An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling

Personalized evaluation of the passive myocardium in ischemic cardiomyopathy via computational modeling using Bayesian optimization

Biomechanics-based patient-specific modeling is a promising approach that has proved invaluable for its clinical potential to assess the adversities caused by ischemic heart disease (IHD). In the present study, we propose a framework to find the passive material properties of the myocardium and the unloaded shape of cardiac ventricles simultaneously in patients diagnosed with ischemic cardiomyopathy (ICM). This was achieved by minimizing the difference between the simulated and the target end-diastolic pressure-volume relationships (EDPVRs) using black-box Bayesian optimization, based on the finite element analysis (FEA). End-diastolic (ED) biventricular geometry and the location of the ischemia were determined from cardiac magnetic resonance (CMR) imaging. We employed our pipeline to model the cardiac ventricles of three patients aged between 57 and 66 years, with and without the inclusion of valves. An excellent agreement between the simulated and the target EDPVRs has been reached. Our results revealed that the incorporation of valvular springs typically leads to lower hyperelastic parameters for both healthy and ischemic myocardium, as well as a higher fiber Green strain in the viable regions compared to models without valvular stiffness. Furthermore, the addition of valve-related effects did not result in significant changes in myofiber stress after optimization. We concluded that more accurate results could be obtained when cardiac valves were considered in modeling ventricles. The present novel and practical methodology paves the way for developing digital twins of ischemic cardiac ventricles, providing a non-invasive assessment for designing optimal personalized therapies in precision medicine.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Implementing new computational methods for the study of JCT and SC inner wall basement membrane biomechanics and hydrodynamics

PURPOSE

The conventional aqueous outflow pathway, which includes the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and the inner wall endothelium of Schlemm's canal (SC), regulates intraocular pressure (IOP) by controlling the aqueous humor outflow resistance. Despite its importance, our understanding of the biomechanics and hydrodynamics within this region remains limited. Fluid-structure interaction (FSI) offers a way to estimate the biomechanical properties of the JCT and SC under various loading and boundary conditions, providing valuable insights that are beyond the reach of current imaging techniques.

METHODS

In this study, a normal human eye was fixed at a pressure of 7 mm Hg, and two radial wedges of the TM tissues, which included the SC inner wall basement membrane and JCT, were dissected, processed, and imaged using 3D serial block-face scanning electron microscopy (SBF-SEM). Four different sets of images were used to create 3D finite element (FE) models of the JCT and inner wall endothelial cells of SC with their basement membrane. The outer JCT portion was carefully removed as the outflow resistance is not in that region, leaving only the SCE inner wall and a few µm of the tissue, which does contain the resistance. An inverse iterative FE algorithm was then utilized to calculate the unloaded geometry of the JCT/SC complex at an aqueous humor pressure of 0 mm Hg. Then in the model, the intertrabecular spaces, pores, and giant vacuole contents were replaced by aqueous humor, and FSI was employed to pressurize the JCT/SC complex from 0 to 15 mm Hg.

RESULTS

In the JCT/SC complex, the shear stress of the aqueous humor is not evenly distributed. Areas proximal to the inner wall of SC experience larger stresses, reaching up to 10 Pa, while those closer to the JCT undergo lower stresses, approximately 4 Pa. Within this complex, giant vacuoles with or without I-pore behave differently. Those without I-pores experience a more significant strain, around 14%, compared to those with I-pores, where the strain is roughly 9%.

CONCLUSIONS

The distribution of aqueous humor wall shear stress is not uniform within the JCT/SC complex, which may contribute to our understanding of the underlying selective mechanisms in the pathway.

Calibration of the Mechanical Boundary Conditions for a Patient-Specific Thoracic Aorta Model Including the Heart Motion Effect

OBJECTIVE

We propose a procedure for calibrating 4 parameters governing the mechanical boundary conditions (BCs) of a thoracic aorta (TA) model derived from one patient with ascending aortic aneurysm. The BCs reproduce the visco-elastic structural support provided by the soft tissue and the spine and allow for the inclusion of the heart motion effect.

