A Pilot Study on Patient-specific Computational Forecasting of Prostate Cancer Growth during Active Surveillance Using an Imaging-informed Biomechanistic Model.

Active surveillance (AS) is a suitable management option for newly diagnosed prostate cancer, which usually presents low to intermediate clinical risk. Patients enrolled in AS have their tumor monitored via longitudinal multiparametric MRI (mpMRI), PSA tests, and biopsies. Hence, treatment is prescribed when these tests identify progression to higher-risk prostate cancer. However, current AS protocols rely on detecting tumor progression through direct observation according to population-based monitoring strategies. This approach limits the design of patient-specific AS plans and may delay the detection of tumor progression. Here, we present a pilot study to address these issues by leveraging personalized computational predictions of prostate cancer growth. Our forecasts are obtained with a spatiotemporal biomechanistic model informed by patient-specific longitudinal mpMRI data (T2-weighted MRI and apparent diffusion coefficient maps from diffusion-weighted MRI). Our results show that our technology can represent and forecast the global tumor burden for individual patients, achieving concordance correlation coefficients from 0.93 to 0.99 across our cohort (n = 7). In addition, we identify a model-based biomarker of higher-risk prostate cancer: the mean proliferation activity of the tumor (P = 0.041). Using logistic regression, we construct a prostate cancer risk classifier based on this biomarker that achieves an area under the ROC curve of 0.83. We further show that coupling our tumor forecasts with this prostate cancer risk classifier enables the early identification of prostate cancer progression to higher-risk disease by more than 1 year. Thus, we posit that our predictive technology constitutes a promising clinical decision-making tool to design personalized AS plans for patients with prostate cancer. SIGNIFICANCE: Personalization of a biomechanistic model of prostate cancer with mpMRI data enables the prediction of tumor progression, thereby showing promise to guide clinical decision-making during AS for each individual patient.

SEM2: Introducing mechanics in cell and tissue modeling using coarse-grained homogeneous particle dynamics.

Modeling multiscale mechanics in shape-shifting engineered tissues, such as organoids and organs-on-chip, is both important and challenging. In fact, it is difficult to model relevant tissue-level large non-linear deformations mediated by discrete cell-level behaviors, such as migration and proliferation. One approach to solve this problem is subcellular element modeling (SEM), where ensembles of coarse-grained particles interacting via empirically defined potentials are used to model individual cells while preserving cell rheology. However, an explicit treatment of multiscale mechanics in SEM was missing. Here, we incorporated analyses and visualizations of particle level stress and strain in the open-source software SEM++ to create a new framework that we call subcellular element modeling and mechanics or SEM2. To demonstrate SEM2, we provide a detailed mechanics treatment of classical SEM simulations including single-cell creep, migration, and proliferation. We also introduce an additional force to control nuclear positioning during migration and proliferation. Finally, we show how SEM2 can be used to model proliferation in engineered cell culture platforms such as organoids and organs-on-chip. For every scenario, we present the analysis of cell emergent behaviors as offered by SEM++ and examples of stress or strain distributions that are possible with SEM2. Throughout the study, we only used first-principles literature values or parametric studies, so we left to the Discussion a qualitative comparison of our insights with recently published results. The code for SEM2 is available on GitHub at https://github.com/Synthetic-Physiology-Lab/sem2.

Current progress toward isogeometric modeling of the heart biophysics.

In this paper, we review a powerful methodology to solve complex numerical simulations, known as isogeometric analysis, with a focus on applications to the biophysical modeling of the heart. We focus on the hemodynamics, modeling of the valves, cardiac tissue mechanics, and on the simulation of medical devices and treatments. For every topic, we provide an overview of the methods employed to solve the specific numerical issue entailed by the simulation. We try to cover the complete process, starting from the creation of the geometrical model up to the analysis and post-processing, highlighting the advantages and disadvantages of the methodology.

Patient-specific forecasting of postradiotherapy prostate-specific antigen kinetics enables early prediction of biochemical relapse.

The detection of prostate cancer recurrence after external beam radiotherapy relies on the measurement of a sustained rise of serum prostate-specific antigen (PSA). However, this biochemical relapse may take years to occur, thereby delaying the delivery of a secondary treatment to patients with recurring tumors. To address this issue, we propose to use patient-specific forecasts of PSA dynamics to predict biochemical relapse earlier. Our forecasts are based on a mechanistic model of prostate cancer response to external beam radiotherapy, which is fit to patient-specific PSA data collected during standard posttreatment monitoring. Our results show a remarkable performance of our model in recapitulating the observed changes in PSA and yielding short-term predictions over approximately 1 year (cohort median root mean squared error of 0.10-0.47 ng/mL and 0.13 to 1.39 ng/mL, respectively). Additionally, we identify 3 model-based biomarkers that enable accurate identification of biochemical relapse (area under the receiver operating characteristic curve > 0.80) significantly earlier than standard practice (p < 0.01).

