Designed especially for neurobiologists, FluoRender is an interactive tool for multi-channel fluorescence microscopy data visualization and analysis.
Deep brain stimulation
BrainStimulator is a set of networks that are used in SCIRun to perform simulations of brain stimulation such as transcranial direct current stimulation (tDCS) and magnetic transcranial stimulation (TMS).
Developing software tools for science has always been a central vision of the SCI Institute.

Biomedical Computing

Biomedical computing combines the diagnostic and investigative aspects of biology and medical science with the power and problem-solving capabilities of modern computing. Computers are used to accelerate research learning, simulate patient behavior and visualize complex biological models.


Chris Johnson

Inverse Problems
Computational Electrophysiology

Rob MacLeod

ECG Imaging
Cardiac Disease
Computational Electrophysiology

Jeff Weiss

Computational Biomechanics

Orly Alter

Computational Biology

Tamara Bidone

Computational Models
Simulations of Biological Systems
Multi-Physics Models of Cancer Cells


Amir Arzani

Cardiovascular biomechanics
Scientific machine learning

Centers and Labs:

Funded Research Projects:

Publications in Biomedical Computing:

Uncertainty quantification of the effect of cardiac position variability in the inverse problem of electrocardiographic imaging
J. A. Bergquist, B. Zenger, L. Rupp, A. Busatto, J. D. Tate, D. H. Brooks, A. Narayan, R. MacLeod. In Journal of Physiological Measurement, IOP Science, 2023.
DOI: 10.1088/1361-6579/acfc32

Electrocardiographic imaging (ECGI) is a functional imaging modality that consists of two related problems, the forward problem of reconstructing body surface electrical signals given cardiac bioelectric activity, and the inverse problem of reconstructing cardiac bioelectric activity given measured body surface signals. ECGI relies on a model for how the heart generates bioelectric signals which is subject to variability in inputs. The study of how uncertainty in model inputs affects the model output is known as uncertainty quantification (UQ). This study establishes develops, and characterizes the application of UQ to ECGI.

We establish two formulations for applying UQ to ECGI: a polynomial chaos expansion (PCE) based parametric UQ formulation (PCE-UQ formulation), and a novel UQ-aware inverse formulation which leverages our previously established ``joint-inverse" formulation (UQ joint-inverse formulation). We apply these to evaluate the effect of uncertainty in the heart position on the ECGI solutions across a range of ECGI datasets.

Main Results:
We demonstrated the ability of our UQ-ECGI formulations to characterize the effect of parameter uncertainty on the ECGI inverse problem. We found that while the PCE-UQ inverse solution provided more complex outputs such as sensitivities and standard deviation, the UQ joint-inverse solution provided a more interpretable output in the form of a single ECGI solution. We find that between these two methods we are able to assess a wide range of effects that heart position variability has on the ECGI solution.

This study, for the first time, characterizes in detail the application of UQ to the ECGI inverse problem. We demonstrated how UQ can provide insight into the behavior of ECGI using variability in cardiac position as a test case. This study lays the groundwork for future development of UQ-ECGI studies, as well as future development of ECGI formulations which are robust to input parameter variability.

Nascent adhesions shorten the period of lamellipodium protrusion through the Brownian ratchet mechanism
K.R. Carney, A.M. Khan, S. Stam, S.C. Samson, N. Mittal, S. Han, T.C. Bidone, M. Mendoza. In Mol Biol Cell, 2023.

Directional cell migration is driven by the conversion of oscillating edge motion into lasting periods of leading edge protrusion. Actin polymerization against the membrane and adhesions control edge motion, but the exact mechanisms that determine protrusion period remain elusive. We addressed this by developing a computational model in which polymerization of actin filaments against a deformable membrane and variable adhesion dynamics support edge motion. Consistent with previous reports, our model showed that actin polymerization and adhesion lifetime power protrusion velocity. However, increasing adhesion lifetime decreased the protrusion period. Measurements of adhesion lifetime and edge motion in migrating cells confirmed that adhesion lifetime is associated with and promotes protrusion velocity, but decreased duration. Our model showed that adhesions’ control of protrusion persistence originates from the Brownian ratchet mechanism for actin filament polymerization. With longer adhesion lifetime or increased adhesion density, the proportion of actin filaments tethered to the substrate increased, maintaining filaments against the cell membrane. The reduced filament-membrane distance generated pushing force for high edge velocity, but limited further polymerization needed for protrusion duration. We propose a mechanism for cell edge protrusion in which adhesion strength regulates actin filament polymerization to control the periods of leading edge protrusion.

