Growth and remodeling of the left ventricle: A case study of myocardial infarction and surgical ventricular restoration

Multiscale Finite Element Modeling of Left Ventricular Growth in Simulations of Valve Disease

Multiscale models of the cardiovascular system are emerging as effective tools for investigating the mechanisms that drive ventricular growth and remodeling. These models can predict how molecular-level mechanisms impact organ-level structure and function and could provide new insights that help improve patient care. MyoFE is a multiscale computer framework that bridges molecular and organ-level mechanisms in a finite element model of the left ventricle that is coupled with the systemic circulation. In this study, we extend MyoFE to include a growth algorithm, based on volumetric growth theory, to simulate concentric growth (wall thickening/thinning) and eccentric growth (chamber dilation/constriction) in response to valvular diseases. Specifically in our model, concentric growth is controlled by time-averaged total stress along the fiber direction over a cardiac cycle while eccentric growth responds to time-averaged intracellular myofiber passive stress over a cardiac cycle. The new framework correctly predicted different forms of growth in response to two types of valvular diseases, namely aortic stenosis and mitral regurgitation. Furthermore, the model predicted that LV size and function are nearly restored (reversal of growth) when the disease-mimicking perturbation was removed in the simulations for each valvular disorder. In conclusion, the simulations suggest that time-averaged total stress along the fiber direction and time-averaged intracellular myofiber passive stress can be used to drive concentric and eccentric growth in simulations of valve disease.

An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling

Progressive left ventricular (LV) growth and remodelling (G&R) is often induced by volume and pressure overload, characterized by structural and functional adaptation through myocyte hypertrophy and extracellular matrix remodelling, which are dynamically regulated by biomechanical factors, inflammation, neurohormonal pathways, etc. When prolonged, it can eventually lead to irreversible heart failure. In this study, we have developed a new framework for modelling pathological cardiac G&R based on constrained mixture theory using an updated reference configuration, which is triggered by altered biomechanical factors to restore biomechanical homeostasis. Eccentric and concentric growth, and their combination have been explored in a patient-specific human LV model under volume and pressure overload. Eccentric growth is triggered by overstretching of myofibres due to volume overload, i.e. mitral regurgitation, whilst concentric growth is driven by excessive contractile stress due to pressure overload, i.e. aortic stenosis. Different biological constituent's adaptations under pathological conditions are integrated together, which are the ground matrix, myofibres and collagen network. We have shown that this constrained mixture-motivated G&R model can capture different phenotypes of maladaptive LV G&R, such as chamber dilation and wall thinning under volume overload, wall thickening under pressure overload, and more complex patterns under both pressure and volume overload. We have further demonstrated how collagen G&R would affect LV structural and functional adaption by providing mechanistic insight on anti-fibrotic interventions. This updated Lagrangian constrained mixture based myocardial G&R model has the potential to understand the turnover processes of myocytes and collagen due to altered local mechanical stimuli in heart diseases, and in providing mechanistic links between biomechanical factors and biological adaption at both the organ and cellular levels. Once calibrated with patient data, it can be used for assessing heart failure risk and designing optimal treatment therapies. STATEMENT OF SIGNIFICANCE: Computational modelling of cardiac G&R has shown high promise to provide insight into heart disease management when mechanistic understandings are quantified between biomechanical factors and underlying cellular adaptation processes. The kinematic growth theory has been dominantly used to phenomenologically describe the biological G&R process but neglecting underlying cellular mechanisms. We have developed a constrained mixture based G&R model with updated reference by taking into account different mechanobiological processes in the ground matrix, myocytes and collagen fibres. This G&R model can serve as a basis for developing more advanced myocardial G&R models further informed by patient data to assess heart failure risk, predict disease progression, select the optimal treatment by hypothesis testing, and eventually towards a truly precision cardiology using in-silico models.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Volumetric growth of soft tissues evaluated in the current configuration