METHODS

We first segment the TA from magnetic resonance imaging (MRI) angiography and derive the heart motion by tracking the aortic annulus from cine-MRI. A rigid-wall fluid-dynamic simulation is performed to derive the time-varying wall pressure field. We build the finite element model considering patient-specific material properties and imposing the derived pressure field and the motion at the annulus boundary. The calibration, which involves the zero-pressure state computation, is based on purely structural simulations. After obtaining the vessel boundaries from the cine-MRI sequences, an iterative procedure is performed to minimize the distance between them and the corresponding boundaries derived from the deformed structural model. A strongly-coupled fluid-structure interaction (FSI) analysis is finally performed with the tuned parameters and compared to the purely structural simulation.

RESULTS AND CONCLUSION

The calibration with structural simulations allows to reduce maximum and mean distances between image-derived and simulation-derived boundaries from 8.64 mm to 6.37 mm and from 2.24 mm to 1.83 mm, respectively. The maximum root mean square error between the deformed structural and FSI surface meshes is 0.19 mm. This procedure may prove crucial for increasing the model fidelity in replicating the real aortic root kinematics.

Influence of tension-band plates on the mechanical loading of the femoral growth plate during guided growth due to coronal plane deformities

Introduction: Correction of knee malalignment by guided growth using a tension-band plate is a common therapy to prevent knee osteoarthritis among other things. This approach is based on the Hueter-Volkmann law stating that the length growth of bones is inhibited by compression and stimulated by tension. How the locally varying mechanical loading of the growth plate is influenced by the implant has not yet been investigated. This study combines load cases from the gait cycle with personalized geometry in order to investigate the mechanical influence of the tension-band plates. Methods: Personalized finite element models of four distal femoral epiphyses of three individuals, that had undergone guided growth, were generated. Load cases from the gait cycles and musculoskeletal modelling were simulated with and without implant. Morphological features of the growth plates were obtained from radiographs. 3D geometries were completed using non-individual Magnetic Resonance Images of age-matched individuals. Boundary conditions for the models were obtained from instrumented gait analyses. Results: The stress distribution in the growth plate was heterogenous and depended on the geometry. In the insertion region, the implants locally induced static stress and reduced the cyclic loading and unloading. Both factors that reduce the growth rate. On the contralateral side of the growth plate, increased tension stress was observed, which stimulates growth. Discussion: Personalized finite element models are able to estimate the changes of local static and cyclic loading of the growth plate induced by the implant. In future, this knowledge can help to better control growth modulation and avoid the return of the malalignment after the treatment. However, this requires models that are completely participant-specific in terms of load cases and 3D geometry.

A review of the characterizations of soft tissues used in human body modeling: Scope, limitations, and the path forward

Soft tissue material properties are vital to human body models that evaluate interactions between the human body and its environment. Such models evaluate internal stress/strain responses in soft tissues to investigate issues like pressure injuries. Numerous constitutive models and parameters have been used to represent mechanical behavior of soft tissues in biomechanical models under quasi-static loading. However, researchers reported that generic material properties cannot accurately represent specific target populations due to large inter-individual variability. Two challenges that exist are experimental mechanical characterization and constitutive modeling of biological soft tissues and personalization of constitutive parameters using non-invasive, non-destructive bedside testing methods. It is imperative to understand the scope and appropriate applications for reported material properties. Thus, the goal of this paper was to compile studies from which soft tissue material properties were obtained and categorize them by source of tissue samples, methods used to quantify deformation, and material models used to describe tissues. The collected studies displayed wide ranges of material properties, and factors that affected the properties included whether tissue samples were in vivo or ex vivo, from humans or animals, the body region tested, body position during in vivo studies, deformation measurements, and material models used to describe tissues. Because of the factors that affected reported material properties, it is clear that much progress has been made in understanding soft tissue responses to loading, yet there is a need to broaden the scope of reported soft tissue material properties and better match reported properties to appropriate human body models.

