Arduino Radar System

Estimation Using Radar Point Clouds

Abstract—Conventional radar segmentation research has typ- ically focused on learning category labels for different moving objects. Although fundamental differences between radar and optical sensors lead to differences in the reliability of predicting accurate and consistent category labels, a review of common radar perception tasks in automotive reveals that determining whether an object is moving or static is a prerequisite for most tasks. To fill this gap, this study proposes a neural network-based solution that can simultaneously segment static and moving objects from radar point clouds. Furthermore, since the measured radial velocity of static objects is correlated with the motion of the radar, this approach can also estimate the instantaneous 2D velocity of the moving platform/vehicle (ego- motion). However, despite performing dual tasks, the proposed method employs very simple yet effective building blocks for feature extraction: multi-layer perceptrons (MLPs) and recurrent neural networks (RNNs). In addition to being the first of its kind in the literature, the proposed method also demonstrates the feasibility of extracting the information required for the dual task directly from unprocessed point clouds, without the need for cloud aggregation, Doppler compensation, motion compensation, or any other intermediate signal processing steps. To measure its performance, this study introduces a set of novel evaluation metrics and tests the proposed method using a challenging real-world radar dataset, RadarScenes. The results show that the proposed method not only performs well on the dual tasks, but also has broad application potential in other radar perception tasks. More qualitative results can be viewed here: https://youtu.be/3ejS1chSvQ8?si=uGRugVA63BCyvNBV.

Index Terms—Radar segmentation, ego-motion estimation, au- tomotive radar, radar point cloud, deep learning.

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VER the past decade, the automotive industry has made tremendous progress in autonomous driving technology, revolutionizing today’s smart vehicles and transportation. As the goal shifts from testing to real-world driving environments, developing reliable sensor perception systems to ensure the safety of autonomous driving systems has become imperative.

Common sensors used in perception systems include cameras, automotive radar, lidar, and sonar . Among these sensor options, autonomous radars play a vital role in providing robust perception information and demonstrate unparalleled advantages in the following aspects: firstly, the performance Simin Zhu, Francesco Fioranelli, Alexander Yarovoy are with the Mi- Satish Ravindran is with NXP Semiconductors, San Jose, CA, USA (e- Fig. 1: The proposed method takes multidimensional radar point clouds as input, uses neural networks (NNs) for auto- matic feature extraction, and then segments static and moving objects. Based on the measured radial velocity of static ob- jects, the method can estimate the ego-motion of the moving vehicle. The distinct moving instances can also be generated after applying a clustering algorithm to the predicted moving objects. In this example, the RadarScenes dataset is used for testing.

of radar perception is very robust to low light and adverse weather conditions such as rain, snow, and fog ; secondly, automotive radar can detect objects that are partially or com- pletely obscured or even out of the line-of-sight of the radar ; thirdly, automotive radar can measure the radial velocity of detected objects, which can be used directly to estimate the speed of the ego-vehicle and other moving objects .

The above advantages make automotive radar a powerful perception sensor in the automotive industry. Among many perception tasks, radar-based segmentation has gained signif- icant attention in the past few years. The main objective in radar segmentation is to assign a class label to each point

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in the radar point cloud or each cell in the radar data cube . The radar point cloud is generated after applying a detector such as one of the Constant False Alarm Rate (CFAR) algorithms on the radar data cube. Both data formats capture information such as range, radial velocity, and angle of arrival (AoA) of objects in the scanned environment.

Therefore, performing segmentation on these data is crucial for scene understanding and driving safety. In the related radar literature, three categories of segmentation tasks have been

Explored, Namely, Semantic Segmentation , , –,

instance segmentation –, and panoptic segmentation . Undoubtedly, these studies have demonstrated the great potential of radar sensors and laid a solid foundation for future perception systems.

However, most segmentation works have focused only on moving objects, while radar point clouds typically contain detections from moving objects (e.g., cars), static objects (e.g., buildings), and false positives (e.g., unidentified objects and multipath reflections). Further literature review shows that in other radar-based perception tasks, identifying which objects are static is also very important –. To locate static detections, some studies have to assume a static environment , , while others usually rely on knowing the vehicle’s

, Such As The Random Sample Consensus (Ransac)

algorithm . While these remedies can help identify static objects, they either require external odometry sensors or assume that most objects are static, and often leave moving objects mixed with false positives, requiring further separation.