The growth and remodelling of soft tissues plays a significant role in many physiological applications, particularly in understanding and managing many diseases. A commonly used approach for soft tissue growth and remodelling is volumetric growth theory, introduced in the framework of finite elasticity. In such an approach, the total deformation gradient tensor is decomposed so that the elastic and growth tensors can be studied separately. A critical element in this approach is to determine the growth tensor and its evolution with time. Most existing volumetric growth theories define the growth tensor in the reference (natural) configuration, which does not reflect the continuous adaptation processes of soft tissues under the current configuration. In a few studies where growth from a loaded configuration was considered, simplifying assumptions, such as compatible deformation or geometric symmetries, were introduced. In this work, we propose a new volumetric growth law that depends on fields evaluated in the current configuration, which is residually stressed and loaded, without any geometrical restrictions. We illustrate our idea using a simplified left ventricle model, which admits inhomogeneous growth in the current configuration. We compare the residual stress distribution of our approach with the traditional volumetric growth theory, that assumes growth occurring from the natural reference configuration. We show that the proposed framework leads to qualitative agreements with experimental measurements. Furthermore, using a cylindrical model, we find an incompatibility index that explains the differences between the two approaches in more depth. We also demonstrate that results from both approaches reach the same steady solution published previously at the limit of a saturated growth. Although we used a left ventricle model as an example, our theory is applicable in modelling the volumetric growth of general soft tissues.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

The impact of myocardial compressibility on organ-level simulations of the normal and infarcted heart

Myocardial infarction (MI) rapidly impairs cardiac contractile function and instigates maladaptive remodeling leading to heart failure. Patient-specific models are a maturing technology for developing and determining therapeutic modalities for MI that require accurate descriptions of myocardial mechanics. While substantial tissue volume reductions of 15-20% during systole have been reported, myocardium is commonly modeled as incompressible. We developed a myocardial model to simulate experimentally-observed systolic volume reductions in an ovine model of MI. Sheep-specific simulations of the cardiac cycle were performed using both incompressible and compressible tissue material models, and with synchronous or measurement-guided contraction. The compressible tissue model with measurement-guided contraction gave best agreement with experimentally measured reductions in tissue volume at peak systole, ventricular kinematics, and wall thickness changes. The incompressible model predicted myofiber peak contractile stresses approximately double the compressible model (182.8 kPa, 107.4 kPa respectively). Compensatory changes in remaining normal myocardium with MI present required less increase of contractile stress in the compressible model than the incompressible model (32.1%, 53.5%, respectively). The compressible model therefore provided more accurate representation of ventricular kinematics and potentially more realistic computed active contraction levels in the simulated infarcted heart. Our findings suggest that myocardial compressibility should be incorporated into future cardiac models for improved accuracy.

Machine learning approaches to surrogate multifidelity Growth and Remodeling models for efficient abdominal aortic aneurysmal applications

Computational Growth and Remodeling (G&R) models have been widely used to capture the pathological development of arterial diseases and have shown promise for aiding clinical diagnosis, prognosis prediction, and staging classification. However, due to the high complexity of the arterial adaptation mechanism, high-fidelity arterial G&R simulation usually takes hours or even days, which hinders its application in clinical practice. To remedy this problem, we develop a computationally efficient arterial G&R simulation framework that comprehensively combines the physics-based G&R simulations and data-driven machine learning approaches. The proposed framework greatly enhances the computational efficiency of arterial G&R simulations, thereby enabling more time-consuming arterial applications, including personalized parameter estimation and arterial disease progression prediction. In particular, we achieve significant computational cost reduction mainly through two methods: (1) constructing a Multifidelity Surrogate (MFS) to approximate multifidelity G&R simulations by using a cokriging approach and (2) developing a novel iterative optimization algorithm for personalized parameter estimation. The proposed framework is demonstrated by estimating G&R model parameters and predicting individual aneurysm growth using follow-up CT images of Abdominal Aortic Aneurysms (AAAs) from 21 patients. Results show that the personalized parameters are satisfactorily estimated and the growth of AAAs is predicted within the clinically relevant time frame, i.e., less than 2 h, without a loss of accuracy.

A Model for Studying the Biomechanical Effects of Varying Ratios of Collagen Types I and III on Cardiomyocytes

PURPOSE

To develop a novel model composed solely of Col I and Col III with the lower and upper limits set to include the ratios of Col I and Col III at 3:1 and 9:1 in which the structural and mechanical behavior of the resident CM can be studied. Further, the progression of fibrosis due to change in ratios of Col I:Col III was tested.

METHODS

Collagen gels with varying Col I:Col III ratios to represent a healthy (3:1) and diseased myocardial tissue were prepared by manually casting them in wells. Absorbance assay was performed to confirm the gelation of the gels. Rheometric analysis was performed on each of the collagen gels prepared to determine the varying stiffnesses and rheological parameters of the gels made with varying ratios of Col I:Col III. Second Harmonic Generation (SHG) was performed to observe the 3D characterization of the collagen samples. Scanning Electron microscopy was used for acquiring cross sectional images of the lyophilized collagen gels. AC16 CM (human) cell lines were cultured in the prepared gels to study cell morphology and behavior as a result of the varying collagen ratios. Cellular proliferation was studied by performing a Cell Trace Violet Assay and the applied force on each cell was measured by means of Finite Element Analysis (FEA) on CM from each sample.

