MicroBundleCompute: Automated segmentation, tracking, and analysis of subdomain deformation in cardiac microbundles.

Advancing human induced pluripotent stem cell derived cardiomyocyte (hiPSC-CM) technology will lead to significant progress ranging from disease modeling, to drug discovery, to regenerative tissue engineering. Yet, alongside these potential opportunities comes a critical challenge: attaining mature hiPSC-CM tissues. At present, there are multiple techniques to promote maturity of hiPSC-CMs including physical platforms and cell culture protocols. However, when it comes to making quantitative comparisons of functional behavior, there are limited options for reliably and reproducibly computing functional metrics that are suitable for direct cross-system comparison. In addition, the current standard functional metrics obtained from time-lapse images of cardiac microbundle contraction reported in the field (i.e., post forces, average tissue stress) do not take full advantage of the available information present in these data (i.e., full-field tissue displacements and strains). Thus, we present "MicroBundleCompute," a computational framework for automatic quantification of morphology-based mechanical metrics from movies of cardiac microbundles. Briefly, this computational framework offers tools for automatic tissue segmentation, tracking, and analysis of brightfield and phase contrast movies of beating cardiac microbundles. It is straightforward to implement, runs without user intervention, requires minimal input parameter setting selection, and is computationally inexpensive. In this paper, we describe the methods underlying this computational framework, show the results of our extensive validation studies, and demonstrate the utility of exploring heterogeneous tissue deformations and strains as functional metrics. With this manuscript, we disseminate "MicroBundleCompute" as an open-source computational tool with the aim of making automated quantitative analysis of beating cardiac microbundles more accessible to the community.

lGeneralized super-resolution 4D Flow MRI-using ensemble learning to extend across the cardiovascular system.

4D Flow Magnetic Resonance Imaging (4D Flow MRI) is a non-invasive measurement technique capable of quantifying blood flow across the cardiovascular system. While practical use is limited by spatial resolution and image noise, incorporation of trained super-resolution (SR) networks has potential to enhance image quality post-scan. However, these efforts have predominantly been restricted to narrowly defined cardiovascular domains, with limited exploration of how SR performance extends across the cardiovascular system; a task aggravated by contrasting hemodynamic conditions apparent across the cardiovasculature. The aim of our study was to explore the generalizability of SR 4D Flow MRI using a combination of heterogeneous training sets and dedicated ensemble learning. With synthetic training data generated across three disparate domains (cardiac, aortic, cerebrovascular), varying convolutional base and ensemble learners were evaluated as a function of domain and architecture, quantifying performance on both in-silico and acquired in-vivo data from the same three domains. Results show that both bagging and stacking ensembling enhance SR performance across domains, accurately predicting high-resolution velocities from low-resolution input data in-silico. Likewise, optimized networks successfully recover native resolution velocities from downsampled in-vivo data, as well as show qualitative potential in generating denoised SR-images from clinicallevel input data. In conclusion, our work presents a viable approach for generalized SR 4D Flow MRI, with ensemble learning extending utility across various clinical areas of interest.

Matrix architecture and mechanics regulate myofibril organization, costamere assembly, and contractility of engineered myocardial microtissues.

The mechanical function of the myocardium is defined by cardiomyocyte contractility and the biomechanics of the extracellular matrix (ECM). Understanding this relationship remains an important unmet challenge due to limitations in existing approaches for engineering myocardial tissue. Here, we established arrays of cardiac microtissues with tunable mechanics and architecture by integrating ECM-mimetic synthetic, fiber matrices and induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs), enabling real-time contractility readouts, in-depth structural assessment, and tissue-specific computational modeling. We find that the stiffness and alignment of matrix fibers distinctly affect the structural development and contractile function of pure iPSC-CM tissues. Further examination into the impact of fibrous matrix stiffness enabled by computational models and quantitative immunofluorescence implicates cell-ECM interactions in myofibril assembly and notably costamere assembly, which correlates with improved contractile function of tissues. These results highlight how iPSC-CM tissue models with controllable architecture and mechanics can inform the design of translatable regenerative cardiac therapies.

A data-driven computational model for engineered cardiac microtissues.