Multi-Omic Integration of Blood-Based Tumor-Associated Genomic and Lipidomic Profiles Using Machine Learning Models in Metastatic Prostate Cancer
S. Fang, S. Zhe, H.M. Lin, A.A. Azad, H. Fettke, E.M. Kwan, L. Horvath, B. Mak, T. Zheng, P. Du, S. Jia, R.M. Kirby, M. Kohli. In Clinical Cancer Informatics, 2023.

To determine prognostic and predictive clinical outcomes in metastatic hormone-sensitive prostate cancer (mHSPC) and metastatic castrate-resistant prostate cancer (mCRPC) on the basis of a combination of plasma-derived genomic alterations and lipid features in a longitudinal cohort of patients with advanced prostate cancer.

A multifeature classifier was constructed to predict clinical outcomes using plasma-based genomic alterations detected in 120 genes and 772 lipidomic species as informative features in a cohort of 71 patients with mHSPC and 144 patients with mCRPC. Outcomes of interest were collected over 11 years of follow-up. These included in mHSPC state early failure of androgen-deprivation therapy (ADT) and exceptional responders to ADT; early death (poor prognosis) and long-term survivors in mCRPC state. The approach was to build binary classification models that identified discriminative candidates with optimal weights to predict outcomes. To achieve this, we built multi-omic feature-based classifiers using traditional machine learning (ML) methods, including logistic regression with sparse regularization, multi-kernel Gaussian process regression, and support vector machines.

The levels of specific ceramides (d18:1/14:0 and d18:1/17:0), and the presence of CHEK2 mutations, AR amplification, and RB1 deletion were identified as the most crucial factors associated with clinical outcomes. Using ML models, the optimal multi-omics feature combination determined resulted in AUC scores of 0.751 for predicting mHSPC survival and 0.638 for predicting ADT failure; and in mCRPC state, 0.687 for prognostication and 0.727 for exceptional survival. The models were observed to be superior than using a limited candidate number of features for developing multi-omic prognostic and predictive signatures.

Using a ML approach that incorporates multiple omic features improves the prediction accuracy for metastatic prostate cancer outcomes significantly. Validation of these models will be needed in independent data sets in future.

Computational model of integrin adhesion elongation under an actin fiber
S. Campbell, M. C. Mendoza, A. Rammohan, M. E. McKenzie, T. C. Bidone. In PLOS Computatonal Biology, Vol. 19, No. 7, Public Library of Science, pp. 1-19. 7, 2023.
DOI: 10.1371/journal.pcbi.1011237

Cells create physical connections with the extracellular environment through adhesions. Nascent adhesions form at the leading edge of migrating cells and either undergo cycles of disassembly and reassembly, or elongate and stabilize at the end of actin fibers. How adhesions assemble has been addressed in several studies, but the exact role of actin fibers in the elongation and stabilization of nascent adhesions remains largely elusive. To address this question, here we extended our computational model of adhesion assembly by incorporating an actin fiber that locally promotes integrin activation. The model revealed that an actin fiber promotes adhesion stabilization and elongation. Actomyosin contractility from the fiber also promotes adhesion stabilization and elongation, by strengthening integrin-ligand interactions, but only up to a force threshold. Above this force threshold, most integrin-ligand bonds fail, and the adhesion disassembles. In the absence of contraction, actin fibers still support adhesions stabilization. Collectively, our results provide a picture in which myosin activity is dispensable for adhesion stabilization and elongation under an actin fiber, offering a framework for interpreting several previous experimental observations.