RESULTS

Second harmonic generation microscopy used to image Col I, displayed a decrease in acquired image intensity with an increase in the non-second harmonic Col III in 3:1 gels. SEM showed a fiber-rich structure in the 3:1 gels with well-distributed pores unlike the 9:1 gels or the 1:0 controls. Rheological analysis showed a decrease in substrate stiffness with an increase of Col III, in comparison with other cases. CM cultured within 3:1 gels exhibited an elongated rod-like morphology with an average end-to-end length of 86 ± 28.8 µm characteristic of healthy CM, accompanied by higher cell growth in comparison with other cases. Finite element analysis used to estimate the forces exerted on CM cultured in the 3:1 gels, showed that the forces were well dispersed, and not concentrated within the center of cells, in comparison with other cases.

CONCLUSION

This study model can be adopted to simulate various biomechanical environments in which cells crosstalk with the Collagen-matrix in diseased pathologies to generate insights on strategies for prevention of fibrosis.

Computational models of cardiac hypertrophy

Cardiac hypertrophy, defined as an increase in mass of the heart, is a complex process driven by simultaneous changes in hemodynamics, mechanical stimuli, and hormonal inputs. It occurs not only during pre- and post-natal development but also in adults in response to exercise, pregnancy, and a range of cardiovascular diseases. One of the most exciting recent developments in the field of cardiac biomechanics is the advent of computational models that are able to accurately predict patterns of heart growth in many of these settings, particularly in cases where changes in mechanical loading of the heart play an import role. These emerging models may soon be capable of making patient-specific growth predictions that can be used to guide clinical interventions. Here, we review the history and current state of cardiac growth models and highlight three main limitations of current approaches with regard to future clinical application: their inability to predict the regression of heart growth after removal of a mechanical overload, inability to account for evolving hemodynamics, and inability to incorporate known growth effects of drugs and hormones on heart growth. Next, we outline growth mechanics approaches used in other fields of biomechanics and highlight some potential lessons for cardiac growth modeling. Finally, we propose a multiscale modeling approach for future studies that blends tissue-level growth models with cell-level signaling models to incorporate the effects of hormones in the context of pregnancy-induced heart growth.

Multiscale Modeling of Cardiovascular Function Predicts That the End-Systolic Pressure Volume Relationship Can Be Targeted via Multiple Therapeutic Strategies

Most patients who develop heart failure are unable to elevate their cardiac output on demand due to impaired contractility and/or reduced ventricular filling. Despite decades of research, few effective therapies for heart failure have been developed. In part, this may reflect the difficulty of predicting how perturbations to molecular-level mechanisms that are induced by drugs will scale up to modulate system-level properties such as blood pressure. Computer modeling might help with this process and thereby accelerate the development of better therapies for heart failure. This manuscript presents a new multiscale model that uses a single contractile element to drive an idealized ventricle that pumps blood around a closed circulation. The contractile element was formed by linking an existing model of dynamically coupled myofilaments with a well-established model of myocyte electrophysiology. The resulting framework spans from molecular-level events (including opening of ion channels and transitions between different myosin states) to properties such as ejection fraction that can be measured in patients. Initial calculations showed that the model reproduces many aspects of normal cardiovascular physiology including, for example, pressure-volume loops. Subsequent sensitivity tests then quantified how each model parameter influenced a range of system level properties. The first key finding was that the End Systolic Pressure Volume Relationship, a classic index of cardiac contractility, was ∼50% more sensitive to parameter changes than any other system-level property. The second important result was that parameters that primarily affect ventricular filling, such as passive stiffness and Ca²⁺ reuptake via sarco/endoplasmic reticulum Ca²⁺-ATPase (SERCA), also have a major impact on systolic properties including stroke work, myosin ATPase, and maximum ventricular pressure. These results reinforce the impact of diastolic function on ventricular performance and identify the End Systolic Pressure Volume Relationship as a particularly sensitive system-level property that can be targeted using multiple therapeutic strategies.