Engineered heart tissues (EHTs) present a potential solution to some of the current challenges in the treatment of heart disease; however, the development of mature, adult-like cardiac tissues remains elusive. Mechanical stimuli have been observed to improve whole-tissue function and cardiomyocyte (CM) maturation, although our ability to fully utilize these mechanisms is hampered, in part, by our incomplete understanding of the mechanobiology of EHTs. In this work, we leverage experimental data, produced by a mechanically tunable experimental setup, to introduce a tissue-specific computational modeling pipeline of EHTs. Our new modeling pipeline generates simulated, image-based EHTs, capturing ECM and myofibrillar structure as well as functional parameters estimated directly from experimental data. This approach enables the unique estimation of EHT function by data-based estimation of CM active stresses. We use this experimental and modeling pipeline to study different mechanical environments, where we contrast the force output of the tissue with the computed active stress of CMs. We show that the significant differences in measured experimental forces can largely be explained by the levels of myofibril formation achieved by the CMs in the distinct mechanical environments, with active stress showing more muted variations across conditions. The presented model also enables us to dissect the relative contributions of myofibrils and extracellular matrix to tissue force output, a task difficult to address experimentally. These results highlight the importance of tissue-specific modeling to augment EHT experiments, providing deeper insights into the mechanobiology driving EHT function. STATEMENT OF SIGNIFICANCE: Engineered heart tissues (EHTs) have the potential to revolutionize the way heart disease is treated. However, developing mature cardiomyocytes (CM) in these tissues remains a challenge due, in part, to our incomplete understanding of the fundamental biomechanical mechanisms that drive EHT development. This work integrates the experimental data of an EHT platform developed to study the influence of mechanics in CM maturation with computational biomechanical models. This approach is used to augment conclusions obtained in-vitro - by measuring quantities such as cell stress and strain - and to dissect the relevance of each component in the whole tissue performance. Our results show how a combination of specialized in-silico and in-vitro approaches can help us better understand the mechanobiology of EHTs.

A viscoelastic constitutive model for human femoropopliteal arteries.

High failure rates present challenges for surgical and interventional therapies for peripheral artery disease of the femoropopliteal artery (FPA). The FPA's demanding biomechanical environment necessitates complex interactions with repair devices and materials. While a comprehensive understanding of the FPA's mechanical characteristics could improve medical treatments, the viscoelastic properties of these muscular arteries remain poorly understood, and the constitutive model describing their time-dependent behavior is absent. We introduce a new viscoelastic constitutive model for the human FPA grounded in its microstructural composition. The model is capable of detailing the contributions of each intramural component to the overall viscoelastic response. Our model was developed utilizing fractional viscoelasticity and tested using biaxial experimental data with hysteresis and relaxation collected from 10 healthy human subjects aged 57 to 65 and further optimized for high throughput and automation. The model accurately described the experimental data, capturing significant nonlinearity and hysteresis that were particularly pronounced circumferentially, and tracked the contribution of passive smooth muscle cells to viscoelasticity that was twice that of the collagen fibers. The high-throughput parameter estimation procedure we developed included a specialized objective function and modifications to enhance convergence for the common exponential-type fiber laws, facilitating computational implementation. Our new model delineates the time-dependent behavior of human FPAs, which will improve the fidelity of computational simulations investigating device-artery interactions and contribute to their greater physical accuracy. Moreover, it serves as a useful tool to investigate the contribution of arterial constituents to overall tissue viscoelasticity, thereby expanding our knowledge of arterial mechanophysiology. STATEMENT OF SIGNIFICANCE: The demanding biomechanical environment of the femoropopliteal artery (FPA) necessitates complex interactions with repair devices and materials, but the viscoelastic properties of these muscular arteries remain poorly understood with the constitutive model describing their time-dependent behavior being absent. We hereby introduce the first viscoelastic constitutive model for the human FPA grounded in its microstructures. This model was tested using biaxial mechanical data collected from 10 healthy human subjects between the ages of 57 to 65. It can detail the contributions of each intramural component to the overall viscoelastic response, showing that the contribution of passive smooth muscle cells to viscoelasticity is twice that of collagen fibers. The usefulness of this model as tool to better understand arterial mechanophysiology was demonstrated.

Non-invasive cardiovascular magnetic resonance assessment of pressure recovery distance after aortic valve stenosis.

