Thinner biological tissues induce leaflet flutter in aortic heart valve replacements.

Valvular heart disease has recently become an increasing public health concern due to the high prevalence of valve degeneration in aging populations. For patients with severely impacted aortic valves that require replacement, catheter-based bioprosthetic valve deployment offers a minimally invasive treatment option that eliminates many of the risks associated with surgical valve replacement. Although recent percutaneous device advancements have incorporated thinner, more flexible biological tissues to streamline safer deployment through catheters, the impact of such tissues in the complex, mechanically demanding, and highly dynamic valvular system remains poorly understood. The present work utilized a validated computational fluid-structure interaction approach to isolate the behavior of thinner, more compliant aortic valve tissues in a physiologically realistic system. This computational study identified and quantified significant leaflet flutter induced by the use of thinner tissues that initiated blood flow disturbances and oscillatory leaflet strains. The aortic flow and valvular dynamics associated with these thinner valvular tissues have not been previously identified and provide essential information that can significantly advance fundamental knowledge about the cardiac system and support future medical device innovation. Considering the risks associated with such observed flutter phenomena, including blood damage and accelerated leaflet deterioration, this study demonstrates the potentially serious impact of introducing thinner, more flexible tissues into the cardiac system.

Image-guided subject-specific modeling of glymphatic transport and amyloid deposition.

The glymphatic system is a brain-wide system of perivascular networks that facilitate exchange of cerebrospinal fluid (CSF) and interstitial fluid (ISF) to remove waste products from the brain. A greater understanding of the mechanisms for glymphatic transport may provide insight into how amyloid beta (Aß) and tau agglomerates, key biomarkers for Alzheimer's disease and other neurodegenerative diseases, accumulate and drive disease progression. In this study, we develop an image-guided computational model to describe glymphatic transport and Aß deposition throughout the brain. Aß transport and deposition are modeled using an advection-diffusion equation coupled with an irreversible amyloid accumulation (damage) model. We use immersed isogeometric analysis, stabilized using the streamline upwind Petrov-Galerkin (SUPG) method, where the transport model is constructed using parameters inferred from brain imaging data resulting in a subject-specific model that accounts for anatomical geometry and heterogeneous material properties. Both short-term (30-min) and long-term (12-month) 3D simulations of soluble amyloid transport within a mouse brain model were constructed from diffusion weighted magnetic resonance imaging (DW-MRI) data. In addition to matching short-term patterns of tracer deposition, we found that transport parameters such as CSF flow velocity play a large role in amyloid plaque deposition. The computational tools developed in this work will facilitate investigation of various hypotheses related to glymphatic transport and fundamentally advance our understanding of its role in neurodegeneration, which is crucial for the development of preventive and therapeutic interventions.

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.

Computational medicine, present and the future: obstetrics and gynecology perspective.

Medicine is, in its essence, decision making under uncertainty; the decisions are made about tests to be performed and treatments to be administered. Traditionally, the uncertainty in decision making was handled using expertise collected by individual providers and, more recently, systematic appraisal of research in the form of evidence-based medicine. The traditional approach has been used successfully in medicine for a very long time. However, it has substantial limitations because of the complexity of the system of the human body and healthcare. The complex systems are a network of highly coupled components intensely interacting with each other. These interactions give those systems redundancy and thus robustness to failure and, at the same time, equifinality, that is, many different causative pathways leading to the same outcome. The equifinality of the complex systems of the human body and healthcare system demand the individualization of medical care, medicine, and medical decision making. Computational models excel in modeling complex systems and, consequently, enabling individualization of medical decision making and medicine. Computational models are theory- or knowledge-based models, data-driven models, or models that combine both approaches. Data are essential, although to a different degree, for computational models to successfully represent complex systems. The individualized decision making, made possible by the computational modeling of complex systems, has the potential to revolutionize the entire spectrum of medicine from individual patient care to policymaking. This approach allows applying tests and treatments to individuals who receive a net benefit from them, for whom benefits outweigh the risk, rather than treating all individuals in a population because, on average, the population benefits. Thus, the computational modeling-enabled individualization of medical decision making has the potential to both improve health outcomes and decrease the costs of healthcare.