Inverse problems in blood flow modeling: A review

Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.

Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration

Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.

An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an isochoric part is a very common approach. However, the finite element analysis of such problems often suffers from severe volumetric locking effects and numerical instabilities. In this paper, we present novel methods to overcome volumetric locking phenomena for using stabilized P1-P1 elements. We introduce different stabilization techniques and demonstrate the high robustness and computational efficiency of the chosen methods. In two benchmark problems from the literature as well as an advanced application to cardiac electromechanics, we compare the approach to standard linear elements and show the accuracy and versatility of the methods to simulate anisotropic, nearly and fully incompressible materials. We demonstrate the potential of this numerical framework to accelerate accurate simulations of biological tissues to the extent of enabling patient-specific parameterization studies, where numerous forward simulations are required.

Estimation of the zero-pressure computational start shape of atherosclerotic plaques: Improving the backward displacement method with deformation gradient tensor

Advances in medical imaging have enabled patient-specific biomechanical modelling of arterial lesions such as atherosclerosis and aneurysm. Geometry acquired from in-vivo imaging is already pressurized and a zero-pressure computational start shape needs to be identified. The backward displacement algorithm was proposed to solve this inverse problem, utilizing fixed-point iterations to gradually approach the start shape. However, classical fixed-point implementations were reported with suboptimal convergence properties under large deformations. In this paper, a dynamic learning rate guided by the deformation gradient tensor was introduced to control the geometry update. The effectiveness of this new algorithm was demonstrated for both idealized and patient-specific models. The proposed algorithm led to faster convergence by accelerating the initial steps and helped to avoid the non-convergence in large-deformation problems.

Characterization of Exercise-Induced Myocardium Growth Using Finite Element Modeling and Bayesian Optimization

Cardiomyocyte growth can occur in both physiological (exercised-induced) and pathological (e.g., volume overload and pressure overload) conditions leading to left ventricular (LV) hypertrophy. Studies using animal models and histology have demonstrated the growth and remodeling process at the organ level and tissue-cellular level, respectively. However, the driving factors of growth and the mechanistic link between organ, tissue, and cellular growth remains poorly understood. Computational models have the potential to bridge this gap by using constitutive models that describe the growth and remodeling process of the myocardium coupled with finite element (FE) analysis to model the biomechanics of the heart at the organ level. Using subject-specific imaging data of the LV geometry at two different time points, an FE model can be created with the inverse method to characterize the growth parameters of each subject. In this study, we developed a framework that takes in vivo cardiac magnetic resonance (CMR) imaging data of exercised porcine model and uses FE and Bayesian optimization to characterize myocardium growth in the transverse and longitudinal directions. The efficacy of this framework was demonstrated by successfully predicting growth parameters of 18 synthetic LV targeted masks which were generated from three LV porcine geometries. The framework was further used to characterize growth parameters in 4 swine subjects that had been exercised. The study suggested that exercise-induced growth in swine is prone to longitudinal cardiomyocyte growth (58.0 ± 19.6% after 6 weeks and 79.3 ± 15.6% after 12 weeks) compared to transverse growth (4.0 ± 8.0% after 6 weeks and 7.8 ± 9.4% after 12 weeks). This framework can be used to characterize myocardial growth in different phenotypes of LV hypertrophy and can be incorporated with other growth constitutive models to study different hypothetical growth mechanisms.