BACKGROUND: Decisions in the management of aortic stenosis are based on the peak pressure drop, captured by Doppler echocardiography, whereas gold standard catheterization measurements assess the net pressure drop but are limited by associated risks. The relationship between these two measurements, peak and net pressure drop, is dictated by the pressure recovery along the ascending aorta which is mainly caused by turbulence energy dissipation. Currently, pressure recovery is considered to occur within the first 40-50 mm distally from the aortic valve, albeit there is inconsistency across interventionist centers on where/how to position the catheter to capture the net pressure drop. METHODS: We developed a non-invasive method to assess the pressure recovery distance based on blood flow momentum via 4D Flow cardiovascular magnetic resonance (CMR). Multi-center acquisitions included physical flow phantoms with different stenotic valve configurations to validate this method, first against reference measurements and then against turbulent energy dissipation (respectively n = 8 and n = 28 acquisitions) and to investigate the relationship between peak and net pressure drops. Finally, we explored the potential errors of cardiac catheterisation pressure recordings as a result of neglecting the pressure recovery distance in a clinical bicuspid aortic valve (BAV) cohort of n = 32 patients. RESULTS: In-vitro assessment of pressure recovery distance based on flow momentum achieved an average error of 1.8 ± 8.4 mm when compared to reference pressure sensors in the first phantom workbench. The momentum pressure recovery distance and the turbulent energy dissipation distance showed no statistical difference (mean difference of 2.8 ± 5.4 mm, R2 = 0.93) in the second phantom workbench. A linear correlation was observed between peak and net pressure drops, however, with strong dependences on the valvular morphology. Finally, in the BAV cohort the pressure recovery distance was 78.8 ± 34.3 mm from vena contracta, which is significantly longer than currently accepted in clinical practise (40-50 mm), and 37.5% of patients displayed a pressure recovery distance beyond the end of the ascending aorta. CONCLUSION: The non-invasive assessment of the distance to pressure recovery is possible by tracking momentum via 4D Flow CMR. Recovery is not always complete at the ascending aorta, and catheterised recordings will overestimate the net pressure drop in those situations. There is a need to re-evaluate the methods that characterise the haemodynamic burden caused by aortic stenosis as currently clinically accepted pressure recovery distance is an underestimation.

Evaluation of aortic stenosis: From Bernoulli and Doppler to Navier-Stokes.

Uni-dimensional Doppler echocardiography data provide the mainstay of quantative assessment of aortic stenosis, with the transvalvular pressure drop a key indicator of haemodynamic burden. Sophisticated methods of obtaining velocity data, combined with improved computational analysis, are facilitating increasingly robust and reproducible measurement. Imaging modalities which permit acquisition of three-dimensional blood velocity vector fields enable angle-independent valve interrogation and calculation of enhanced measures of the transvalvular pressure drop. This manuscript clarifies the fundamental principles of physics that underpin the evaluation of aortic stenosis and explores modern techniques that may provide more accurate means to grade aortic stenosis and inform appropriate management.

Personalization of biomechanical simulations of the left ventricle by in-vivo cardiac DTI data: Impact of fiber interpolation methods.

Simulations of cardiac electrophysiology and mechanics have been reported to be sensitive to the microstructural anisotropy of the myocardium. Consequently, a personalized representation of cardiac microstructure is a crucial component of accurate, personalized cardiac biomechanical models. In-vivo cardiac Diffusion Tensor Imaging (cDTI) is a non-invasive magnetic resonance imaging technique capable of probing the heart's microstructure. Being a rather novel technique, issues such as low resolution, signal-to noise ratio, and spatial coverage are currently limiting factors. We outline four interpolation techniques with varying degrees of data fidelity, different amounts of smoothing strength, and varying representation error to bridge the gap between the sparse in-vivo data and the model, requiring a 3D representation of microstructure across the myocardium. We provide a workflow to incorporate in-vivo myofiber orientation into a left ventricular model and demonstrate that personalized modelling based on fiber orientations from in-vivo cDTI data is feasible. The interpolation error is correlated with a trend in personalized parameters and simulated physiological parameters, strains, and ventricular twist. This trend in simulation results is consistent across material parameter settings and therefore corresponds to a bias introduced by the interpolation method. This study suggests that using a tensor interpolation approach to personalize microstructure with in-vivo cDTI data, reduces the fiber uncertainty and thereby the bias in the simulation results.

Role of the mitral valve in left ventricular assist device pathophysiology.