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.

Tissue-scale, personalized modeling and simulation of prostate cancer growth.

Recently, mathematical modeling and simulation of diseases and their treatments have enabled the prediction of clinical outcomes and the design of optimal therapies on a personalized (i.e., patient-specific) basis. This new trend in medical research has been termed "predictive medicine." Prostate cancer (PCa) is a major health problem and an ideal candidate to explore tissue-scale, personalized modeling of cancer growth for two main reasons: First, it is a small organ, and, second, tumor growth can be estimated by measuring serum prostate-specific antigen (PSA, a PCa biomarker in blood), which may enable in vivo validation. In this paper, we present a simple continuous model that reproduces the growth patterns of PCa. We use the phase-field method to account for the transformation of healthy cells to cancer cells and use diffusion-reaction equations to compute nutrient consumption and PSA production. To accurately and efficiently compute tumor growth, our simulations leverage isogeometric analysis (IGA). Our model is shown to reproduce a known shape instability from a spheroidal pattern to fingered growth. Results of our computations indicate that such shift is a tumor response to escape starvation, hypoxia, and, eventually, necrosis. Thus, branching enables the tumor to minimize the distance from inner cells to external nutrients, contributing to cancer survival and further development. We have also used our model to perform tissue-scale, personalized simulation of a PCa patient, based on prostatic anatomy extracted from computed tomography images. This simulation shows tumor progression similar to that seen in clinical practice.

Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines.

This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid-structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem. We focus, in particular, on the immersogeometric method developed in our earlier work, analyze its convergence for linear model problems, then apply it to FSI analysis of heart valves, using divergence-conforming B-splines to discretize the fluid subproblem. Poor mass conservation can manifest as effective leakage of fluid through thin solid barriers. This leakage disrupts the qualitative behavior of FSI systems such as heart valves, which exist specifically to block flow. Divergence-conforming discretizations can enforce mass conservation exactly, avoiding this problem. To demonstrate the practical utility of immersogeometric FSI analysis with divergence-conforming B-splines, we use the methods described in this paper to construct and evaluate a computational model of an in vitro experiment that pumps water through an artificial valve.

An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves.

In this paper, we develop a geometrically flexible technique for computational fluid-structure interaction (FSI). The motivating application is the simulation of tri-leaflet bioprosthetic heart valve function over the complete cardiac cycle. Due to the complex motion of the heart valve leaflets, the fluid domain undergoes large deformations, including changes of topology. The proposed method directly analyzes a spline-based surface representation of the structure by immersing it into a non-boundary-fitted discretization of the surrounding fluid domain. This places our method within an emerging class of computational techniques that aim to capture geometry on non-boundary-fitted analysis meshes. We introduce the term "immersogeometric analysis" to identify this paradigm. The framework starts with an augmented Lagrangian formulation for FSI that enforces kinematic constraints with a combination of Lagrange multipliers and penalty forces. For immersed volumetric objects, we formally eliminate the multiplier field by substituting a fluid-structure interface traction, arriving at Nitsche's method for enforcing Dirichlet boundary conditions on object surfaces. For immersed thin shell structures modeled geometrically as surfaces, the tractions from opposite sides cancel due to the continuity of the background fluid solution space, leaving a penalty method. Application to a bioprosthetic heart valve, where there is a large pressure jump across the leaflets, reveals shortcomings of the penalty approach. To counteract steep pressure gradients through the structure without the conditioning problems that accompany strong penalty forces, we resurrect the Lagrange multiplier field. Further, since the fluid discretization is not tailored to the structure geometry, there is a significant error in the approximation of pressure discontinuities across the shell. This error becomes especially troublesome in residual-based stabilized methods for incompressible flow, leading to problematic compressibility at practical levels of refinement. We modify existing stabilized methods to improve performance. To evaluate the accuracy of the proposed methods, we test them on benchmark problems and compare the results with those of established boundary-fitted techniques. Finally, we simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions, demonstrating the effectiveness of the proposed techniques in practical computations.