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network.

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

Phase-field approach to evolution and interaction of twins in single crystal magnesium.

Crack initiation and propagation as well as abrupt occurrence of twinning are challenging fracture problems where the transient phase-field approach is proven to be useful. Early-stage twinning growth and interactions are in focus herein for a magnesium single crystal at the nanometer length-scale. We demonstrate a basic methodology in order to determine the mobility parameter that steers the kinetics of phase-field propagation. The concept is to use already existing molecular dynamics simulations and analytical solutions in order to set the mobility parameter correctly. In this way, we exercise the model for gaining new insights into growth of twin morphologies, temporally-evolving spatial distribution of the shear stress field in the vicinity of the nanotwin, multi-twin, and twin-defect interactions. Overall, this research addresses gaps in our fundamental understanding of twin growth, while providing motivation for future discoveries in twin evolution and their effect on next-generation material performance and design.

Data-Driven Simulation of Fisher-Kolmogorov Tumor Growth Models Using Dynamic Mode Decomposition.

The computer simulation of organ-scale biomechanistic models of cancer personalized via routinely collected clinical and imaging data enables to obtain patient-specific predictions of tumor growth and treatment response over the anatomy of the patient's affected organ. These patient-specific computational forecasts have been regarded as a promising approach to personalize the clinical management of cancer and derive optimal treatment plans for individual patients, which constitute timely and critical needs in clinical oncology. However, the computer simulation of the underlying spatiotemporal models can entail a prohibitive computational cost, which constitutes a barrier to the successful development of clinically-actionable computational technologies for personalized tumor forecasting. To address this issue, here we propose to utilize dynamic-mode decomposition (DMD) to construct a low-dimensional representation of cancer models and accelerate their simulation. DMD is an unsupervised machine learning method based on the singular value decomposition that has proven useful in many applications as both a predictive and a diagnostic tool. We show that DMD may be applied to Fisher-Kolmogorov models, which constitute an established formulation to represent untreated solid tumor growth that can further accommodate other relevant cancer phenomena (e.g., therapeutic effects, mechanical deformation). Our results show that a DMD implementation of this model over a clinically relevant parameter space can yield promising predictions, with short to medium-term errors remaining under 1% and long-term errors remaining under 20%, despite very short training periods. In particular, we have found that, for moderate to high tumor cell diffusivity and low to moderate tumor cell proliferation rate, DMD reconstructions provide accurate, bounded-error reconstructions for all tested training periods. Additionally, we also show that the three-dimensional DMD reconstruction of the tumor field can be leveraged to accurately reconstruct the displacement fields of the tumor-induced deformation of the host tissue. Thus, we posit the proposed data-driven approach has the potential to greatly reduce the computational overhead of personalized simulations of cancer models, thereby facilitating tumor forecasting, parameter identification, uncertainty quantification, and treatment optimization.

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations.

Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion-reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD's ability to extrapolate in time (short-time future estimates).

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil.

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

Simulating the spread of COVID-19 via a spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion.

We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.

Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study.

The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

Mechanistic modelling of prostate-specific antigen dynamics shows potential for personalized prediction of radiation therapy outcome.

External beam radiation therapy is a widespread treatment for prostate cancer. The ensuing patient follow-up is based on the evolution of the prostate-specific antigen (PSA). Serum levels of PSA decay due to the radiation-induced death of tumour cells and cancer recurrence usually manifest as a rising PSA. The current definition of biochemical relapse requires that PSA reaches nadir and starts increasing, which delays the use of further treatments. Also, these methods do not account for the post-radiation tumour dynamics that may contain early information on cancer recurrence. Here, we develop three mechanistic models of post-radiation PSA evolution. Our models render superior fits of PSA data in a patient cohort and provide a biological justification for the most common empirical formulation of PSA dynamics. We also found three model-based prognostic variables: the proliferation rate of the survival fraction, the ratio of radiation-induced cell death rate to the survival proliferation rate, and the time to PSA nadir since treatment termination. We argue that these markers may enable the early identification of biochemical relapse, which would permit physicians to subsequently adapt patient monitoring to optimize the detection and treatment of cancer recurrence.

Computer simulations suggest that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth.