Editorial: Image-based computational approaches for personalized cardiovascular medicine: improving clinical applicability and reliability through medical imaging and experimental data
S. Pirola, A. Arzani, C. Chiastra, F. Sturla. In Frontiers in Medical Technology, Vol. 5, 2023.
DOI: 10.3389/fmedt.2023.1222837

Halide Code Generation Framework in Phylanx,
R. Tohid, S. Shirzad, C. Taylor, S.A. Sakin, K.E. Isaacs, H. Kaiser. In Euro-Par 2022: Parallel Processing Workshops, Springer Nature Switzerland, pp. 32--45. 2023.
ISBN: 978-3-031-31209-0
DOI: 10.1007/978-3-031-31209-0_3

Separating algorithms from their computation schedule has become a de facto solution to tackle the challenges of developing high performance code on modern heterogeneous architectures. Common approaches include Domain-specific languages (DSLs) which provide familiar APIs to domain experts, code generation frameworks that automate the generation of fast and portable code, and runtime systems that manage threads for concurrency and parallelism. In this paper, we present the Halide code generation framework for Phylanx distributed array processing platform. This extension enables compile-time optimization of Phylanx primitives for target architectures. To accomplish this, (1) we implemented new Phylanx primitives using Halide, and (2) partially exported Halide's thread pool API to carry out parallelism on HPX (Phylanx's runtime) threads. (3) showcased HPX performance analysis tools made available to Halide applications. The evaluation of the work has been done in two steps. First, we compare the performance of Halide applications running on its native runtime with that of the new HPX backend to verify there is no cost associated with using HPX threads. Next, we compare performances of a number of original implementations of Phylanx primitives against the new ones in Halide to verify performance and portability benefits of Halide in the context of Phylanx.

Multiscale models of integrins and cellular adhesions
T.C. Bidone, D.J. Odde. In Current Opinion in Structural Biology, Vol. 80, Elsevier, 2023.

Computational models of integrin-based adhesion complexes have revealed important insights into the mechanisms by which cells establish connections with their external environment. However, how changes in conformation and function of individual adhesion proteins regulate the dynamics of whole adhesion complexes remains largely elusive. This is because of the large separation in time and length scales between the dynamics of individual adhesion proteins (nanoseconds and nanometers) and the emergent dynamics of the whole adhesion complex (seconds and micrometers), and the limitations of molecular simulation approaches in extracting accurate free energies, conformational transitions, reaction mechanisms, and kinetic rates, that can inform mechanisms at the larger scales. In this review, we discuss models of integrin-based adhesion complexes and highlight their main findings regarding: (i) the conformational transitions of integrins at the molecular and macromolecular scales and (ii) the molecular clutch mechanism at the mesoscale. Lastly, we present unanswered questions in the field of modeling adhesions and propose new ideas for future exciting modeling opportunities.

Protein-metabolite interactomics of carbohydrate metabolism reveal regulation of lactate dehydrogenase
K. G. Hicks, A. A. Cluntun, H. L. Schubert, S. R. Hackett, J. A. Berg, P. G. Leonard, M. A. Ajalla Aleixo, Y. Zhou, A. J. Bott, S. R. Salvatore, F. Chang, A. Blevins, P. Barta, S. Tilley, A. Leifer, A. Guzman, A. Arok, S. Fogarty, J. M. Winter, H. Ahn, K. N. Allen, S. Block, I. A. Cardoso, J. Ding, I. Dreveny, C. Gasper, Q. Ho, A. Matsuura, M. J. Palladino, S. Prajapati, P. Sun, K. Tittmann, D. R. Tolan, J. Unterlass, A. P. VanDemark, M. G. Vander Heiden, B. A. Webb, C. Yun, P. Zhap, B. Wang, F. J. Schopfer, C. P. Hill, M. C. Nonato, F. L. Muller, J. E. Cox, J. Rutter. In Science, Vol. 379, No. 6636, pp. 996-1003. 2023.
DOI: 10.1126/science.abm3452