A parametric study of the effect of 3D plaque shape on local hemodynamics and implications for plaque instability.

The vast majority of heart attacks occur when vulnerable plaques rupture, releasing their lipid content into the blood stream leading to thrombus formation and blockage of a coronary artery. Detection of these unstable plaques before they rupture remains a challenge. Hemodynamic features including wall shear stress (WSS) and wall shear stress gradient (WSSG) near the vulnerable plaque and local inflammation are known to affect plaque instability. In this work, a computational workflow has been developed to enable a comprehensive parametric study detailing the effects of 3D plaque shape on local hemodynamics and their implications for plaque instability. Parameterized geometric 3D plaque models are created within a patient-specific coronary artery tree using a NURBS (non-uniform rational B-splines)-based vascular modeling pipeline. Realistic blood flow features are simulated by using a Navier-Stokes solver within an isogeometric finite-element analysis framework. Near wall hemodynamic quantities such as WSS and WSSG are quantified, and vascular distribution of an inflammatory marker (VCAM-1) is estimated. Results show that proximally skewed eccentric plaques have the most vulnerable combination of high WSS and high positive spatial WSSG, and the presence of multiple lesions increases risk of rupture. The computational tool developed in this work, in conjunction with clinical data, -could help identify surrogate markers of plaque instability, potentially leading to a noninvasive clinical procedure for the detection of vulnerable plaques before rupture.

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.

Patient specific, imaging-informed modeling of rhenium-186 nanoliposome delivery via convection-enhanced delivery in glioblastoma multiforme.

Convection-enhanced delivery of rhenium-186 (186Re)-nanoliposomes is a promising approach to provide precise delivery of large localized doses of radiation for patients with recurrent glioblastoma multiforme. Current approaches for treatment planning utilizing convection-enhanced delivery are designed for small molecule drugs and not for larger particles such as186Re-nanoliposomes. To enable the treatment planning for186Re-nanoliposomes delivery, we have developed a computational fluid dynamics approach to predict the distribution of nanoliposomes for individual patients. In this work, we construct, calibrate, and validate a family of computational fluid dynamics models to predict the spatio-temporal distribution of186Re-nanoliposomes within the brain, utilizing patient-specific pre-operative magnetic resonance imaging (MRI) to assign material properties for an advection-diffusion transport model. The model family is calibrated to single photon emission computed tomography (SPECT) images acquired during and after the infusion of186Re-nanoliposomes for five patients enrolled in a Phase I/II trial (NCT Number NCT01906385), and is validated using a leave-one-out bootstrapping methodology for predicting the final distribution of the particles. After calibration, our models are capable of predicting the mid-delivery and final spatial distribution of186Re-nanoliposomes with a Dice value of 0.69 ± 0.18 and a concordance correlation coefficient of 0.88 ± 0.12 (mean ± 95% confidence interval), using only the patient-specific, pre-operative MRI data, and calibrated model parameters from prior patients. These results demonstrate a proof-of-concept for a patient-specific modeling framework, which predicts the spatial distribution of nanoparticles. Further development of this approach could enable optimizing catheter placement for future studies employing convection-enhanced delivery.

An Automatic 3D Mesh Generation Method for Domains with Multiple Materials.

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.

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.

A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects.

We review the treatment of trimmed geometries in the context of design, data exchange, and computational simulation. Such models are omnipresent in current engineering modeling and play a key role for the integration of design and analysis. The problems induced by trimming are often underestimated due to the conceptional simplicity of the procedure. In this work, several challenges and pitfalls are described.

Erratum to: A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects.

[This corrects the article DOI: 10.1007/s11831-017-9220-9.].

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.

Patient-Specific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow.