The Geometry of Incompatibility in Growing Soft Tissues: Theory and Numerical Characterization

Tissues in vivo are not stress-free. As we grow, our tissues adapt to different physiological and disease conditions through growth and remodeling. This adaptation occurs at the microscopic scale, where cells control the microstructure of their immediate extracellular environment to achieve homeostasis. The local and heterogeneous nature of this process is the source of residual stresses. At the macroscopic scale, growth and remodeling can be accurately captured with the finite volume growth framework within continuum mechanics, which is akin to plasticity. The multiplicative split of the deformation gradient into growth and elastic contributions brings about the notion of incompatibility as a plausible description for the origin of residual stress. Here we define the geometric features that characterize incompatibility in biological materials. We introduce the geometric incompatibility tensor for different growth types, showing that the constraints associated with growth lead to specific patterns of the incompatibility metrics. To numerically investigate the distribution of incompatibility measures, we implement the analysis within a finite element framework. Simple, illustrative examples are shown first to explain the main concepts. Then, numerical characterization of incompatibility and residual stress is performed on three biomedical applications: brain atrophy, skin expansion, and cortical folding. Our analysis provides new insights into the role of growth in the development of tissue defects and residual stresses. Thus, we anticipate that our work will further motivate additional research to characterize residual stresses in living tissue and their role in development, disease, and clinical intervention.

Nonlinear, dissipative phenomena in whole blood clot mechanics

When a thrombus breaks off and embolizes it can occlude vital vessels such as those of the heart, lung, or brain. These thromboembolic conditions are responsible for 1 in 4 deaths worldwide. Thrombus resistance to embolization is driven by its intrinsic fracture toughness as well as other, non-surface-creating dissipative mechanisms. In our current work, we identify and quantify these latter mechanisms toward future studies that aim to delineate fracture from other forms of dissipation. To this end, we use an in vitro thrombus mimic system to produce whole blood clots and explore their dissipative mechanics under simple uniaxial extension, cyclic loading, and stress-relaxation. We found that whole blood clots exhibit Mullins-like effect, hysteresis, permanent set, strain-rate dependence, and nonlinear stress-relaxation. Interestingly, we found that performing these tests under dry or submerged conditions did not change our results. However, performing these tests under room temperature or body temperature conditions yielded differences. Importantly, because we use venous blood our work is most closely related to venous in vivo blood clots. Overall, we have demonstrated that whole blood clots show several dissipative phenomena - similarly to hydrogels - that will be critical to our understanding of thrombus embolization.

A backward pre-stressing algorithm for efficient finite element implementation of in vivo material and geometrical parameters into fibril-reinforced mixture models of articular cartilage

Classical continuum mechanics has been widely used for implementation of the material models of articular cartilage (AC) mainly with the aid of the finite element (FE) method, which, in many cases, considers the stress-free configuration as the initial configuration. On the contrary, the AC experimental tests typically begin with the pre-stressed state of both material and geometrical properties. Indeed, imposing the initial pre-stress onto AC models with the in vivo values as the initial state would result in nonphysiologically expansion of the FE mesh due to the soft nature of AC. This change in the model configuration can also affect the material behavior kinematically in the mixture models of cartilage due to the intrinsic compressibility of the tissue. Although several different fixed-point backward algorithms, as the most straightforward pre-stressing methods, have already been developed to incorporate these initial conditions into FE models iteratively, such methods focused merely on the geometrical parameters, and they omitted the material variations of the anisotropic mixture models of AC. To address this issue, we propose an efficient algorithm generalizing the backward schemes to restore stress-free conditions by optimizing both the involving variables, and we hypothesize that it can affect the results considerably. To this end, a comparative simulation was implemented on an advanced and validated multiphasic model by the new and conventional algorithms. The results are in support of the hypothesis, as in our illustrative general AC model, the material parameters experienced a maximum error of 16% comparing to the initial in vivo data when the older algorithm was employed, and it led to a maximum variation of 44% in the recorded stresses comparing to the results of the new method. We conclude that our methodology enhanced the model fidelity, and it is applicable in most of the existing FE solvers for future mixture studies with accurate stress distributions.