Biomechanics of infarcted left ventricle: a review of modelling

Mathematical modelling in biomechanics of infarcted left ventricle (LV) serves as an indispensable tool for remodelling mechanism exploration, LV biomechanical property estimation and therapy assessment after myocardial infarction (MI). However, a review of mathematical modelling after MI has not been seen in the literature so far. In the paper, a systematic review of mathematical models in biomechanics of infarcted LV was established. The models include comprehensive cardiovascular system model, essential LV pressure-volume and stress-stretch models, constitutive laws for passive myocardium and scars, tension models for active myocardium, collagen fibre orientation optimization models, fibroblast and collagen fibre growth/degradation models and integrated growth-electro-mechanical model after MI. The primary idea, unique characteristics and key equations of each model were identified and extracted. Discussions on the models were provided and followed research issues on them were addressed. Considerable improvements in the cardiovascular system model, LV aneurysm model, coupled agent-based models and integrated electro-mechanical-growth LV model are encouraged. Substantial attention should be paid to new constitutive laws with respect to stress-stretch curve and strain energy function for infarcted passive myocardium, collagen fibre orientation optimization in scar, cardiac rupture and tissue damage and viscoelastic effect post-MI in the future.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Biomechanics of infarcted left Ventricle-A review of experiments

Myocardial infarction (MI) is one of leading diseases to contribute to annual death rate of 5% in the world. In the past decades, significant work has been devoted to this subject. Biomechanics of infarcted left ventricle (LV) is associated with MI diagnosis, understanding of remodelling, MI micro-structure and biomechanical property characterizations as well as MI therapy design and optimization, but the subject has not been reviewed presently. In the article, biomechanics of infarcted LV was reviewed in terms of experiments achieved in the subject so far. The concerned content includes experimental remodelling, kinematics and kinetics of infarcted LVs. A few important issues were discussed and several essential topics that need to be investigated further were summarized. Microstructure of MI tissue should be observed even carefully and compared between different methods for producing MI scar in the same animal model, and eventually correlated to passive biomechanical property by establishing innovative constitutive laws. More uniaxial or biaxial tensile tests are desirable on MI, border and remote tissues, and viscoelastic property identification should be performed in various time scales. Active contraction experiments on LV wall with MI should be conducted to clarify impaired LV pumping function and supply necessary data to the function modelling. Pressure-volume curves of LV with MI during diastole and systole for the human are also desirable to propose and validate constitutive laws for LV walls with MI.

Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression

A key feature of living tissues is their capacity to remodel and grow in response to environmental cues. Within continuum mechanics, this process can be captured with the multiplicative split of the deformation gradient into growth and elastic contributions. The mechanical and biological response during tissue adaptation is characterized by inherent variability. Accounting for this uncertainty is critical to better understand tissue mechanobiology, and, moreover, it is of practical importance if we aim to develop predictive models for clinical use. However, the current gold standard in computational models of growth and remodeling remains the use of deterministic finite element (FE) simulations. Here we focus on tissue expansion, a popular technique in which skin is stretched by a balloon-like device inducing its growth. We construct FE models of tissue expansion with various levels of detail, and show that a sufficiently broad set of FE simulations from these models can be used to train an accurate and efficient multi-fidelity Gaussian process (GP) surrogate. The approach is not limited to simulation data, rather, it can fuse different kinds of data, including from experiments. The main appeal of the framework relies on the common experience that highly detailed models (or experiments) are more accurate but also more costly, while simpler models (or experiments) can be easily evaluated but are bound to have some error. In these situations, doing uncertainty analysis tasks with the high fidelity models alone is not feasible and, conversely, relying solely on low fidelity approximations is also undesirable. We show that a multi-fidelity GP outperforms the high fidelity GP and low fidelity GP when tested against the most detailed FE model. In turn, having trained the multi-fidelity GP model, we showcase the propagation of uncertainty from the mechanical and biological response parameters to the spatio-temporal growth outcomes. We expect that the methods and applications in this paper will enable future research in parameter calibration under uncertainty and uncertainty propagation in real clinical scenarios involving tissue growth and remodeling.