Therefore, to bridge the gap between the unprocessed radar point cloud and various perception applications that either require knowing the positions of static or moving objects, or the vehicle’s speed, this study redefines the objective in conventional radar segmentation tasks. For this, it proposes a unified solution that can simultaneously perform the dual task of static and moving object segmentation and vehicle ego-motion estimation, as illustrated in Figure 1. To the best of our knowledge, this method is the first attempt to enable this dual task, and the results demonstrate that raw radar point clouds contain sufficient information to achieve both.

In addition to this primary contribution, the proposed method

Offers The Following Advancements:

1) Radar-only: Unlike many other studies, the proposed method performs the dual tasks using only radar data. For example, it eliminates the need for odometry sensors to measure vehicle ego-motion to assist with radial velocity compensation or motion compensation. This preserves sensor independence and removes concerns about errors introduced by sensor synchronization or output glitches.

2) No Aggregation: The Proposed Method Can Handle

sparse radar point clouds and does not require cloud aggregation from multiple radars or radar frames. In- stead, to extract temporal features, the proposed method uses a moving window and takes multiple radar point clouds as input. This preserves temporal features and removes the need for direct coordinate transformation or transformation with motion compensation1, making it robust in highly dynamic scenes.

3) Lightweight: The proposed method uses simple yet ef- fective neural network backbones for feature extraction, where the multi-layer perceptron (MLP) is used for spatial features and the recurrent neural network (RNN) is used for temporal features. The resulting model is lightweight (0.15 M parameters) while providing critical information for understanding vehicle motion and other downstream perception tasks.

4) Dataset: As no existing radar dataset fully supports the objective of the proposed method, this work reorganized the ground-truth (GT) class labels of the RadarScenes dataset . Specifically, vehicle ego-motion was used to separate static from non-static objects; the output of the DeepEgo+ approach was incorporated to compensate for the effects of vehicle acceleration , which can oth- erwise cause mislabeling of static objects; and moving versus non-moving objects were subsequently classified using the dataset’s original labels.

Finally, it must be noted that the goal of this study is different from previous studies on radar-based segmentation. While previous studies have focused on assigning detailed class labels, which is undoubtedly important and meaningful, this study began by seeking a continuation of traditional seg- mentation, but ended by filling an important gap in the radar perception processing chain. Therefore, it is unfair to compare this work via previous research aiming only at assigning class labels to pixels or points. Instead, the proposed method should be viewed as complementary to traditional radar segmentation and to other radar perception tasks.

The rest of this paper follows this structure. Section II pro- vides an overview of existing research on this topic. Section III presents the detailed design of the proposed method. Section IV first introduces the testing radar dataset and evaluation metrics, and then measures the performance of the proposed method. Finally, Section V draws conclusions and outlines future research directions.

Ii. Related Works

This section reviews the relevant literature. It first outlines prior work on radar-based segmentation and recent advances in the field. It then examines studies on other radar perception tasks to highlight the importance of performing the proposed dual tasks on radar point clouds. Finally, a brief summary of the literature review is provided.

A. Radar-Based Segmentation

According to its objectives, previous radar-based segmen- tation studies can be divided into three categories: semantic

Segmentation , , –, Which Assigns A Class Label

1Radar point cloud aggregation with motion compensation means that several point clouds are transferred to a reference point cloud and their positions in the reference cloud are compensated for the vehicle ego-motion.

In other words, motion compensation requires knowledge of the vehicle’s ego-motion, while direct aggregation does not.

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to each radar point (detection); instance segmentation – , which not only classifies each point but also distinguishes between individual objects within the same class; and panop- tic segmentation , which combines both approaches by providing semantic labels for all points while also separating instances for object classes. In addition, previous studies can also be divided according to the format of radar data, where except , , , which use radar cubes (before detection), all of the rest use radar point clouds (after detection). Methods using radar cubes claim they are superior in segmenting small objects, as information can be lost during the detection process , . Nevertheless, there are currently no conclusive experimental comparisons demonstrating their effectiveness.

