.

Finally, the gate-level rewrites also modify the program at the operator level but target bit-level hardware customization. Most gate-level rewrites are well exploited by the logic syn- thesis optimization in HLS tools. However, data path and bit-level rewriting can often interact providing a mutual bene- fit. SEER restricts the number of gate minimization techniques to improve scalability. We group these into the data path set.

E-Graph Rewriting For Super-Optimization

SEER alternates between iterations of control flow rewriting and data path rewriting. At each iteration all rules within the

Unconditional

Figure 7: E-graph exploration of the motivational example (Figure 2) using SEER. The e-graph is simplified by merging subgraphs of loops into single nodes. The green nodes represents the initial e-graph obtained from Listing 1. 1⃝illustrates an example of an unconditional rewrite for a sequential association inside egg. For rewrite 1⃝, the original sub-expression in the shaded red region is rewritten to the red node in the same e-class. 2⃝illustrates an example of a conditional rewrite for loop fusion through MLIR. For rewrite 2⃝, the original sub-expression in the shaded blue region is rewritten to the blue node in the same e-class.

Hardware Synthesis

Figure 8: An example of extracting representations using cost functions for static analysis and hardware synthesis.

Static Analysis

Figure 9: An example of using program invariants from static analysis one representation for transformation of another. given rewrite set are applied, growing the e-graph. SEER interleaves the exploration of these rewrite sets since one might introduce more rewriting opportunities for the other.

For instance, dead code elimination, a data path rewrite, can change the dependence constraints, enabling more control path rewrites. Loop fusion, a control path rewrite, can enable further rewrites for the fused loop body.

Figure 7 shows the e-graph exploration of the motivating example introduced in Figure 2. To the initial e-graph, repre- sented by the green nodes, SEER applies an internal rewrite rule from Table 2, seq associativity. The general rule, shown in the top middle of the figure, matches the sub-expression covered by the red shading and returns an equivalent SeerLang expression. This new expression is unioned into the matched e-class, where the new nodes are shown in red.

Next SEER applies the external loop fusion MLIR transfor- mation, that represents the transformation from Listing 1 to Listing 3. The loop fusion rule searches for two sequential loops and checks if they satisfy the particular dependency con- straints. First, the sub-expression covered by the blue shading matches the pattern of the loop fusion rewrite. The matched SeerLang is translated into the equivalent MLIR. Then SEER calls the existing loop fusion pass in MLIR, generating a new MLIR implementation. The loop fusion pass performs the dependence check internally before the transformation. If the dependence constraints are unsatisfied or the transformation fails, the pass returns the original MLIR. The loop fusion rule in egg checks that there were no errors in the pass and that the returned MLIR differs from the input then converts this back to SeerLang and performs the union. In this example, the result from fusing loop_2 and loop_3 is added to the e-graph, as the blue loop_2_3 node.

Many other SEER rewrites can be applied to grow a larger e-graph than the one presented in Figure 7. Thanks to the e- graph representation, despite fusing loop_2 and loop_3, the fusion of loop_1 and loop_2 can also still be triggered. This would not be possible in a traditional compiler. Note that the fusion of loop_1 and loop_2_3 will be attempted but will fail due to the validity checks. The e-graph grown after several rewriting iterations, represents the explored design space of equivalent implementations. From this e-graph SEER must now select an efficient HLS implementation.

Eeper Optimization Opportunities

Prior work observed how retaining multiple representations in an e-graph can improve program analysis . Here we observe a practical benefit of this, allowing SEER to discover implementations that are unreachable with existing compiler passes. SEER can learn program invariants from one represen- tation which it can use to rewrite any equivalent representation.

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.

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

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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