Model of Anisotropic Reverse Cardiac Growth in Mechanical Dyssynchrony

Based on recent single-cell experiments showing that longitudinal myocyte stretch produces both parallel and serial addition of sarcomeres, we developed an anisotropic growth constitutive model with elastic myofiber stretch as the growth stimuli to simulate long-term changes in biventricular geometry associated with alterations in cardiac electromechanics. The constitutive model is developed based on the volumetric growth framework. In the model, local growth evolutions of the myocyte’s longitudinal and transverse directions are driven by the deviations of maximum elastic myofiber stretch over a cardiac cycle from its corresponding local homeostatic set point, but with different sensitivities. Local homeostatic set point is determined from a simulation with normal activation pattern. The growth constitutive model is coupled to an electromechanics model and calibrated based on both global and local ventricular geometrical changes associated with chronic left ventricular free wall pacing found in previous animal experiments. We show that the coupled electromechanics-growth model can quantitatively reproduce the following: (1) Thinning and thickening of the ventricular wall respectively at early and late activated regions and (2) Global left ventricular dilation as measured in experiments. These findings reinforce the role of elastic myofiber stretch as a growth stimulant at both cellular level and tissue-level.

Multiscale characterization of heart failure

Dilated cardiomyopathy is a progressive irreversible disease associated with contractile dysfunction and heart failure. During dilated cardiomyopathy, elevated diastolic wall strains trigger mechanotransduction pathways that initiate the addition of sarcomeres in series and an overall increase in myocyte length. At the whole organ level, this results in a chronic dilation of the ventricles, an increase in end diastolic and end systolic volumes, and a decrease in ejection fraction. However, how exactly changes in sarcomere number translate into changes in myocyte morphology, and how these cellular changes translate into ventricular dilation remains incompletely understood. Here we combined a chronic animal study, continuum growth modeling, and machine learning to quantify correlations between sarcomere dynamics, myocyte morphology, and ventricular dilation. In an eight-week long volume overload study of six pigs, we found that the average sarcomere number increased by +3.8%/week, from 47 to 62, resulting in a myocyte lengthening of +3.3%/week, from 85 to 108 μm, while the sarcomere length and myocyte width remained unchanged. At the same time, the average end diastolic volume increased by +6.0%/week. Using continuum growth modeling and Bayesian inference, we correlated alterations on the subcellular, cellular, and organ scales and found that the serial sarcomere number explained 88% of myocyte lengthening, which, in turn, explained 54% of cardiac dilation. Our results demonstrate that sarcomere number and myocyte length are closely correlated and constitute the major determinants of dilated heart failure. We anticipate our study to be a starting point for more sophisticated multiscale models of heart failure. Our study suggests that altering sarcomere turnover-and with it myocyte morphology and ventricular dimensions-could be a potential therapeutic target to attenuate or reverse the progression of heart failure. STATEMENT OF SIGNIFICANCE: Heart failure is a significant global health problem that affects more than 25 million people worldwide and increases in prevalence as the population ages. Heart failure has been studied excessively at various scales; yet, there is no compelling concept to connect knowledge from the subcellular, cellular, and organ level across the scales. Here we combined a chronic animal study, continuum growth modeling, and machine learning to quantify correlations between sarcomere dynamics, myocyte morphology, and ventricular dilation. We found that the serial sarcomere number explained 88% of myocyte lengthening, which, in turn, explained 54% of cardiac dilation. Our results show that sarcomere number and myocyte length are closely correlated and constitute the major determinants of dilated heart failure. This suggests that altering the sarcomere turnover-and with it myocyte morphology and ventricular dimensions-could be a potential therapeutic target to attenuate or reverse heart failure.

Comprehensive computational assessment of blood flow characteristics of left ventricle based on in-vivo MRI in presence of artificial myocardial infarction

BACKGROUND

Understanding the effects of cardiac diseases on the heart's functionality which is the purpose of many biomedical researches, directly affects the diagnostic and therapeutic methods. Myocardial infarction (MI) is a common complication of cardiac ischemia, however, the impact of MI on the left ventricle (LV) flow patterns has not been widely considered by computational fluid dynamics studies thus far.

METHODS

In this study, we present an insightful numerical method that creates an artificial MI on an image-based fluid-structure interactional model of normal LV to investigate its influence on the flow in comparison with the normal case. Seventeen different models were developed to evaluate the effects of location, percentage, myocardial material properties and dilation size of MI on the LV's performance, area strain, wall displacement, pressure-volume loop, wall shear stress and velocity field.

RESULTS

The results show that MI considerably changes blood flow features which are fully dependent on MI parameters. For the case of constant MI location, the effect of a decrease of infarcted myocardium stiffness, increase of dilation size and increase of MI percentage are mostly similar. Although the location differences of MI under other constant conditions have similar impact on the ejection fraction, they also lead to dissimilar variations in the LV flow pattern and other indicators.