For methods that rely on radar point clouds, the RadarScenes dataset appears to be a popular choice since all methods use it to evaluate their performance. Although the RadarScenes dataset provides 10 different classes for moving objects, almost all studies use less than half of them, reflecting the challenges of performing detailed semantic segmentation using sparse and noisy radar data. To handle this challenge, PointNet++ ,

, , And Transformer , , , Become

the most commonly used feature extraction backbones in these studies. Theoretically, Transformer outperforms PointNet++ in handling sparsity and long-range dependencies; experimen- tally, Transformer also demonstrates better performance than PointNet++ , , .

Based on this brief literature review, it is evident that many studies have extensively explored the topic of radar-based segmentation from various perspectives, such as in terms of objectives, data formats, and feature extraction backbones.

It is a solid start, especially in such a pioneering field as automotive radar. However, there are still areas for further improvement. Firstly, except for studies using stationary ego- vehicle datasets , , nearly all prior research requires knowledge of vehicle ego-motion provided by odometry sen- sors. Ego-motion is often used to compensate for the measured radial velocity, which is then used as an important input object feature. However, if ego-motion is known, segmenting the static background becomes straightforward, as was done in . Furthermore, since almost 97% of radar detections come from static objects , the computational complexity of these methods can be significantly reduced by removing static points from the input. Also, with the compensated radial velocity, it is understandable that most studies achieve scores exceeding 99% on the Intersection over Union (IoU) metric for classifying ‘static’2 objects. Last but not least, relying on external sensors may compromise sensor independence and system robustness due to potential erroneous outputs or synchronization issues.

Secondly, to address the sparsity problem, some studies ,

, , Rely On Combining Radar Point Clouds Over A

fixed time period (e.g., 500 ms), regardless of the number of clouds aggregated. However, this approach can adversely increase inference latency and system memory consumption

. In Contrast, Other Studies , , , Also

2In the RadarScenes dataset, radar detections from static objects and false positives are both labeled as ‘static’, whereas in this study, they are treated separately.

merge clouds, but they only allow each radar to contribute once per fused cloud. Given a 60 ms update rate per radar, this can shorten aggregation time while still benefiting from the increased cloud density due to overlapping fields of view (FoVs). Nevertheless, all of the above solutions still introduce some degree of inference latency. Moreover, without motion compensation, they may experience performance degradation in highly dynamic scenes, especially when moving objects are present in the overlap region. Furthermore, since the radars in the RadarScenes dataset are fully unsynchronized3, fusing radar point clouds cannot be done directly but requires a heuristic process .

Thirdly, to handle the challenging task of labeling objects in sparse and noisy radar point clouds, previous studies usually adopt NNs with sophisticated feature extraction backbones, such as Transformer and PointNet++. While Transformer outperforms PointNet++, they are typically too bulky to be suitable for radar processing systems that require real-time prediction and immediate feedback . In addition, these backbones are often described as ‘data-hungry’, but large radar datasets are expensive to generate and annotate. In any way, due to the fundamental limitations of radar sensors, the performance gains from using complex backbones are not as significant as with optical sensors , , leading one to wonder: why not use radar for tasks that are better suited to its characteristics? For example, recent studies , no longer search for specific object types or bounding boxes, but instead focus on a simpler task of class-agnostic segmentation and tracking.

Last but not least, it is worth noting that most previous studies have only focused on segmenting moving objects from radar point clouds, labeling static objects and false positives together as ‘static’. From the perspective of various radar perception tasks, it is important to conduct a comprehensive segmentation, the reasons for which will be further explained in the next section.

B. Other Radar-Based Tasks

A radar point cloud typically contains a mix of detections from moving objects (e.g., vehicles), static objects (e.g., buildings), and false positives (e.g., false detections from sidelobes). Most existing radar-based segmentation tasks focus on separating moving objects, leaving static objects mixed with false positives. However, static objects also play a vital role in many radar perception tasks. For example, the measured radial velocity of static objects can be used to estimate the vehicle’s ego-motion , and thus calibrate the radar’s extrinsic parameters , . Additionally, knowing where static objects are located allows for the implementation of algorithms such as semantic grid mapping , simultaneous

Localization And Mapping (Slam) , , And Amplitude

and phase calibration . Furthermore, separating static points from the radar point cloud can help perform free space

Detection , , Road Course Estimation , , And

multi-object tracking . Among these studies, most rely 3The time intervals between individual radar outputs are not uniform, and radar transmit and receive operations are not ordered.