Prostate cancer and benign prostatic hyperplasia are common genitourinary diseases in aging men. Both pathologies may coexist and share numerous similarities, which have suggested several connections or some interplay between them. However, solid evidence confirming their existence is lacking. Recent studies on extensive series of prostatectomy specimens have shown that tumors originating in larger prostates present favorable pathological features. Hence, large prostates may exert a protective effect against prostate cancer. In this work, we propose a mechanical explanation for this phenomenon. The mechanical stress fields that originate as tumors enlarge have been shown to slow down their dynamics. Benign prostatic hyperplasia contributes to these mechanical stress fields, hence further restraining prostate cancer growth. We derived a tissue-scale, patient-specific mechanically coupled mathematical model to qualitatively investigate the mechanical interaction of prostate cancer and benign prostatic hyperplasia. This model was calibrated by studying the deformation caused by each disease independently. Our simulations show that a history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that impede prostatic tumor growth and limit its invasiveness. The technology presented herein may assist physicians in the clinical management of benign prostate hyperplasia and prostate cancer by predicting pathological outcomes on a tissue-scale, patient-specific basis.

A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis.

Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient-specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid-structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient-specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian-Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient-specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta.

An Integrated Design, Material, and Fabrication Platform for Engineering Biomechanically and Biologically Functional Soft Tissues.

We present a design rationale for stretchable soft network composites for engineering tissues that predominantly function under high tensile loads. The convergence of 3D-printed fibers selected from a design library and biodegradable interpenetrating polymer networks (IPNs) result in biomimetic tissue engineered constructs (bTECs) with fully tunable properties that can match specific tissue requirements. We present our technology platform using an exemplary soft network composite model that is characterized to be flexible, yet ∼125 times stronger (E = 3.19 MPa) and ∼100 times tougher (WExt = ∼2000 kJ m-3) than its hydrogel counterpart.

Dynamic and fluid-structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models.

This paper builds on a recently developed immersogeometric fluid-structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of automation, robustness and physical realism. In addition, the paper presents a comparison between FSI analysis and standalone structural dynamics simulation driven by prescribed transvalvular pressure, the latter being a more common modeling choice for this class of problems. The FSI computation achieved better physiological realism in predicting the valve leaflet deformation than its standalone structural dynamics counterpart.

An Efficient Finite Element Framework to Assess Flexibility Performances of SMA Self-Expandable Carotid Artery Stents.

Computer-based simulations are nowadays widely exploited for the prediction of the mechanical behavior of different biomedical devices. In this aspect, structural finite element analyses (FEA) are currently the preferred computational tool to evaluate the stent response under bending. This work aims at developing a computational framework based on linear and higher order FEA to evaluate the flexibility of self-expandable carotid artery stents. In particular, numerical simulations involving large deformations and inelastic shape memory alloy constitutive modeling are performed, and the results suggest that the employment of higher order FEA allows accurately representing the computational domain and getting a better approximation of the solution with a widely-reduced number of degrees of freedom with respect to linear FEA. Moreover, when buckling phenomena occur, higher order FEA presents a superior capability of reproducing the nonlinear local effects related to buckling phenomena.

Aortic hemodynamics after thoracic endovascular aortic repair, with particular attention to the bird-beak configuration.

PURPOSE: To quantitatively evaluate the impact of thoracic endovascular aortic repair (TEVAR) on aortic hemodynamics, focusing on the implications of a bird-beak configuration. METHODS: Pre- and postoperative CTA images from a patient treated with TEVAR for post-dissecting thoracic aortic aneurysm were used to evaluate the anatomical changes induced by the stent-graft and to generate the computational network essential for computational fluid dynamics (CFD) analysis. These analyses focused on the bird-beak configuration, flow distribution into the supra-aortic branches, and narrowing of the distal descending thoracic aorta. Three different CFD analyses (A: preoperative lumen, B: postoperative lumen, and C: postoperative lumen computed without stenosis) were compared at 3 time points during the cardiac cycle (maximum acceleration of blood flow, systolic peak, and maximum deceleration of blood flow). RESULTS: Postoperatively, disturbance of flow was reduced at the bird-beak location due to boundary conditions and change of geometry after TEVAR. Stent-graft protrusion with partial coverage of the origin of the left subclavian artery produced a disturbance of flow in this vessel. Strong velocity increase and flow disturbance were found at the aortic narrowing in the descending thoracic aorta when comparing B and C, while no effect was seen on aortic arch hemodynamics. CONCLUSION: CFD may help physicians to understand aortic hemodynamic changes after TEVAR, including the change in aortic arch geometry, the effects of a bird-beak configuration, the supra-aortic flow distribution, and the aortic true lumen dynamics. This study is the first step in establishing a computational framework that, when completed with patient-specific data, will allow us to study thoracic aortic pathologies and their endovascular management.