Metabolic networks are interconnected and influence diverse cellular processes. The protein-metabolite interactions that mediate these networks are frequently low affinity and challenging to systematically discover. We developed mass spectrometry integrated with equilibrium dialysis for the discovery of allostery systematically (MIDAS) to identify such interactions. Analysis of 33 enzymes from human carbohydrate metabolism identified 830 protein-metabolite interactions, including known regulators, substrates, and products as well as previously unreported interactions. We functionally validated a subset of interactions, including the isoform-specific inhibition of lactate dehydrogenase by long-chain acyl–coenzyme A. Cell treatment with fatty acids caused a loss of pyruvate-lactate interconversion dependent on lactate dehydrogenase isoform expression. These protein-metabolite interactions may contribute to the dynamic, tissue-specific metabolic flexibility that enables growth and survival in an ever-changing nutrient environment. Understanding how metabolic state influences cellular processes requires systematic analysis of low-affinity interactions of metabolites with proteins. Hicks et al. describe a method called MIDAS (mass spectrometry integrated with equilibrium dialysis for the discovery of allostery systematically), which allowed them to probe such interactions for 33 enzymes of human carbohydrate metabolism and more than 400 metabolites. The authors detected many known and many new interactions, including regulation of lactate dehydrogenase by ATP and long-chain acyl coenzyme A, which may help to explain known physiological relations between fat and carbohydrate metabolism in different tissues. —LBR A mass spectrometry and dialysis method detects metabolite-protein interactions that help to control physiology.

Contribution of atrial myofiber architecture to atrial fibrillation
R. Kamali, E. Kwan, M. Regouski, T.J. Bunch, D.J. Dosdall, E. Hsu, R. S. Macleod, I. Polejaeva, R. Ranjan. In PLOS ONE, Vol. 18, No. 1, Public Library of Science, pp. 1--16. Jan, 2023.
DOI: 10.1371/journal.pone.0279974


The role of fiber orientation on a global chamber level in sustaining atrial fibrillation (AF) is unknown. The goal of this study was to correlate the fiber direction derived from Diffusion Tensor Imaging (DTI) with AF inducibility.


Transgenic goats with cardiac-specific overexpression of constitutively active TGF-β1 (n = 14) underwent AF inducibility testing by rapid pacing in the left atrium. We chose a minimum of 10 minutes of sustained AF as a cut-off for AF inducibility. Explanted hearts underwent DTI to determine the fiber direction. Using tractography data, we clustered, visualized, and quantified the fiber helix angles in 8 different regions of the left atrial wall using two reference vectors defined based on anatomical landmarks.

Sustained AF was induced in 7 out of 14 goats. The mean helix fiber angles in 7 out of 8 selected regions were statistically different (P-Value < 0.05) in the AF inducible group. The average fractional anisotropy (FA) and the mean diffusivity (MD) were similar in the two groups with FA of 0.32±0.08 and MD of 8.54±1.72 mm2/s in the non-inducible group and FA of 0.31±0.05 (P-value = 0.90) and MD of 8.68±1.60 mm2/s (P-value = 0.88) in the inducible group.

DTI based fiber direction shows significant variability across subjects with a significant difference between animals that are AF inducible versus animals that are not inducible. Fiber direction might be contributing to the initiation and sustaining of AF, and its role needs to be investigated further.

Heart Position Uncertainty Quantification in the Inverse Problem of ECGI
J.A. Bergquist, L.C. Rupp, A. Busatto, B. Orkild, B. Zenger, W. Good, J. Coll-Font, A. Narayan, J. Tate, D. Brooks, R.S. MacLeod. In Computing in Cardiology, Vol. 49, 2022.

Electrocardiographic imaging (ECGI) is a clinical and research tool for noninvasive diagnosis of cardiac electrical dysfunction. The position of the heart within the torso is both an input and common source of error in ECGI. Many studies have sought to improve cardiac localization accuracy, however, few have examined quantitatively the effects of uncertainty in the position of the heart within the torso. Recently developed uncertainty quantification (UQ) tools enable the robust application of UQ to ECGI reconstructions. In this study, we developed an ECGI formulation, which for the first time, directly incorporated uncertainty in the heart position. The result is an ECGI solution that is robust to variation in heart position. Using data from two Langendorff experimental preparations, each with 120 heartbeats distributed across three activation sequences, we found that as heart position uncertainty increased above ±10 mm, the solution quality of the ECGI degraded. However, even at large heart position uncertainty (±40 mm) our novel UQ-ECGI formulation produced reasonable solutions (root mean squared error < 1 mV, spatial correlation >0.6, temporal correlation >0.75).

Unipolar R:S Development in Chronic Atrial Fibrillation
E. Paccione, B. Hunt, E. Kwan, D. Dosdall, R. MacLeod, R. Ranjan. In Computing in Cardiology, Vol. 49, 2022.