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Fig. 2: Architecture of the proposed neural network for simultaneous static-moving object segmentation and vehicle ego- motion estimation. The network takes multidimensional radar point clouds as input, performs automatic spatial-temporal feature extraction, predicts static labels and moving labels for each detection point, and implements the weighted least squares (w- LSQ) for ego-motion estimation. As an illustrative application, moving instances can be generated after applying a clustering algorithm to the grouped moving objects.

on knowing the vehicle’s ego-motion provided by external sensors to localize static objects; some use neural networks , ; and some assume a majority of static points and employ one additional processing step such as RANSAC

Or M-Estimator Sample Consensus (Msac) . However,

while these solutions can help localize static objects, they leave moving objects mixed with false positives.

C. Summary

In summary, it is essential to point out that in the current radar perception processing chain, there is a missing compo- nent that can not only explicitly but also simultaneously seg- ment static objects, moving objects, and false positives from the radar point cloud, which, according to the literature review, is considered crucial for various downstream applications.

Furthermore, as the first processing unit after CFAR detectors, this component should be able to work independently, extract important segmentation features automatically from sparse and noisy radar point clouds, and provide fast, accurate, and reliable predictions. The realization of this component summarizes the goals of this research, which will be further described in the next section.

Iii. Methodology

Figure 2 presents the architecture of the proposed method for simultaneous static-moving object segmentation and ve- hicle ego-motion estimation. The proposed method: takes unprocessed radar point clouds as input, which will be detailed in Section III-A; performs automatic spatial-temporal feature extraction, as explained in Section III-B; predicts static and moving objects and estimates ego-motion in Section III-C; and finally outputs detailed object type labels and moving object instances after several processing steps as detailed in Section III-D. Implementation details will be presented in Section

A. Network Input Analysis

The proposed method takes T, unprocessed and chrono- logically ordered, radar point clouds as input. Typically, the radar point cloud is generated after the application of CFAR algorithms. Each point cloud is assumed to have N radar detection points, and each detection point contains M object features. In this work, M is assumed to be greater than or equal to 3, thus containing at least the uncompensated radial velocity (vr), range (R), and angle of arrival (AoA) (α) information of the detected objects. The reason for including at least the three selected object features and having T consecutive radar clouds is that they contain the necessary spatial and temporal features for the network to distinguish between moving and static objects, which can also be visually seen in Figure 3.

In the Doppler profile, not only is there a clear spatial distinction between static and non-static objects, but there is also a strong temporal correlation between consecutive point clouds of the static detections. In this work, static objects refer to detection points whose measured radial velocity is solely determined by the measurement angle and ego-radar motion, thereby forming a characteristic sine-like pattern in the Doppler profile. In contrast, non-static objects are detec- tion points that deviate from this pattern due to additional velocity contributions, such as independent target motion or false positives. The temporal correlation of static detections is dominated by the continuous motion of the ego-vehicle; consequently, the sine-like pattern remains stable over time, enabling estimation of the radar/vehicle motion from the measured features of static objects, see e.g., .

In the polar profile, there are also spatial and temporal corre- lations between objects in consecutive point clouds. However, because the ego-vehicle is moving and there is no motion compensation, all objects appear to ‘move’ across frames.

Furthermore, due to the nature of radar data, the shape and density of detected objects may vary between frames, making reliable discrimination of static objects more challenging. In contrast, detection points from moving objects are usually more spatially concentrated in the polar profile than in the

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Doppler profile, especially when they are near the radar. This is because, in the Doppler profile, the measured radial velocity at different points on a moving object can vary greatly depending on the measurement angle. Thus, once static objects are first separated in the Doppler profile, the polar profile can help refine the identification of moving objects. In this study, moving objects are defined as detection points originating from targets physically in motion at the time of measurement, whereas non-moving objects comprise static detections, false positives, and inherently mobile targets that are currently stationary (e.g., parked or waiting vehicles).