We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, lumenal surfaces are extracted by isocontouring the preprocessed data, followed by the extraction of vascular skeleton via Voronoi and Delaunay diagrams. Next, the skeleton-based sweeping method is used to construct hexahedral control meshes. Templates are designed for various branching configurations to decompose the geometry into mapped meshable patches. Each patch is then meshed using one-to-one sweeping techniques, and boundary vertices are projected to the lumenal surface. Finally, hexahedral solid NURBS are constructed and used in isogeometric analysis of blood flow. Piecewise linear hexahedral meshes can also be obtained using this approach. Examples of patient-specific arterial models are presented.

Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease.

Peripheral arterial disease (PAD) is generally attributed to the progressive vascular accumulation of lipoproteins and circulating monocytes in the vessel walls leading to the formation of atherosclerotic plaques. This is known to be regulated by the local vascular geometry, haemodynamics and biophysical conditions. Here, an isogeometric analysis framework is proposed to analyse the blood flow and vascular deposition of circulating nanoparticles (NPs) into the superficial femoral artery (SFA) of a PAD patient. The local geometry of the blood vessel and the haemodynamic conditions are derived from magnetic resonance imaging (MRI), performed at baseline and at 24 months post intervention. A dramatic improvement in blood flow dynamics is observed post intervention. A 500% increase in peak flow rate is measured in vivo as a consequence of luminal enlargement. Furthermore, blood flow simulations reveal a 32% drop in the mean oscillatory shear index, indicating reduced disturbed flow post intervention. The same patient information (vascular geometry and blood flow) is used to predict in silico in a simulation of the vascular deposition of systemically injected nanomedicines. NPs, targeted to inflammatory vascular molecules including VCAM-1, E-selectin and ICAM-1, are predicted to preferentially accumulate near the stenosis in the baseline configuration, with VCAM-1 providing the highest accumulation (approx. 1.33 and 1.50 times higher concentration than that of ICAM-1 and E-selectin, respectively). Such selective deposition of NPs within the stenosis could be effectively used for the detection and treatment of plaques forming in the SFA. The presented MRI-based computational protocol can be used to analyse data from clinical trials to explore possible correlations between haemodynamics and disease progression in PAD patients, and potentially predict disease occurrence as well as the outcome of an intervention.

In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts.

Current practice in vascular surgery utilizes only diagnostic and empirical data to plan treatments and does not enable quantitative a priori prediction of the outcomes of interventions. We have previously described a new approach to vascular surgery planning based on solving the governing equations of blood flow in patient-specific models. A one-dimensional finite-element method was used to simulate blood flow in eight porcine thoraco-thoraco aortic bypass models. The predicted flow rate was compared to in vivo data obtained using cine phase-contrast magnet resonance imaging. The mean absolute difference between computed and measured flow distribution in the stenosed aorta was found to be 4.2% with the maximum difference of 10.6% anda minimum difference of 0.4%. Furthermore, the sensitivity of the flow rate and distribution with respect to stenosis and branch losses were quantified.

A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease.

We have previously described a new approach to planning treatments for cardiovascular disease, Simulation-Based Medical Planning, whereby a physician utilizes computational tools to construct and evaluate a combined anatomic/physiologic model to predict the outcome of alternative treatment plans for an individual patient. Current systems for Simulation-Based Medical Planning utilize finite element methods to solve the time-dependent, three-dimensional equations governing blood flow and provide detailed data on blood flow distribution, pressure gradients and locations of flow recirculation, low wall shear stress and high particle residence. However, these methods are computationally expensive and often require hours of time on parallel computers. This level of computation is necessary for obtaining detailed information about blood flow, but likely is unnecessary for obtaining information about mean flow rates and pressure losses. We describe, herein, a space-time finite element method for solving the one-dimensional equations of blood flow. This method is applied to compute flow rate and pressure in a single segment model, a bifurcation, an idealized model of the abdominal aorta, in three alternate treatment plans for a case of aorto-iliac occlusive disease and in a vascular bypass graft. All of these solutions were obtained in less than 5 min of computation time on a personal computer.