CONCLUSIONS

The presented model showed a capable computational method for investigating various mechanical MI conditions with respect to cardiac flow pattern. The perspective of this model development seems to be an applicable tool for MI clinical diagnosis and prediction of complications related to MI.

MODELING HEART TISSUE AS A MICROMORPHIC MEDIUM: A NUMERICAL INVESTIGATION

Recent years have seen a renewed interest in the theories of extended continuum mechanics. These allow for a finer and relatively simple modeling of physical phenomena occurring on the microscopic level. The Eringen’s micromorphic medium belongs to this class and allows accounting for the material microstructure. A subclass of this model was applied to model the mechanical behavior of cardiac tissue. With the aid of a specifically developed numerical tool, the validity of the approach is demonstrated using different myocardial infarct scenario.

On the biomechanical analysis of the calories expended in a straight boxing jab

Boxing and related sports activities have become a standard workout regime at many fitness studios worldwide. Oftentimes, people are interested in the calories expended during these workouts. This note focuses on determining the calories in a boxer's jab, using kinematic vector-loop relations and basic work-energy principles. Numerical simulations are undertaken to illustrate the basic model. Multi-limb extensions of the model are also discussed.

In vivo assessment of regional mechanics post-myocardial infarction: A focus on the road ahead

Cardiovascular disease, particularly the occurrence of myocardial infarction (MI), remains a leading cause of morbidity and mortality (Go et al., Circulation 127: e6-e245, 2013; Go et al. Circulation 129: e28-e292, 2014). There is growing recognition that a key factor for post-MI outcomes is adverse remodeling and changes in the regional structure, composition, and mechanical properties of the MI region itself. However, in vivo assessment of regional mechanics post-MI can be confounded by the species, temporal aspects of MI healing, as well as size, location, and extent of infarction across myocardial wall. Moreover, MI regional mechanics have been assessed over varying phases of the cardiac cycle, and thus, uniform conclusions regarding the material properties of the MI region can be difficult. This review assesses past studies that have performed in vivo measures of MI mechanics and attempts to provide coalescence on key points from these studies, as well as offer potential recommendations for unifying approaches in terms of regional post-MI mechanics. A uniform approach to biophysical measures of import will allow comparisons across studies, as well as provide a basis for potential therapeutic markers.

Sonomicrometry-Based Analysis of Post-Myocardial Infarction Regional Mechanics

Following myocardial infarction (MI), detrimental changes to the geometry, composition, and mechanical properties of the left ventricle (LV) are initiated in a process generally termed adverse post-MI remodeling. Cumulatively, these changes lead to a loss of LV function and are deterministic factors in the progression to heart failure. Proposed therapeutic strategies to target aberrant LV mechanics post-MI have shown potential to stabilize LV functional indices throughout the remodeling process. The in vivo quantification of LV mechanics, particularly within the MI region, is therefore essential to the continued development and evaluation of strategies to interrupt the post-MI remodeling process. The present study utilizes a porcine MI model and in vivo sonomicrometry to characterize MI region stiffness at 14 days post-MI. Obtained results demonstrate a significant dependence of mechanical properties on location and direction within the MI region, as well as cardiac phase. While approaches for comprehensive characterization of LV mechanics post-MI still need to be improved and standardized, our findings provide insight into the issues and complexities that must be considered within the MI region itself.

An integrated electromechanical-growth heart model for simulating cardiac therapies

An emerging class of models has been developed in recent years to predict cardiac growth and remodeling (G&R). We recently developed a cardiac G&R constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this G&R model to an existing strongly coupled electromechanical model of the heart. A separation of timescale between growth deformation and elastic deformation was invoked in this integrated electromechanical-growth heart model. To test our model, we applied the G&R scheme to simulate the effects of myocardial infarction in a realistic left ventricular (LV) geometry using the finite element method. We also simulate the effects of a novel therapy that is based on alteration of the infarct mechanical properties. We show that our proposed model is able to predict key features that are consistent with experiments. Specifically, we show that the presence of a non-contractile infarct leads to a dilation of the left ventricle that results in a rightward shift of the pressure volume loop. Our model also predicts that G&R is attenuated by a reduction in LV dilation when the infarct stiffness is increased.