In summary, unlike previous studies, the proposed method does not require point cloud aggregation, knowledge of the vehicle’s ego-motion, or compensation for radial velocity or ego-motion. In contrast, the authors believe that using T con- secutive raw radar point clouds is sufficient to simultaneously distinguish between static and moving objects and estimate the vehicle’s ego-motion. Regarding the latency issue, for real- time applications, the requirement of T radar frames can be formulated as a moving window so that the proposed method can provide instantaneous predictions. Lastly, the remaining issues are how to effectively extract relevant features for segmentation, which will be detailed in the next section.

B. Feature Extraction

As a result of clear spatial distinctions and strong temporal correlation in the input radar point clouds, the proposed method is able to perform effective feature extraction with simple neural network backbones. For spatial feature extrac- tion, this work employs the PointNet architecture , which consists of a shared multi-layer perceptron (MLP) followed by an average pooling. Specifically, the MLP is applied indepen- dently to each radar detection point in each input point cloud.

Afterwards, the pooling layer is used to aggregate a global feature vector for each input point cloud. Despite its simple architecture, the combination of MLP and average pooling has demonstrated effectiveness in extracting the sine-like spatial feature for static object segmentation and vehicle ego-motion estimation , . Furthermore, because the MLP is shared across input point clouds, the network complexity does not increase with the number of input point clouds. However, it must be acknowledged that this combination has limited ability to capture relationships between neighboring detection points and may therefore be insufficient for tasks requiring fine-grained spatial understanding. Nevertheless, given the sparse radar point clouds, it remains to be seen how much performance improvement more advanced feature extraction backbones (with local details) can bring, as a previous explo- ration has shown only modest gains .

For temporal feature extraction, the proposed method uses the gated recurrent unit (GRU). GRU is a type of recurrent neural network (RNN) that can extract long-term dependencies in sequential data. In this study, the global feature vectors generated by the previous pooling layer are first arranged in chronological order. The GRU then processes these feature vectors sequentially, capturing the hidden relationships within them and outputting a feature vector that contains both spatial and temporal information. It is important to mention that the temporal dependencies between radar point clouds are governed by the continuous motion of the ego-vehicle and moving objects. However, since the input data has no radial velocity compensation or motion compensation, the authors hypothesize that temporal feature extraction is more beneficial for the segmentation of moving objects, while static objects already provide strong differentiation in spatial features, and temporal features are only supplementary.

C. Prediction

The previous section extracts spatial features from the input radar point cloud and captures the temporal dependencies caused by the continuous object motion. This section explains how to make predictions for each radar detection point. Firstly, the generated spatial-temporal feature vector by the GRU is backpropagated to the original input point cloud and the outputs of different layers in the first shared-MLP through feature concatenation. The concatenation outputs a 2D matrix that still contains N points in one dimension, but in the other dimension contains more global and spatial details in addition to the original M input features. Then, another shared-MLP acts as a decoder, refining the fused features and producing a rich feature vector (per-point) that is based on both spatial- temporal context and local details. After that, the decoder output is sent to two prediction heads, one for static and non-static prediction (static head) and the other for moving and non-moving prediction (moving head). Each head consists of three 1D convolutional layers with the last layer having a sigmoid activation function. The static head outputs a N × 1 vector, where each element contains a value from 0 to 1, indicating the probability of being non-static (0) or static (1). The moving head functions similarly, with its elements representing the probability of a detection point being non- moving (0) or moving (1).

Until here, the output of the static head is sufficient for the task of ego-motion estimation. However, since one of the goals is to localize all static objects, the chosen feature extraction backbone has limited ability to capture local context, which is the price of a lightweight network. Consequently, some static objects may be misclassified as non-static and assigned lower weights in the static head, or misclassified as moving and assigned higher weights in the motion head. To address this issue, the proposed method employs two update heads: one for the static weight update and the other for the moving weight update. The initial prediction of the static weight is updated first, based on the fact that knowing the radar motion helps to localize all static objects. Therefore, in the static update head, initial static weights are used to first compute the radar motion via the weighted least squares (w-LSQ) method. Then the estimated radar motion is used to update the static weights

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Fig. 3: An illustration of how moving and static objects appear in radar point clouds across multiple consecutive frames. The first row shows the polar profile, which presents the radar point cloud in the Range-AoA domain. The moving objects, marked in red, exhibit clear spatial concentration and temporal correlation in the polar profile. The second row shows the Doppler profile, which presents the radar point cloud in the radial velocity-AoA domain. The static objects, marked in red, exhibit distinct sine-like spatial pattern with little temporal variation. In this example, the RadarScenes dataset is used.