Past studies have examined the differences between R and S waves of unipolar atrial signals in patients with atrial fibrillation (AF) and have shown a difference in the R to S ratio (R:S) in certain regions of the atria compared to a healthy population. This work indicates a potential use of R:S as a marker for AF. In this study, we further examine these claims and investigate temporal changes in R:S over AF development in animals.

Four canines underwent AF development protocols and endocardial sinus rhythm maps were recorded as AF progressed. Unipolar signals gathered from mapping were used to calculate R:S within the left atrium of each animal. Calculations were performed at time points: before AF initiation, 3-4 months of chronic AF, and 6 months of chronic AF. From our analysis, we observed an increase in R-dominant signals within the left atrium once AF is induced. Temporal results show that R dominance may be an indicator for chronic AF patients and may be associated with the presence of arrhythmogenic substrate. With the addition of regional information, this unipolar signal analysis could guide therapeutic strategies.

A Sliding Window Approach to Regularization in Electrocardiographic Imaging
B.A. Orkild, J.A. Bergquist, L.C. Rupp, A. Busatto, B. Zenger, W.W. Good, J. Coll-Font, R.S. MacLeod. In Computing in Cardiology, Vol. 49, 2022.

Introduction: The inverse problem of ECGI is ill-posed, so regularization must be applied to constrain the solution. Regularization is typically applied to each individual time point (instantaneous) or to the beat as a whole (global). These techniques often lead to over- or underregularization. We aimed to develop an inverse formulation that strikes a balance between these two approaches that would realize the benefits of both by implementing a sliding-window regularization. Methods: We formulated sliding-window regularization using the boundary element method with Tikhonov 0 and 2nd order regularization. We applied regularization to a varying time window of the body-surface potentials centered around each time sample. We compared reconstructed potentials from the sliding-window, instantaneous, and global regularization techniques to ground truth potentials for 10 heart beats paced from the ventricle in a large-animal model. Results: The sliding-window technique provided smoother transitions of regularization weights than instantaneous regularization while improving spatial correlation over global regularization. Discussion: Although the differences in regularization weights were nuanced, smoother transitions provided by the sliding-window regularization have the ability to eliminate discontinuities in potential seen with instantaneous regularization.

The Role of Beta-1 Receptors in the Response to Myocardial Ischemia
L.C. Rupp, B. Zenger, J.A. Bergquist, A. Busatto, R.S. MacLeod. In Computing in Cardiology, Vol. 49, 2022.

Acute myocardial ischemia is commonly diagnosed by ST-segment deviations. These deviations, however, can show a paradoxical recovery even in the face of ongoing ischemic stress. A possible mechanism for this response may be the cardio-protective effects of the autonomic nervous system (ANS) via beta-1 receptors. We assessed the role of norepinephrine (NE), a beta-1 agonist, and esmolol (ES), a beta-1 antagonist, in the recovery of ST-segment deviations during myocardial ischemia. We used an experimental model of controlled myocardial ischemia in which we simultaneously recorded electrograms intramurally and on the epicardial surface. We measured ischemia as deviations in the potentials measured at 40% of the ST-segment duration. During control intervention, 27% of epicardial electrodes showed no ischemic ST-segment deviations, whereas during the interventions with NE and ES, 100% of epicardial electrodes showed no ischemic ST-segment deviations. Intramural electrodes revealed a different behavior with 71% of electrodes showing no ischemic ST-segment deviations during control ischemia, increasing to 79% and 82% for NE infusion and ES infusion interventions, respectively. These preliminary results suggest that recovery of intramural regions of the heart is delayed by the presence of both beta-1 agonists and antagonists even as epicardial potentials show almost complete recovery.

Uncertainty Quantification of Cardiac Position on Deep Graph Network ECGI
X. Jiang, J. Tate, J. Bergquist, A. Narayan, R. MacLeod, L. Wang. In Computing in Cardiology, Vol. 49, 2022.

Subject-specific geometry such as cardiac position and torso size plays an important role in electrocardiographic imaging (ECGI). Previously, we introduced a graph-based neural network (GNN) that is dependent on patient-specific geometry to improve reconstruction accuracy. However, geometric uncertainty, including changes in cardiac position and torso size, has not been addressed in network-based methods. In this study, we estimate geometrical uncertainty on GNN by applying uncertainty quantification with polynomial chaos emulators (PCE). To estimate the effect of geometric variation from common motions, we evaluated the model on samples generated by different heart torso geometries. The experiments shows that the GNN is less sensitive to heart position and torso shape and helps us direct development of similar models to account of possible variability.