Functional mitral regurgitation (MR) in the setting of heart failure results from progressive dilatation of the left ventricle (LV) and mitral annulus. This leads to leaflet tethering with posterior displacement. Contrary to common assumptions, MR often does not resolve with LVAD decompression of the LV alone. The negative impact of significant (moderate-severe) mitral regurgitation in the LVAD setting is becoming better recognized in terms of its harmful effect on right heart function, pulmonary vascular resistance and hospital readmissions. However, controversies remain regarding the threshold for intervention and management. At present, there are no consensus indications for the repair of significant mitral regurgitation at the time of LVAD implantation due to the conflicting data regarding potential adverse effects of MR on clinical outcomes. In this review, we summarize the current understanding of MR pathophysiology in patients supported with LVAD and potential future management strategies.

Left ventricular remodeling following aortic root and ascending aneurysm repair.

Objective: Adverse left ventricular remodeling due to a mismatch between stiffness of native aortic tissue and current polyester grafts may be under-recognized. This study was conducted to evaluate the impact of proximal aortic replacement on adverse remodeling of the left ventricle. Materials and methods: All aortic root and ascending aortic aneurysm patients were identified (n = 2,001, 2006-2019). The study cohort consisted of a subset of patients (n = 98) with two or more electrocardiogram (ECG)-gated CT angiograms, but without concomitant aortic valve disease or bicuspid aortic valve, connective tissue disease, acute aortic syndrome or prior history of aortic repair or mitral valve surgery. LV myocardial mass was measured from CT data and indexed to body surface area (LVMI). The study cohort was divided into a surgery group (n = 47) and a control group; optimal medical therapy group (OMT, n = 51). Results: The mean age was 60 ± 11 years (80% male). Beta-blocker use was significantly more frequent in the surgery group (89 vs. 57%, p < 0.001), whereas, all other antihypertensive drugs were more frequent in the OMT group. The average follow-up was 9.1 ± 4.0 months for the surgery group and 13.7 ± 6.3 months for the OMT group. Average LVMI at baseline was similar in both groups (p = 0.934). LVMI increased significantly in the surgery group compared to the OMT group (3.7 ± 4.1 vs. 0.6 ± 4.4 g/m2, p = 0.001). Surgery, baseline LVMI, age, and sex were found to be independent predictors of LVMI increased on multivariable analysis. Conclusion: Proximal aortic repair with stiff polyester grafts was associated with increased LV mass in the first-year post-operative and may promote long-term adverse cardiac remodeling. Further studies should be considered to evaluate the competing effects of aortic aneurysm related mortality against risks of long-term graft induced aortic stiffening and the potential implications on current size thresholds for intervention.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension.

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

Unlocking the Non-invasive Assessment of Conduit and Reservoir Function in the Aorta : The Obstructive Descending Aorta in HLHS.

Aortic surgeries in congenital conditions, such as hypoplastic left heart syndrome (HLHS), aim to restore and maintain the conduit and reservoir functions of the aorta. We proposed a method to assess these two functions based on 4D flow MRI, and we applied it to study the aorta in pre-Fontan HLHS. Ten pre-Fontan HLHS patients and six age-matched controls were studied to derive the advective pressure difference and viscous dissipation for conduit function, and pulse wave velocity and elastic modulus for reservoir function. The reconstructed neo-aorta in HLHS subjects achieved a good conduit function at a cost of an impaired reservoir function (69.7% increase of elastic modulus). The native descending HLHS aorta displayed enhanced reservoir (elastic modulus being 18.4% smaller) but impaired conduit function (three-fold increase in peak advection). A non-invasive and comprehensive assessment of aortic conduit and reservoir functions is feasible and has potentially clinical relevance in congenital vascular conditions.

The effects of viscoelasticity on residual strain in aortic soft tissues.