R

.

Sin(Α1)

.

(4)

Where vr is the measured radial velocity, α is the AoA measurement, σ is the standard deviation of the assumed Gaussian error distribution in the radial velocity measurement,

W Ini

static is the diagonal matrix which contains the predicted

Static Is The Vector Of Updated Static

weights, and Vradar is the estimated radar velocity on its x- and y-axes. As for updating the moving weights, the method uses the assumption that a detection point cannot have high weights in both the static head and the moving head, which means that an object cannot be stationary and moving at the same time. Therefore, the updated static weights are used to refine the initial moving weights, as shown below:

(5)

Where cstatic is the empirical parameter of the threshold. Lastly, Figure 4 presents a visual illustration of the update process of the static weights and the moving weights.

Finally, it is important to clarify that although a single 3- class prediction head (moving–static–false positives) is possi- ble, the problem exhibits a hierarchical structure, as shown pre- viously. In this hierarchy, the initial static prediction provides the basis for estimating radar motion, which in turn updates the initial static prediction and cross-checks subsequent moving predictions. Using two prediction heads allows the architecture to explicitly encode this structure, enabling the network to solve simpler binary classification tasks rather than implicitly learning the full set of relationships. Moreover, the two-head approach avoids the need to directly model false positives, which is inherently ill-defined and highly variable, thereby improving robustness and overall classification accuracy.

D. Output Processing

For the current radar input point cloud, the proposed method can simultaneously estimate the vehicle’s ego-motion and provide labels for static and moving objects. Given the radar extrinsic parameters and the estimated radar motion, the

Is The Vehicle’S Translational Speed, Ω Is Its

rotation rate, and the vehicle is assumed to have no lateral

= 0. X, Y, And Θ Are The Mounting Position

and angle of the radar sensor with respect to the rear center of the vehicle. The labels for static and moving objects can be obtained directly by applying thresholds to the updated static and moving weights respectively. In this study, both thresholds are set empirically to 0.1. As shown in the rightmost sub-figure of Figure 2, the static and moving labels can be merged together to achieve a clear separation of false positives.

Furthermore, since moving objects are explicitly separated, clustering algorithms such as the DBSCAN can be applied to them to achieve moving instance segmentation. However, the instance segmentation is just one illustrative example, and as discussed in Section II, many radar perception tasks can be connected to the output of the proposed method.

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Fig. 4: An illustration of how the initial weights for static and moving objects are updated in the two weight update heads. The yellow blocks represent the static update head, and the cyan blocks represent the moving update head. In this example, the RadarScenes dataset is used, and the plots show the radar point cloud in the radial velocity-AoA domain.

E. Implementation Details

The proposed method is trained with one Nvidia A100 GPU provided by the Delft High Performance Computing Centre (DHPC) . The batch size is 64 and the maximum training epoch is 400, but training can be stopped when the training loss stops improving after more than 10 epochs. The Adam optimizer is used and the initial learning rate is 0.001. The learning rate is decreased by a factor of 0.5 when the training loss stops improving after more than 5 epochs. The tuning parameter σ is empirically set to 0.013. For the shared-MLP, it contains three 1D convolutional layers, each followed by a batch normalization layer and a ReLU layer for non-linearity.

In the second shared-MLP (the decoder), the second 1D convolutional layer is followed by an additional dropout layer with a dropout rate of 0.3, and the randomly generated dropout mask is identical for the feature vector of each detection point.

Finally, this study uses two cross-entropy losses to measure the difference between the predicted results and the true values of static labels and moving labels, respectively. Since the loss of ego-motion estimation is closely related to the loss of static prediction, errors in ego-motion are not backpropagated. To mitigate the influence of low-quality training examples, the final loss is the sum of the two cross-entropy losses multiplied by the sample weight (described in more details in ).

Iv. Results And Discussion

This section presents the evaluation results of the proposed method. Specifically, the used radar dataset and the generation of ground truth will be introduced first, followed by a compre- hensive performance study of the proposed method and related methods in the literature.