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Tricuspid Valve Anterior Leaflet Strains in Ovine Functional Tricuspid Regurgitation

Functional tricuspid regurgitation (FTR) is thought to arise due to annular dilation and alteration of right ventricular (RV) geometry in the presence of normal leaflets, yet mitral leaflets have been shown to remodel significantly in functional mitral regurgitation. We set out to evaluate tricuspid valve anterior leaflet deformations in ovine FTR. Eleven animals (FTR group) underwent implantation of a pacemaker with high rate pacing to induce biventricular dysfunction and at least moderate TR. Subsequently, both FTR (n = 11) and Control (n = 12) animals underwent implantation of 6 sonomicrometry crystals around the tricuspid annulus, 4 on the anterior leaflet, and 14 on RV epicardium. Tricuspid valve geometry and anterior leaflet strains were calculated from crystal coordinates. Left ventricular ejection fraction and RV fractional area change were significantly lower in FTR animals versus Control. Tricuspid annular area, septo-lateral diameter, RV pressures were all significantly greater in the FTR group. Mean TR grade (+0-3) was 0.7 ± 0.5 in Control and 2.4 ± 0.5 in FTR (P = < 0.001). The anterior leaflet area and length increased significantly. Global radial leaflet strain was significantly lower in FTR mostly driven by decreased free edge leaflet strain. Global circumferential anterior leaflet strain was also significantly lower in FTR with more remarkable reduction in the belly region. Rapid ventricular pacing in sheep resulted in a clinically pertinent model of RV and annular dilation with FTR and leaflet enlargement. Both circumferential and radial anterior leaflet strains were significantly reduced with FTR. Functional TR may be associated with alteration of leaflet mechanical properties.

Impact of Aortic Stenosis on Myofiber Stress: Translational Application of Left Ventricle-Aortic Coupling Simulation

The severity of aortic stenosis (AS) has traditionally been graded by measuring hemodynamic parameters of transvalvular pressure gradient, ejection jet velocity, or estimating valve orifice area. Recent research has highlighted limitations of these criteria at effectively grading AS in presence of left ventricle (LV) dysfunction. We hypothesized that simulations coupling the aorta and LV could provide meaningful insight into myocardial biomechanical derangements that accompany AS. A realistic finite element model of the human heart with a coupled lumped-parameter circulatory system was used to simulate AS. Finite element analysis was performed with Abaqus FEA. An anisotropic hyperelastic model was assigned to LV passive properties, and a time-varying elastance function governed the LV active response. Global LV myofiber peak systolic stress (mean ± standard deviation) was 9.31 ± 10.33 kPa at baseline, 13.13 ± 10.29 kPa for moderate AS, and 16.18 ± 10.59 kPa for severe AS. Mean LV myofiber peak systolic strains were −22.40 ± 8.73%, −22.24 ± 8.91%, and −21.97 ± 9.18%, respectively. Stress was significantly elevated compared to baseline for moderate (p < 0.01) and severe AS (p < 0.001), and when compared to each other (p < 0.01). Ventricular regions that experienced the greatest systolic stress were (severe AS vs. baseline) basal inferior (39.87 vs. 30.02 kPa; p < 0.01), mid-anteroseptal (32.29 vs. 24.79 kPa; p < 0.001), and apex (27.99 vs. 23.52 kPa; p < 0.001). This data serves as a reference for future studies that will incorporate patient-specific ventricular geometries and material parameters, aiming to correlate LV biomechanics to AS severity.

COMPARISON OF TWO METHODS FOR ESTIMATING THE UNLOADED STATE FOR ABDOMINAL AORTIC ANEURYSM STRESS CALCULATIONS

Biomechanical analyses can be used to better understand the rupture risk of abdominal aortic aneurysms (AAAs) on a patient-specific basis using vascular geometries obtained from medical imaging. Methodologies of varying complexity are used to estimate the unloaded state of the imaged vessel to provide a reference configuration for finite element simulations. In this work, we compare the implementation and results of two of these methods, one based on geometric scaling and the other using an iterative determination of unloaded vessel geometry. We find that the two methods result in significantly different stress predictions, and that the iterative method offers superior geometric accuracy. Our findings lend context to the variation in finite element results presented in the AAA stress analysis literature.