Residual stress is thought to play a critical role in modulating stress distributions in soft biological tissues and in maintaining the mechanobiological stress environment of cells. Residual stresses in arteries and other tissues are classically assessed through opening angle experiments, which demonstrate the continuous release of residual stresses over hours. These results are then assessed through nonlinear biomechanical models to provide estimates of the residual stresses in the intact state. Although well studied, these analyses typically focus on hyperelastic material models despite significant evidence of viscoelastic phenomena over both short and long timescales. In this work, we extended the state-of-the-art structural tensor model for arterial tissues from Holzapfel and Ogden for fractional viscoelasticity. Models were tuned to capture consistent levels of hysteresis observed in biaxial experiments, while also minimizing the fractional viscoelastic weighting and opening angles to correctly capture opening angle dynamics. Results suggest that a substantial portion of the human abdominal aorta is viscoelastic, but exhibits a low fractional order (i.e. more elastically). Additionally, a significantly larger opening angle in the fully unloaded state is necessary to produce comparable hysteresis in biaxial testing. As a consequence, conventional estimates of residual stress using hyperelastic approaches over-estimate their viscoelastic counterparts by a factor of 2. Thus, a viscoelastic approach, such as the one illustrated in this study, in combination with an additional source of rate-controlled viscoelastic data is necessary to accurately analyze the residual stress distribution in soft biological tissues. STATEMENT OF SIGNIFICANCE: Residual stress plays a crucial role in achieving a homeostatic stress environment in soft biological tissues. However, the analysis of residual stress typically focuses on hyperelastic material models despite evidence of viscoelastic behavior. This work is the first attempt at analyzing the effects of viscoelasticity on residual stress. The application of viscoelasticity was crucial for producing realistic opening dynamics in arteries. The overall residual stresses were estimated to be 50% less than those from using hyperelastic material models, while the opening angles were projected to be 25% more than those measured after 16 hours, suggesting underestimated residual strain. This study highlights the importance viscoelasticity in the analysis of residual stress even in weakly dissipative materials like the human aorta.

Altered Aortic Hemodynamics and Relative Pressure in Patients with Dilated Cardiomyopathy.

Ventricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol.

Imaging and biophysical modelling of thrombogenic mechanisms in atrial fibrillation and stroke.

Atrial fibrillation (AF) underlies almost one third of all ischaemic strokes, with the left atrial appendage (LAA) identified as the primary thromboembolic source. Current stroke risk stratification approaches, such as the CHA2DS2-VASc score, rely mostly on clinical comorbidities, rather than thrombogenic mechanisms such as blood stasis, hypercoagulability and endothelial dysfunction-known as Virchow's triad. While detection of AF-related thrombi is possible using established cardiac imaging techniques, such as transoesophageal echocardiography, there is a growing need to reliably assess AF-patient thrombogenicity prior to thrombus formation. Over the past decade, cardiac imaging and image-based biophysical modelling have emerged as powerful tools for reproducing the mechanisms of thrombogenesis. Clinical imaging modalities such as cardiac computed tomography, magnetic resonance and echocardiographic techniques can measure blood flow velocities and identify LA fibrosis (an indicator of endothelial dysfunction), but imaging remains limited in its ability to assess blood coagulation dynamics. In-silico cardiac modelling tools-such as computational fluid dynamics for blood flow, reaction-diffusion-convection equations to mimic the coagulation cascade, and surrogate flow metrics associated with endothelial damage-have grown in prevalence and advanced mechanistic understanding of thrombogenesis. However, neither technique alone can fully elucidate thrombogenicity in AF. In future, combining cardiac imaging with in-silico modelling and integrating machine learning approaches for rapid results directly from imaging data will require development under a rigorous framework of verification and clinical validation, but may pave the way towards enhanced personalised stroke risk stratification in the growing population of AF patients. This Review will focus on the significant progress in these fields.

An Implementation of Patient-Specific Biventricular Mechanics Simulations With a Deep Learning and Computational Pipeline.

Parameterised patient-specific models of the heart enable quantitative analysis of cardiac function as well as estimation of regional stress and intrinsic tissue stiffness. However, the development of personalised models and subsequent simulations have often required lengthy manual setup, from image labelling through to generating the finite element model and assigning boundary conditions. Recently, rapid patient-specific finite element modelling has been made possible through the use of machine learning techniques. In this paper, utilising multiple neural networks for image labelling and detection of valve landmarks, together with streamlined data integration, a pipeline for generating patient-specific biventricular models is applied to clinically-acquired data from a diverse cohort of individuals, including hypertrophic and dilated cardiomyopathy patients and healthy volunteers. Valve motion from tracked landmarks as well as cavity volumes measured from labelled images are used to drive realistic motion and estimate passive tissue stiffness values. The neural networks are shown to accurately label cardiac regions and features for these diverse morphologies. Furthermore, differences in global intrinsic parameters, such as tissue anisotropy and normalised active tension, between groups illustrate respective underlying changes in tissue composition and/or structure as a result of pathology. This study shows the successful application of a generic pipeline for biventricular modelling, incorporating artificial intelligence solutions, within a diverse cohort.

Physiologic biomechanics enhance reproducible contractile development in a stem cell derived cardiac muscle platform.