Unexpected Errors in the Electrocardiographic Forward Problem
A. Busatto, J.A. Bergquist, L.C. Rupp, B. Zenger, R.S. MacLeod. In Computing in Cardiology, Vol. 49, 2022.

Previous studies have compared recorded torso potentials with electrocardiographic forward solutions from a pericardial cage. In this study, we introduce new comparisons of the forward solutions from the sock and cage with each other and with respect to the measured potentials on the torso. The forward problem of electrocardiographic imaging is expected to achieve high levels of accuracy since it is mathematically well posed. However, unexpectedly high residual errors remain between the computed and measured torso signals in experiments. A possible source of these errors is the limited spatial coverage of the cardiac sources in most experiments; most capture potentials only from the ventricles. To resolve the relationship between spatial coverage and the accuracy of the forward simulations, we combined two methods of capturing cardiac potentials using a 240-electrode sock and a 256-electrode cage, both surrounding a heart suspended in a 192-electrode torso tank. We analyzed beats from three pacing sites and calculated the RMSE, spatial correlation, and temporal correlation. We found that the forward solutions using the sock as the cardiac source were poorer compared to those obtained from the cage. In this study, we explore the differences in forward solution accuracy using the sock and the cage and suggest some possible explanations for these differences.

αIIbβ3 integrin intermediates: from molecular dynamics to adhesion assembly
D. Tong, N. Soley, R. Kolasangiani, M.A. Schwartz, T.C. Bidone. In Biophysical Journal, 2022.

The platelet integrin αIIbβ3 undergoes long range conformational transitions associated with its functional conversion from inactive (low affinity) to active (high affinity) states during hemostasis. Although new conformations intermediate between the well-characterized bent and extended states have been identified, their molecular dynamic properties and functions in the assembly of adhesions remain largely unexplored. In this study, we evaluated the properties of intermediate conformations of integrin αIIbβ3 and characterized their effects on the assembly of adhesions by combining all-atom simulations, principal component analysis, and mesoscale modeling. Our results show that in the low affinity, bent conformation, the integrin ectodomain tends to pivot around the legs; in intermediate conformations the upper headpiece becomes partially extended, away from the lower legs. In the fully open, active state, αIIbβ3 is flexible and the motions between upper headpiece and lower legs are accompanied by fluctuations of the transmembrane helices. At the mesoscale, bent integrins form only unstable adhesions, but intermediate or open conformations stabilize the adhesions. These studies reveal a mechanism by which small variations in ligand binding affinity and enhancement of the ligand-bound lifetime in the presence of actin retrograde flow stabilize αIIbβ3 integrin adhesions.

UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering
A. Narayan, Z. Liu, J. A. Bergquist, C. Charlebois, S. Rampersad, L. Rupp, D. Brooks, D. White, J. Tate, R. S. MacLeod. In Computers in Biology and Medicine, 2022.


Computational biomedical simulations frequently contain parameters that model physical features, material coefficients, and physiological effects, whose values are typically assumed known a priori. Understanding the effect of variability in those assumed values is currently a topic of great interest. A general-purpose software tool that quantifies how variation in these parameters affects model outputs is not broadly available in biomedicine. For this reason, we developed the ‘UncertainSCI’ uncertainty quantification software suite to facilitate analysis of uncertainty due to parametric variability.


We developed and distributed a new open-source Python-based software tool, UncertainSCI, which employs advanced parameter sampling techniques to build polynomial chaos (PC) emulators that can be used to predict model outputs for general parameter values. Uncertainty of model outputs is studied by modeling parameters as random variables, and model output statistics and sensitivities are then easily computed from the emulator. Our approaches utilize modern, near-optimal techniques for sampling and PC construction based on weighted Fekete points constructed by subsampling from a suitably randomized candidate set.

Concentrating on two test cases—modeling bioelectric potentials in the heart and electric stimulation in the brain—we illustrate the use of UncertainSCI to estimate variability, statistics, and sensitivities associated with multiple parameters in these models.