Tricuspid valve leaflet strains in the beating ovine heart

The tricuspid leaflets coapt during systole to facilitate proper valve function and, thus, ensure efficient transport of deoxygenated blood to the lungs. Between their open state and closed state, the leaflets undergo large deformations. Quantification of these deformations is important for our basic scientific understanding of tricuspid valve function and for diagnostic or prognostic purposes. To date, tricuspid valve leaflet strains have never been directly quantified in vivo. To fill this gap in our knowledge, we implanted four sonomicrometry crystals per tricuspid leaflet and six crystals along the tricuspid annulus in a total of five sheep. In the beating ovine hearts, we recorded crystal coordinates alongside hemodynamic data. Once recorded, we used a finite strain kinematic framework to compute the temporal evolutions of area strain, radial strain, and circumferential strain for each leaflet. We found that leaflet strains were larger in the anterior leaflet than the posterior and septal leaflets. Additionally, we found that radial strains were larger than circumferential strains. Area strains were as large as 97% in the anterior leaflet, 31% in the posterior leaflet, and 31% in the septal leaflet. These data suggest that tricuspid valve leaflet strains are significantly larger than those in the mitral valve. Should our findings be confirmed they could suggest either that the mechanobiological equilibrium of tricuspid valve resident cells is different than that of mitral valve resident cells or that the mechanotransductive apparatus between the two varies. Either phenomenon may have important implications for the development of tricuspid valve-specific surgical techniques and medical devices.

A fiduciary marker-based framework to assess heterogeneity and anisotropy of right ventricular epicardial strains in the beating ovine heart

Quantifying ventricular deformation in health and disease is critical to our understanding of normal heart function, heart disease mechanisms, and the effect of medical treatments. Imaging modalities have been developed that can measure ventricular deformation non-invasively. However, because of the small thickness, complex shape, and anatomic position of the right ventricle, using these technologies to determine its deformation remains challenging. Here we develop a first fiduciary marker-based method to assess heterogeneity and anisotropy of right ventricular epicardial strain across the entire free wall. To this end, we combine a high-density array of sonomicrometry crystals implanted across the entire right ventricular epicardial surface with a subdivision surface algorithm and a large deformation kinematics framework. We demonstrate our approach on four beating ovine hearts and present a preliminary regional analysis of circumferential, longitudinal, and areal strain. Moreover, we illustrate maps of the same strains across the entire right ventricular epicardial surface to highlight their spatial heterogeneity and anisotropy. We observe in these animals that RV epicardial strains vary throughout the cardiac cycle, are heterogeneous across the RV free wall, and are anisotropic with larger compressive strains, i.e., contraction, in the longitudinal direction than in the circumferential direction. Average peak compressive strains vary by region between -3.34% and -8.29% in circumferential direction, and -4.02% and -10.57% in longitudinal direction. In summary, we introduce an experimental framework that will allow us to study disease- and device-induced deformations, and long-term consequences of these deformations, including heterogeneous and anisotropic effects.

Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization

Individually personalized computational models of heart mechanics can be used to estimate important physiological and clinically-relevant quantities that are difficult, if not impossible, to directly measure in the beating heart. Here, we present a novel and efficient framework for creating patient-specific biventricular models using a gradient-based data assimilation method for evaluating regional myocardial contractility and estimating myofiber stress. These simulations can be performed on a regular laptop in less than 2 h and produce excellent fit between measured and simulated volume and strain data through the entire cardiac cycle. By applying the framework using data obtained from 3 healthy human biventricles, we extracted clinically important quantities as well as explored the role of fiber angles on heart function. Our results show that steep fiber angles at the endocardium and epicardium are required to produce simulated motion compatible with measured strain and volume data. We also find that the contraction and subsequent systolic stresses in the right ventricle are significantly lower than that in the left ventricle. Variability of the estimated quantities with respect to both patient data and modeling choices are also found to be low. Because of its high efficiency, this framework may be applicable to modeling of patient specific cardiac mechanics for diagnostic purposes.