Heterogeneous growth-induced prestrain in the heart

Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung׳s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6±13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

The Living Heart Project: A robust and integrative simulator for human heart function

The heart is not only our most vital, but also our most complex organ: Precisely controlled by the interplay of electrical and mechanical fields, it consists of four chambers and four valves, which act in concert to regulate its filling, ejection, and overall pump function. While numerous computational models exist to study either the electrical or the mechanical response of its individual chambers, the integrative electro-mechanical response of the whole heart remains poorly understood. Here we present a proof-of-concept simulator for a four-chamber human heart model created from computer topography and magnetic resonance images. We illustrate the governing equations of excitation-contraction coupling and discretize them using a single, unified finite element environment. To illustrate the basic features of our model, we visualize the electrical potential and the mechanical deformation across the human heart throughout its cardiac cycle. To compare our simulation against common metrics of cardiac function, we extract the pressure-volume relationship and show that it agrees well with clinical observations. Our prototype model allows us to explore and understand the key features, physics, and technologies to create an integrative, predictive model of the living human heart. Ultimately, our simulator will open opportunities to probe landscapes of clinical parameters, and guide device design and treatment planning in cardiac diseases such as stenosis, regurgitation, or prolapse of the aortic, pulmonary, tricuspid, or mitral valve.

A computational model that predicts reverse growth in response to mechanical unloading

Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure-volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.

Computational modeling of hypertensive growth in the human carotid artery

Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.

Distribution of normal human left ventricular myofiber stress at end diastole and end systole: a target for in silico design of heart failure treatments

Ventricular wall stress is believed to be responsible for many physical mechanisms taking place in the human heart, including ventricular remodeling, which is frequently associated with heart failure. Therefore, normalization of ventricular wall stress is the cornerstone of many existing and new treatments for heart failure. In this paper, we sought to construct reference maps of normal ventricular wall stress in humans that could be used as a target for in silico optimization studies of existing and potential new treatments for heart failure. To do so, we constructed personalized computational models of the left ventricles of five normal human subjects using magnetic resonance images and the finite-element method. These models were calibrated using left ventricular volume data extracted from magnetic resonance imaging (MRI) and validated through comparison with strain measurements from tagged MRI (950 ± 170 strain comparisons/subject). The calibrated passive material parameter values were C0 = 0.115 ± 0.008 kPa and B0 = 14.4 ± 3.18; the active material parameter value was Tmax = 143 ± 11.1 kPa. These values could serve as a reference for future construction of normal human left ventricular computational models. The differences between the predicted and the measured circumferential and longitudinal strains in each subject were 3.4 ± 6.3 and 0.5 ± 5.9%, respectively. The predicted end-diastolic and end-systolic myofiber stress fields for the five subjects were 2.21 ± 0.58 and 16.54 ± 4.73 kPa, respectively. Thus these stresses could serve as targets for in silico design of heart failure treatments.

Mechanically driven accumulation of microscale material at coupled solid-fluid interfaces in biological channels

The accumulation of microscale materials at solid-fluid interfaces in biological channels is often the initial stage of certain growth processes, which are present in some forms of atherosclerosis. The objective of this work is to develop a relatively simple model for such accumulation, which researchers can use to qualitatively guide their analyses. Specifically, the approach is to construct rate equations for the accumulation at the solid-fluid interface as a function of the intensity of the shear stress. The accumulation of material subsequently reduces the cross-sectional area of the channel until the fluid-induced shear stress at the solid-fluid interface reaches a critical value, which terminates the accumulation rate. Characteristics of the model are explored analytically and numerically.

Growing matter: a review of growth in living systems

Living systems can grow, develop, adapt, and evolve. These phenomena are non-intuitive to traditional engineers and often difficult to understand. Yet, classical engineering tools can provide valuable insight into the mechanisms of growth in health and disease. Within the past decade, the concept of incompatible configurations has evolved as a powerful tool to model growing systems within the framework of nonlinear continuum mechanics. However, there is still a substantial disconnect between the individual disciplines, which explore the phenomenon of growth from different angles. Here we show that the nonlinear field theories of mechanics provide a unified concept to model finite growth by means of a single tensorial internal variable, the second order growth tensor. We review the literature and categorize existing growth models by means of two criteria: the microstructural appearance of growth, either isotropic or anisotropic; and the microenvironmental cues that drive the growth process, either chemical or mechanical. We demonstrate that this generic concept is applicable to a broad range of phenomena such as growing arteries, growing tumors, growing skin, growing airway walls, growing heart valve leaflets, growing skeletal muscle, growing plant stems, growing heart valve annuli, and growing cardiac muscle. The proposed approach has important biological and clinical applications in atherosclerosis, in-stent restenosis, tumor invasion, tissue expansion, chronic bronchitis, mitral regurgitation, limb lengthening, tendon tear, plant physiology, dilated and hypertrophic cardiomyopathy, and heart failure. Understanding the mechanisms of growth in these chronic conditions may open new avenues in medical device design and personalized medicine to surgically or pharmacologically manipulate development and alter, control, or revert disease progression.

