publications | Zexin(泽新) Liu(刘)

2024

BMMB
Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification

Caleb C. Berggren, David Jiang, Y. F. Jack Wang, and 6 more authors

Biomechanics and Modeling in Mechanobiology , 2024

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Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification–finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.
@article{Berggren2024, author = {Berggren, Caleb C. and Jiang, David and Jack Wang, Y. F. and Bergquist, Jake A. and Rupp, Lindsay C. and Liu, Zexin and MacLeod, Rob and Narayan, Akil and Timmins, Lucas H.}, title = {Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification}, journal = {Biomechanics and Modeling in Mechanobiology}, volume = {23}, number = {}, pages = {927-940}, year = {2024}, doi = {10.1007/s10237-023-01814-2}, url = {https://link.springer.com/article/10.1007/s10237-023-01814-2}, publisher = {Springer}, }

2023

CBM
UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering

Akil Narayan, Zexin Liu, Jake A. Bergquist, and 7 more authors

Computers in Biology and Medicine. More Information can be found here , 2023

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Background: 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. Methods: 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. Results: 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. Conclusion: 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.
@article{Narayan2023cbm, title = {UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering}, journal = {Computers in Biology and Medicine}, volume = {152}, pages = {106407}, year = {2023}, issn = {0010-4825}, doi = {10.1016/j.compbiomed.2022.106407}, url = {https://www.sciencedirect.com/science/article/pii/S0010482522011155}, author = {Narayan, Akil and Liu, Zexin and Bergquist, Jake A. and Charlebois, Chantel and Rampersad, Sumientra and Rupp, Lindsay and Brooks, Dana and White, Dan and Tate, Jess and MacLeod, Rob S.}, keywords = {Biomedical simulations, Uncertainty quantification, Open-source software}, publisher = {Elsevier}, }
JOSS
UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines

Jess Tate, Zexin Liu, Jake Bergquist, and 7 more authors

The Journal of Open Source Software. More Information can be found here , 2023

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We have developed UncertainSCI (UncertainSCI, 2020) as an open-source tool designed to make modern uncertainty quantification (UQ) techniques more accessible in biomedical simulation applications. UncertainSCI is implemented in Python with a noninvasive interface to meet our software design goals of 1) numerical accuracy, 2) simple application programming interface (API), 3) adaptability to many applications and methods, and 4) interfacing with diverse simulation software. Using a Python implementation in UncertainSCI allowed us to utilize the popularity and low barrier-to-entry of Python and its common packages and to leverage the built-in integration and support for Python in common simulation software packages and languages. Additionally, we used noninvasive UQ techniques and created a similarly noninvasive interface to external modeling software that can be called in diverse ways, depending on the complexity and level of Python integration in the external simulation pipeline. We have developed and included examples applying UncertainSCI to relatively simple 1D simulations implemented in Python, and to bioelectric field simulations implemented in external software packages, which demonstrate the use of UncertainSCI and the effectiveness of the architecture and implementation in achieving our design goals. UnceratainSCI differs from similar software, notably UQLab, Uncertainpy, and Simnibs, in that it can be efficiently and non-invasively used with external simulation software, specifically with high resolution 3D simulations often used in Bioelectric field simulations. Figure 1 illustrates the use of UncertainSCI in computing UQ with modeling pipelines for bioelectricity simulations.
@article{Tate2023joss, title = {{UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines}}, author = {Tate, Jess and Liu, Zexin and Bergquist, Jake and Sumientra, Rampersad and White, Dan and Charlebois, Chantel and Rupp, Lindsay and Brooks, Dana and MacLeod, Rob and Narayan, Akil}, journal = {The Journal of Open Source Software}, volume = {8}, number = {90}, issue = {}, pages = {}, numpages = {}, year = {2023}, publisher = {The Open Journal}, doi = {10.21105/joss.04249}, url = {https://joss.theoj.org/papers/10.21105/joss.04249}, }
SISC
A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials

Zexin Liu and Akil Narayan

SIAM Journal on Scientific Computing. More Information can be found here , 2023

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Abstract. Orthogonal polynomials of several variables have a vector-valued three-term recurrence relation, much like the corresponding one-dimensional relation. This relation requires only knowledge of certain recurrence matrices, and allows simple and stable evaluation of multivariate orthogonal polynomials. In the univariate case, various algorithms can stably and accurately evaluate the recurrence coefficients given the ability to compute polynomial moments, but it is difficult to identify analogous procedures in multiple dimensions. We present a new Multivariate Stieltjes (MS) algorithm that fills this gap in the multivariate case, allowing computation of recurrence matrices assuming moments are available. The algorithm is essentially explicit in two and three dimensions, but requires the numerical solution to a nonconvex problem in more than three dimensions. Compared to direct Gram–Schmidt-type orthogonalization, we demonstrate on several examples in up to three dimensions that the MS algorithm is far more stable, and allows accurate computation of orthogonal bases in the multivariate setting, in contrast to direct orthogonalization approaches.
@article{Liu2023sisc, author = {Liu, Zexin and Narayan, Akil}, title = {A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials}, journal = {SIAM Journal on Scientific Computing}, volume = {45}, number = {3}, pages = {A1125-A1147}, year = {2023}, doi = {10.1137/22M1477131}, url = {https://epubs.siam.org/doi/abs/10.1137/22M1477131}, publisher = {Society for Industrial & Applied Mathematics (SIAM)}, }

2021

JSC
On the Computation of Recurrence Coefficients for Univariate Orthogonal Polynomials

Zexin Liu and Akil Narayan

Journal of Scientific Computing. More Information can be found here , 2021

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Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure. These recurrence coefficients are frequently inputs to modern computational tools that facilitate evaluation and manipulation of polynomials with respect to the measure, and such tasks are foundational in numerical approximation and quadrature. Although the recurrence coefficients for classical measures are known explicitly, those for nonclassical measures must typically be numerically computed. We survey and review existing approaches for computing these recurrence coefficients for univariate orthogonal polynomial families and propose a novel “predictor–corrector” algorithm for a general class of continuous measures. We combine the predictor–corrector scheme with a stabilized Lanczos procedure for a new hybrid algorithm that computes recurrence coefficients for a fairly wide class of measures that can have both continuous and discrete parts. We evaluate the new algorithms against existing methods in terms of accuracy and efficiency.
@article{Liu2021ttr, title = {On the Computation of Recurrence Coefficients for Univariate Orthogonal Polynomials}, author = {Liu, Zexin and Narayan, Akil}, journal = {Journal of Scientific Computing}, volume = {88}, number = {53}, issue = {3}, pages = {}, numpages = {}, year = {2021}, publisher = {Springer US}, doi = {10.1007/s10915-021-01586-w}, url = {https://link.springer.com/article/10.1007/s10915-021-01586-w}, }
Brain Stimulation
Uncertainty Quantification in Brain Stimulation using UncertainSCI

Jess Tate, Rampersad Sumientra, Chantel Charlebois, and 7 more authors

Brain Stimulation: Basic, Translational, and Clinical Research in Neuromodulation. More Information can be found here , 2021