Human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) allow investigations in a human cardiac model system, but disorganized mechanics and immaturity of hPSC-CMs on standard two-dimensional surfaces have been hurdles. Here, we developed a platform of micron-scale cardiac muscle bundles to control biomechanics in arrays of thousands of purified, independently contracting cardiac muscle strips on two-dimensional elastomer substrates with far greater throughput than single cell methods. By defining geometry and workload in this reductionist platform, we show that myofibrillar alignment and auxotonic contractions at physiologic workload drive maturation of contractile function, calcium handling, and electrophysiology. Using transcriptomics, reporter hPSC-CMs, and quantitative immunofluorescence, these cardiac muscle bundles can be used to parse orthogonal cues in early development, including contractile force, calcium load, and metabolic signals. Additionally, the resultant organized biomechanics facilitates automated extraction of contractile kinetics from brightfield microscopy imaging, increasing the accessibility, reproducibility, and throughput of pharmacologic testing and cardiomyopathy disease modeling.

A viscoelastic model for human myocardium.

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena. STATEMENT OF SIGNIFICANCE: The viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.

Magnetic Resonance Elastography Reconstruction for Anisotropic Tissues.

Elastography has become widely used clinically for characterising changes in soft tissue mechanics that are associated with altered tissue structure and composition. However, some soft tissues, such as muscle, are not isotropic as is assumed in clinical elastography implementations. This limits the ability of these methods to capture changes in anisotropic tissues associated with disease. The objective of this study was to develop and validate a novel elastography reconstruction technique suitable for estimating the linear viscoelastic mechanical properties of transversely isotropic soft tissues. We derived a divergence-free formulation of the governing equations for acoustic wave propagation through a linearly transversely isotropic viscoelastic material, and transformed this into a weak form. This was then implemented into a finite element framework, enabling the analysis of wave input data and tissue structural fibre orientations, in this case based on diffusion tensor imaging. To validate the material constants obtained with this method, numerous in silico phantom experiments were run which encompassed a range of variations in wave input directions, material properties, fibre structure and noise. The method was also tested on ex vivo muscle and in vivo human volunteer calf muscles, and compared with a previous curl-based inversion method. The new method robustly extracted the transversely isotropic shear moduli (G⊥', G∥', G″) from the in silico phantom tests with minimal bias, including in the presence of experimentally realistic levels of noise in either fibre orientation or wave data. This new method performed better than the previous method in the presence of noise. Anisotropy estimates from the ex vivo muscle phantom agreed well with rheological tests. In vivo experiments on human calf muscles were able to detect increases in muscle shear moduli with passive muscle stretch. This new reconstruction method can be applied to quantify tissue mechanical properties of anisotropic soft tissues, such as muscle, in health and disease.

Noninvasive quantification of cerebrovascular pressure changes using 4D Flow MRI.

PURPOSE: Hemodynamic alterations are indicative of cerebrovascular disease. However, the narrow and tortuous cerebrovasculature complicates image-based assessment, especially when quantifying relative pressure. Here, we present a systematic evaluation of image-based cerebrovascular relative pressure mapping, investigating the accuracy of the routinely used reduced Bernoulli (RB), the extended unsteady Bernoulli (UB), and the full-field virtual work-energy relative pressure ( ν WERP) method. METHODS: Patient-specific in silico models were used to generate synthetic cerebrovascular 4D Flow MRI, with RB, UB, and ν WERP performance quantified as a function of spatiotemporal sampling and image noise. Cerebrovascular relative pressures were also derived in 4D Flow MRI from healthy volunteers ( n=8 ), acquired at two spatial resolutions (dx = 1.1 and 0.8 mm). RESULTS: The in silico analysis indicate that accurate relative pressure estimations are inherently coupled to spatial sampling: at dx = 1.0 mm high errors are reported for all methods; at dx = 0.5 mm ν WERP recovers relative pressures at a mean error of 0.02 ± 0.25 mm Hg, while errors remain higher for RB and UB (mean error of -2.18 ± 1.91 and -2.18 ± 1.87 mm Hg, respectively). The dependence on spatial sampling is also indicated in vivo, albeit with higher correlative dependence between resolutions using ν WERP (k = 0.64, R2 = 0.81 for dx = 1.1 vs. 0.8 mm) than with RB or UB (k = 0.04, R2 = 0.03, and k = 0.07, R2 = 0.07, respectively). CONCLUSION: Image-based full-field methods such as ν WERP enable cerebrovascular relative pressure mapping; however, accuracy is directly dependent on utilized spatial resolution.