A. Radar Dataset

Following the practice in previous studies on ego-motion

Estimation , And Radar Segmentation , , This

study uses the RadarScenes dataset to evaluate the pro- posed method. RadarScenes is a challenging radar dataset collected from real-world traffic and driving. During data collection, four automotive radars were installed on the front of the vehicle, two of which faced forward (hereinafter referred to as ‘Radar 2’ and ‘Radar 3’), and the other two faced the side (hereinafter referred to as ‘Radar 1’ and ‘Radar 4’). After collection, the radar data is preprocessed to generate radar point clouds containing detection range, AoA, radial velocity, and radar cross section (RCS). In addition, moving objects are manually annotated by human experts and classified into 10 different object categories. The ego-motion information of the vehicle is recorded using the vehicle’s odometry sensors and a differential global positioning system (DGPS).

Although the RadarScenes dataset records accurate vehicle motion and provides manually labeled point clouds, due to the new task proposed in this study, four additional processing steps are required, in order to generate ground truth (GT) data for model training and evaluation. Firstly, radar detections of static objects and false positives are not individually labeled in the dataset. To distinguish them, the recorded vehicle motion is used to localize static detections from the radar point cloud. Specifically, similar to Eq. 2, the vehicle motion is first transformed to radar motion, and then the GT static labels can be calculated. For moving objects, the GT moving labels are generated based on the class labels provided by the dataset, where 0 represents non-moving (‘Class 11’) and 1 represents moving (‘Class 1 to 10’). If a detection is neither labeled as static nor moving, it is defined as one of the false positives.

Conversely, if a detection is labeled as both static and moving due to, for example, mislabeling in the GT, it is corrected to static but non-moving, as vehicle GT motion is more reliable and trustworthy than human annotations.

In the second processing step, the effect of vehicle ac- celeration on the measured radial velocity is resolved. As detailed in Section-IV-G (Fig. 9-(c)), due to vehicle non-

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zero acceleration, the Doppler frequency and the associated phase shift will vary with slow time and the estimated radial velocity will not match the vehicle velocity. Therefore, the GT static labels generated solely based on vehicle motion may be inaccurate. As shown in , DeepEgo+ can mitigate this effect by using a two-step signal processing with NNs. The first step locates the static detection points, and the second step compensates for the effect of non-zero acceleration and estimates the vehicle ego-motion. Therefore, in this study, if the DeepEgo+ ego-motion estimation error is below a preset threshold, its output is used to help better localize static objects; otherwise, the vehicle’s GT motion is used.

Thirdly, the RadarScenes dataset contains 158 2-minute- long individual sequences from each of the four radars. In almost half of the sequences, the ego-vehicle is (or almost is) stationary and monitors moving objects. This is well-suited for tasks such as object detection and motion segmentation.

However, for the dual task of ego-motion estimation and static-moving object segmentation, a dataset containing an ego-vehicle in constant motion is desired for both training and evaluation. Therefore, this work uses a minimum driving distance of 500 meters for sequence selection, resulting in 63 radar sequences captured in challenging scenarios such as highways and city traffic. Nevertheless, these 63 radar sequences still contributed more than 2 hours of recording time, which is equivalent to a driving distance of more than 70 km. It is worth mentioning that the reduction in the number of sequences necessarily increases the difficulty of the task, because not only is it more difficult and meaningful to distinguish between static and moving objects when the vehicle is in constant motion rather than stationary, but also training neural networks on smaller datasets can lead to some well-known challenges such as overfitting and generalization problems.

The last processing step is to deal with short-lived la- beled moving objects. As shown in Table I, due to different installation angles, the number of moving objects observed by the four radars varies greatly. Radar 1 faces the side of the street and picks up minimal objects, while Radar 2 and Radar 3 face forward, cover both lanes, and pick up the most objects. In addition, since Radar 1 and Radar 4 face sideways, moving objects often appear at close range and enter and leave the radar field of view quickly, resulting in a very short lifespan. Moving objects with short lifespans contain little temporal features and may confuse model training and increase false alarm rates. Therefore, moving objects with a lifespan shorter than 5 radar frames (around 0.3 s) are labeled as non-moving for the sake of training. Also, the data from Radar 1 is not used for performance evaluation because there are only about 10 moving objects per sequence on average.