Construction and Validation of Subject-Specific Biventricular Finite-Element Models of Healthy and Failing Swine Hearts From High-Resolution DT-MRI

Predictive computational modeling has revolutionized classical engineering disciplines and is in the process of transforming cardiovascular research. This is particularly relevant for investigating emergent therapies for heart failure, which remains a leading cause of death globally. The creation of subject-specific biventricular computational cardiac models has been a long-term endeavor within the biomedical engineering community. Using high resolution (0.3 × 0.3 × 0.8 mm) ex vivo data, we constructed a precise fully subject-specific biventricular finite-element model of healthy and failing swine hearts. Each model includes fully subject-specific geometries, myofiber architecture and, in the case of the failing heart, fibrotic tissue distribution. Passive and active material properties are prescribed using hyperelastic strain energy functions that define a nearly incompressible, orthotropic material capable of contractile function. These materials were calibrated using a sophisticated multistep approach to match orthotropic tri-axial shear data as well as subject-specific hemodynamic ventricular targets for pressure and volume to ensure realistic cardiac function. Each mechanically beating heart is coupled with a lumped-parameter representation of the circulatory system, allowing for a closed-loop definition of cardiovascular flow. The circulatory model incorporates unidirectional fluid exchanges driven by pressure gradients of the model, which in turn are driven by the mechanically beating heart. This creates a computationally meaningful representation of the dynamic beating of the heart coupled with the circulatory system. Each model was calibrated using subject-specific experimental data and compared with independent in vivo strain data obtained from echocardiography. Our methods produced highly detailed representations of swine hearts that function mechanically in a remarkably similar manner to the in vivo subject-specific strains on a global and regional comparison. The degree of subject-specificity included in the models represents a milestone for modeling efforts that captures realism of the whole heart. This study establishes a foundation for future computational studies that can apply these validated methods to advance cardiac mechanics research.

A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta

Advances in structural finite element analysis (FEA) and medical imaging have made it possible to investigate the in vivo biomechanics of human organs such as blood vessels, for which organ geometries at the zero-pressure level need to be recovered. Although FEA-based inverse methods are available for zero-pressure geometry estimation, these methods typically require iterative computation, which are time-consuming and may be not suitable for time-sensitive clinical applications. In this study, by using machine learning (ML) techniques, we developed an ML model to estimate the zero-pressure geometry of human thoracic aorta given 2 pressurized geometries of the same patient at 2 different blood pressure levels. For the ML model development, a FEA-based method was used to generate a dataset of aorta geometries of 3125 virtual patients. The ML model, which was trained and tested on the dataset, is capable of recovering zero-pressure geometries consistent with those generated by the FEA-based method. Thus, this study demonstrates the feasibility and great potential of using ML techniques as a fast surrogate of FEA-based inverse methods to recover zero-pressure geometries of human organs.

Multi-view stereo in the operating room allows prediction of healing complications in a patient-specific model of reconstructive surgery

Excessive mechanical stress leads to wound healing complications following reconstructive surgery. However, this knowledge is not easily applicable in clinical scenarios due to the difficulty in measuring stress contours during complex tissue rearrangement procedures. Computational tools have been proposed as an alternative to address this need, but obtaining patient specific geometries with an affordable and flexible setup has remained a challenge. Here we present a methodology to determine the stress contours from a reconstructive procedure on a patient-specific finite element model based on multi-view stereo (MVS). MVS is a noninvasive technology that allows reconstruction of 3D geometries using a standard digital camera, making it ideal for the operating room. Finite element analysis can then be used on the patient-specific geometry to perform a virtual surgery and predict regions at risk of complications. We applied our approach to the case of a 7-year-old patient who was treated to correct a cranial contour deformity and resect two large areas of scalp scarring. The simulation showed several zones of high stress, particularly near the suture lines at the distal ends of the flaps. The patient did show delayed healing and partial flap tip necrosis at one of such predicted regions at the 30-day follow up visit. Our results further establish the application of computational tools in individualized medical scenarios to advance preoperative planing and anticipate regions of concern immediately after surgery.