Stretching skeletal muscle: chronic muscle lengthening through sarcomerogenesis

Skeletal muscle responds to passive overstretch through sarcomerogenesis, the creation and serial deposition of new sarcomere units. Sarcomerogenesis is critical to muscle function: It gradually re-positions the muscle back into its optimal operating regime. Animal models of immobilization, limb lengthening, and tendon transfer have provided significant insight into muscle adaptation in vivo. Yet, to date, there is no mathematical model that allows us to predict how skeletal muscle adapts to mechanical stretch in silico. Here we propose a novel mechanistic model for chronic longitudinal muscle growth in response to passive mechanical stretch. We characterize growth through a single scalar-valued internal variable, the serial sarcomere number. Sarcomerogenesis, the evolution of this variable, is driven by the elastic mechanical stretch. To analyze realistic three-dimensional muscle geometries, we embed our model into a nonlinear finite element framework. In a chronic limb lengthening study with a muscle stretch of 1.14, the model predicts an acute sarcomere lengthening from 3.09m to 3.51m, and a chronic gradual return to the initial sarcomere length within two weeks. Compared to the experiment, the acute model error was 0.00% by design of the model; the chronic model error was 2.13%, which lies within the rage of the experimental standard deviation. Our model explains, from a mechanistic point of view, why gradual multi-step muscle lengthening is less invasive than single-step lengthening. It also explains regional variations in sarcomere length, shorter close to and longer away from the muscle-tendon interface. Once calibrated with a richer data set, our model may help surgeons to prevent muscle overstretch and make informed decisions about optimal stretch increments, stretch timing, and stretch amplitudes. We anticipate our study to open new avenues in orthopedic and reconstructive surgery and enhance treatment for patients with ill proportioned limbs, tendon lengthening, tendon transfer, tendon tear, and chronically retracted muscles.

Frontiers in growth and remodeling

Unlike common engineering materials, living matter can autonomously respond to environmental changes. Living structures can grow stronger, weaker, larger, or smaller within months, weeks, or days as a result of a continuous microstructural turnover and renewal. Hard tissues can adapt by increasing their density and grow strong. Soft tissues can adapt by increasing their volume and grow large. For more than three decades, the mechanics community has actively contributed to understand the phenomena of growth and remodeling from a mechanistic point of view. However, to date, there is no single, unified characterization of growth, which is equally accepted by all scientists in the field. Here we shed light on the continuum modeling of growth and remodeling of living matter, and give a comprehensive overview of historical developments and trends. We provide a state-of-the-art review of current research highlights, and discuss challenges and potential future directions. Using the example of volumetric growth, we illustrate how we can establish and utilize growth theories to characterize the functional adaptation of soft living matter. We anticipate this review to be the starting point for critical discussions and future research in growth and remodeling, with a potential impact on life science and medicine.

Kinematics of cardiac growth: in vivo characterization of growth tensors and strains

Progressive growth and remodeling of the left ventricle are part of the natural history of chronic heart failure and strong clinical indicators for survival. Accompanied by changes in cardiac form and function, they manifest themselves in alterations of cardiac strains, fiber stretches, and muscle volume. Recent attempts to shed light on the mechanistic origin of heart failure utilize continuum theories of growth to predict the maladaptation of the heart in response to pressure or volume overload. However, despite a general consensus on the representation of growth through a second order tensor, the precise format of this growth tensor remains unknown. Here we show that infarct-induced cardiac dilation is associated with a chronic longitudinal growth, accompanied by a chronic thinning of the ventricular wall. In controlled in vivo experiments throughout a period of seven weeks, we found that the lateral left ventricular wall adjacent to the infarct grows longitudinally by more than 10%, thins by more than 25%, lengthens in fiber direction by more than 5%, and decreases its volume by more than 15%. Our results illustrate how a local loss of blood supply induces chronic alterations in structure and function in adjacent regions of the ventricular wall. We anticipate our findings to be the starting point for a series of in vivo studies to calibrate and validate constitutive models for cardiac growth. Ultimately, these models could be useful to guide the design of novel therapies, which allow us to control the progression of heart failure.