Finally, unless otherwise specified, the following experiments are all conducted using Radar 3 data, and the ‘leave-one- out’4 training, validation, and testing strategy is adopted so 4The test radar sequences are taken out, one by one, from the selected 63 radar sequences, and the remaining sequences are used for model training and validation following the 80%-20% rule. After all 63 sequences have been used once as the test sequence, the final performance of the tested method is measured and averaged.

the performance on ‘unseen’ data can be measured.

B. Evaluation Metrics

Due to the dual task of the proposed method, this study proposes a series of evaluation metrics to measure its per- formance in ego-motion estimation and static-moving object segmentation. For moving object segmentation, inspired by one downstream application of radar-based object tracking , the moving objects predicted by the proposed method and identified by the GT labels are first clustered into moving instances, respectively. The density-based spatial clustering of applications with noise method (DBSCAN) is used for clustering. Then, the grouped moving objects are converted into point target lists by finding the average position of all points in the same cluster. Afterwards, the cost matrix is cal- culated based on the L2 distance between the point objects in the GT list and the prediction list. Next, the Jonker–Volgenant algorithm is implemented to solve the data association problem. Based on its output, three numbers can be determined for a given radar frame: the number of correctly detected moving objects (TP), the number of false detections (FP), and the number of missed detections (FN). Finally, the TP, FP, and FN of all radar frames are summed separately, and the

Following Evaluation Metrics Can Be Calculated:

1) False Discovery Rate (FDR) shows the proportion of false detections among all detected moving instances. In other words, it reflects the frequency of false detections.

(7)

2) Missed Detection Rate (MDR) measures how often true moving instances are misclassified as non-moving. It is

(8)

3) F1 Score (F1) is the harmonic mean of Precision and Recall. Therefore, the F1 Score will be high only when both Precision and Recall are high. This property makes it well-suited for summarizing detection performance, especially in the case of class imbalance. It is defined

(9)

4) Intersection over Union (IoU) is a commonly used evaluation metric for computer vision tasks such as detection and segmentation. Traditionally, it is com- puted geometrically based on the overlap between the predicted region (for example, the bounding box) and the actual region. However, due to the characteristics of radar sensors, the shape of detected objects changes with distance and angle, and they have fewer geometric features due to low azimuth resolution. In addition, the actual area may also be erroneous and incomplete due to errors in the GT label. Therefore, in order to adapt

Authors:

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

94143, Usa.

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

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

14Jlvmi Consulting Llc, Dousman, Wi, Usa

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

Abstract

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

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

Introduction

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

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

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

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

●

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

●

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

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

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

Hyperpolarized 13C-Pyruvate Preparation

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

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

General Considerations

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

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

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

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

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

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

Personnel

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

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

Equipment And Facility

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

Material Handling

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

Pharmacy Kit Filling And Assembling

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

Quality Control And Dose Release

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

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

The Final Dose Release And Injection

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

Some Key Challenges

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

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

Current Practices

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

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

In House

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

Summary

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

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

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

Mri System Setup And Calibrations

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

Imaging System

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

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

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

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

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

Rf Coils

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

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

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

Provide B1 Transmit Across The Fov (B1

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

B1

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

+ Profile But Has Been Used Because Of

relatively easy integration into the scanner bore. B1

+ Variation Results In Variations In The Flip

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

Homogeneous B1

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

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

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

(1)

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

Tx = Transmit

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

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

Phantoms

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

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

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

+) And Receive (B1

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

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

Prescan Calibration

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

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

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

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

+ Inhomogeneity As Well

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

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

Power [Kw]

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

8

13C-bicarbonate doped with dimethyl silicone, various

Maximum Values

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

Summary

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

+ Profiles. The

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

For Calibration Of B1

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

Acquisition And Reconstruction

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

+ Inhomogeneity,

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

Acquisition And Reconstruction Methods

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

Mrs/I Methods Specifically

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

Chemical Shift

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

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

Their Application To Different

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

The Majority Of

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

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

Prostate Studies

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

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

Heart Studies

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

Brain Studies

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

Abdomen And Breast Studies

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

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

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

1H Imaging

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

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

Reported Study Parameters

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

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

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

(B)

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

Summary

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

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

Data Analysis And Quantification

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

Metrics

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

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

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

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

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

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

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

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

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

Visualization

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

Metrics

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

Parameter Encoding

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

Anatomical Context

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

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