UncertainSCI is a powerful yet lightweight tool enabling sophisticated probing of parametric variability and uncertainty in biomedical simulations. Its non-intrusive pipeline allows users to leverage existing software libraries and suites to accurately ascertain parametric uncertainty in a variety of applications.

Comparing different nonlinear dimensionality reduction techniques for data-driven unsteady fluid flow modeling
H. Csala, S.T.M. Dawson, A. Arzani. In Physics of Fluids, AIP Publishing, 2022.

Computational fluid dynamics (CFD) is known for producing high-dimensional spatiotemporal data. Recent advances in machine learning (ML) have introduced a myriad of techniques for extracting physical information from CFD. Identifying an optimal set of coordinates for representing the data in a low-dimensional embedding is a crucial first step toward data-driven reduced-order modeling and other ML tasks. This is usually done via principal component analysis (PCA), which gives an optimal linear approximation. However, fluid flows are often complex and have nonlinear structures, which cannot be discovered or efficiently represented by PCA. Several unsupervised ML algorithms have been developed in other branches of science for nonlinear dimensionality reduction (NDR), but have not been extensively used for fluid flows. Here, four manifold learning and two deep learning (autoencoder)-based NDR methods are investigated and compared to PCA. These are tested on two canonical fluid flow problems (laminar and turbulent) and two biomedical flows in brain aneurysms. The data reconstruction capabilities of these methods are compared, and the challenges are discussed. The temporal vs spatial arrangement of data and its influence on NDR mode extraction is investigated. Finally, the modes are qualitatively compared. The results suggest that using NDR methods would be beneficial for building more efficient reduced-order models of fluid flows. All NDR techniques resulted in smaller reconstruction errors for spatial reduction. Temporal reduction was a harder task; nevertheless, it resulted in physically interpretable modes. Our work is one of the first comprehensive comparisons of various NDR methods in unsteady flows.

Improving Generalization by Learning Geometry-Dependent and Physics-Based Reconstruction of Image Sequences
X. Jiang, M. Toloubidokhti, J. Bergquist, B. Zenger, w. Good, R.S. MacLeod, L. Wang. In IEEE Transactions on Medical Imaging, 2022.
DOI: 10.1109/TMI.2022.3218170

Deep neural networks have shown promise in image reconstruction tasks, although often on the premise of large amounts of training data. In this paper, we present a new approach to exploit the geometry and physics underlying electrocardiographic imaging (ECGI) to learn efficiently with a relatively small dataset. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then explicitly model the geometry-dependent physics in between the two domains via a bipartite graph over their graphical embeddings. We applied the resulting network to reconstruct electrical activity on the heart surface from body-surface potentials. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the network to generalize across geometrical changes underlying the data using less than 10% of training data and fewer variations of training geometry in comparison to its Euclidean alternatives. In both simulation and real-data experiments, we further demonstrated its ability to be quickly fine-tuned to new geometry using a modest amount of data.

Interpretable Modeling and Reduction of Unknown Errors in Mechanistic Operators,
M. Toloubidokhti, N. Kumar, Z. Li, P. K. Gyawali, B. Zenger, W. W. Good, R. S. MacLeod, L. Wang . In Medical Image Computing and Computer Assisted Intervention -- MICCAI 2022, Springer Nature Switzerland, pp. 459--468. 2022.
ISBN: 978-3-031-16452-1
DOI: 10.1007/978-3-031-16452-1_44

Prior knowledge about the imaging physics provides a mechanistic forward operator that plays an important role in image reconstruction, although myriad sources of possible errors in the operator could negatively impact the reconstruction solutions. In this work, we propose to embed the traditional mechanistic forward operator inside a neural function, and focus on modeling and correcting its unknown errors in an interpretable manner. This is achieved by a conditional generative model that transforms a given mechanistic operator with unknown errors, arising from a latent space of self-organizing clusters of potential sources of error generation. Once learned, the generative model can be used in place of a fixed forward operator in any traditional optimization-based reconstruction process where, together with the inverse solution, the error in prior mechanistic forward operator can be minimized and the potential source of error uncovered. We apply the presented method to the reconstruction of heart electrical potential from body surface potential. In controlled simulation experiments and in-vivo real data experiments, we demonstrate that the presented method allowed reduction of errors in the physics-based forward operator and thereby delivered inverse reconstruction of heart-surface potential with increased accuracy.