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Predicting the effects of brain stimulation with computer models presents many challenges, including estimating the possible error from the propagation of uncertain input parameters through the model. Quantification and control of these errors through uncertainty quantification (UQ) provide statistics on the likely impact of parameter variation on solution accuracy, including total variance and sensitivity associated to each parameter. While the need and importance of UQ in clinical modeling is generally accepted, tools for implementing UQ techniques remain limited or inaccessible for many researchers. We have developed UncertainSCI as an open-source, flexible, and easy-to-use tool to make modern UQ techniques more accessible in biomedical simulation applications. Our goals in developing UncertainSCI were to provide numerical accuracy, a simple application programming interface (API), adaptability to many applications and methods, and an interface with diverse simulation software. UncertainSCI implements polynomial chaos expansion (PCE) to estimate uncertainty of a model non-invasively, allowing UQ with a vast array of modeling applications, and uses Python to create a simple API that can interface with many simulation packages. To demonstrate the functionality and adaptability of UncertainSCI, we implemented UQ on three brain stimulation modeling pipelines: electrocorticography (ECoG) stimulation, transcranial current stimulation (tCS), and transcranial magnetic stimulation (TMS). We used UncertainSCI to predict the model uncertainty due to variations in tissue conductivities and electrode positions in simulations of ECoG, tCS, and TMS with realistic human head models solved in SCIRun. We compared the results between these modalities and with other UQ packages, which showed that UncertainSCI was equally accurate and more efficient. The UQ predicted by UncertainSCI allows researchers to gain insight into the behavior of these three pipelines as a result of parameter variability and where researchers may focus efforts to improve model accuracy.
@article{Tate2021brs, title = {Uncertainty Quantification in Brain Stimulation using UncertainSCI}, author = {Tate, Jess and Sumientra, Rampersad and Charlebois, Chantel and Liu, Zexin and Bergquist, Jake and White, Dan and Rupp, Lindsay and Brooks, Dana and Narayan, Akil and MacLeod, Rob}, journal = {Brain Stimulation: Basic, Translational, and Clinical Research in Neuromodulation}, volume = {14}, number = {}, issue = {6}, pages = {1659-1660}, numpages = {2}, year = {2021}, publisher = {Elsevier}, doi = {10.1016/j.brs.2021.10.226}, url = {https://www.brainstimjrnl.com/article/S1935-861X(21)00472-1/fulltext}, }

2020

CinC
Using UncertainSCI to Quantify Uncertainty in Cardiac Simulations

Lindsay C Rupp, Zexin Liu, Jake A Bergquist, and 6 more authors

In 2020 Computing in Cardiology, 2020

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Cardiac simulations have become increasingly accurate at representing physiological processes. However, simulations often fail to capture the impact of parameter uncertainty in predictions. Uncertainty quantification (UQ) is a set of techniques that captures variability in simulation output based on model assumptions. Although many UQ methods exist, practical implementation can be challenging. We created UncertainSCI, a UQ framework that uses polynomial chaos (PC) expansion to model the forward stochastic error in simulations parameterized with random variables. UncertainSCI uses non-intrusive methods that parsimoniously explores parameter space. The result is an efficient, stable, and accurate PC emulator that can be analyzed to compute output statistics. We created a Python API to run UncertainSCI, minimizing user inputs needed to guide the UQ process. We have implemented UncertainSCI to: (1) quantify the sensitivity of computed torso potentials using the boundary element method to uncertainty in the heart position, and (2) quantify the sensitivity of computed torso potentials using the finite element method to uncertainty in the conductivities of biological tissues. With UncertainSCI, it is possible to evaluate the robustness of simulations to parameter uncertainty and establish realistic expectations on the accuracy of the model results and the clinical guidance they can provide.
@inproceedings{9344443, author = {Rupp, Lindsay C and Liu, Zexin and Bergquist, Jake A and Rampersad, Sumientra and White, Dan and Tate, Jess D and Brooks, Dana H and Narayan, Akil and MacLeod, Rob S}, booktitle = {2020 Computing in Cardiology}, title = {Using UncertainSCI to Quantify Uncertainty in Cardiac Simulations}, year = {2020}, volume = {}, number = {}, pages = {1-4}, keywords = {Torso;Uncertain systems;Uncertainty;Sensitivity;Computational modeling;Biological system modeling;Stochastic processes}, publisher = {IEEE}, doi = {10.22489/CinC.2020.275}, url = {https://ieeexplore.ieee.org/abstract/document/9344443}, }