Multiscale homogenized constrained mixture model of the bio-chemo-mechanics of soft tissue growth and remodeling.

Constrained mixture models have successfully simulated many cases of growth and remodeling in soft biological tissues. So far, extensions of these models have been proposed to include either intracellular signaling or chemo-mechanical coupling on the organ-scale. However, no version of constrained mixture models currently exists that includes both aspects. Here, we propose such a version that resolves cellular signal processing by a set of logic-gated ordinary differential equations and captures chemo-mechanical interactions between cells by coupling a reaction-diffusion equation with the equations of nonlinear continuum mechanics. To demonstrate the potential of the model, we present 2 case studies within vascular solid mechanics: (i) the influence of angiotensin II on aortic growth and remodeling and (ii) the effect of communication between endothelial and intramural arterial cells via nitric oxide and endothelin-1.

Computational analysis of heart valve growth and remodeling after the Ross procedure.

During the Ross procedure, an aortic heart valve is replaced by a patient's own pulmonary valve. The pulmonary autograft subsequently undergoes substantial growth and remodeling (G&R) due to its exposure to increased hemodynamic loads. In this study, we developed a homogenized constrained mixture model to understand the observed adaptation of the autograft leaflets in response to the changed hemodynamic environment. This model was based on the hypothesis that tissue G&R aims to preserve mechanical homeostasis for each tissue constituent. To model the Ross procedure, we simulated the exposure of a pulmonary valve to aortic pressure conditions and the subsequent G&R of the valve. Specifically, we investigated the effects of assuming either stress- or stretch-based mechanical homeostasis, the use of blood pressure control, and the effect of root dilation. With this model, we could explain different observations from published clinical studies, such as the increase in thickness, change in collagen organization, and change in tissue composition. In addition, we found that G&R based on stress-based homeostasis could better capture the observed changes in tissue composition than G&R based on stretch-based homeostasis, and that root dilation or blood pressure control can result in more leaflet elongation. Finally, our model demonstrated that successful adaptation can only occur when the mechanically induced tissue deposition is sufficiently larger than tissue degradation, such that leaflet thickening overrules leaflet dilation. In conclusion, our findings demonstrated that G&R based on mechanical homeostasis can capture the observed heart valve adaptation after the Ross procedure. Finally, this study presents a novel homogenized mixture model that can be used to investigate other cases of heart valve G&R as well.

Dynamic biaxial loading of vascular smooth muscle cell seeded tissue equivalents.

An intricate reciprocal relationship exists between adherent synthetic cells and their extracellular matrix (ECM). These cells deposit, organize, and degrade the ECM, which in turn influences cell phenotype via responses that include sensitivity to changes in the mechanical state that arises from changes in external loading. Collagen-based tissue equivalents are commonly used as simple but revealing model systems to study cell-matrix interactions. Nevertheless, few quantitative studies report changes in the forces that the cells establish and maintain in such gels under dynamic loading. Moreover, most prior studies have been limited to uniaxial experiments despite many soft tissues, including arteries, experiencing multiaxial loading in vivo. To begin to close this gap, we use a custom biaxial bioreactor to subject collagen gels seeded with primary aortic smooth muscle cells to different biaxial loading conditions. These conditions include cyclic loading with different amplitudes as well as different mechanical constraints at the boundaries of a cruciform sample. Irrespective of loading amplitude and boundary condition, similar mean steady-state biaxial forces emerged across all tests. Additionally, stiffness-force relationships assessed via intermittent equibiaxial force-extension tests showed remarkable similarity for ranges of forces to which the cells adapted during periods of cyclic loading. Taken together, these findings are consistent with a load-mediated homeostatic response by vascular smooth muscle cells.

Gene regulatory network analysis identifies MYL1, MDH2, GLS, and TRIM28 as the principal proteins in the response of mesenchymal stem cells to Mg2+ ions.

Magnesium (Mg)-based implants have emerged as a promising alternative for orthopedic applications, owing to their bioactive properties and biodegradability. As the implants degrade, Mg2+ ions are released, influencing all surrounding cell types, especially mesenchymal stem cells (MSCs). MSCs are vital for bone tissue regeneration, therefore, it is essential to understand their molecular response to Mg2+ ions in order to maximize the potential of Mg-based biomaterials. In this study, we conducted a gene regulatory network (GRN) analysis to examine the molecular responses of MSCs to Mg2+ ions. We used time-series proteomics data collected at 11 time points across a 21-day period for the GRN construction. We studied the impact of Mg2+ ions on the resulting networks and identified the key proteins and protein interactions affected by the application of Mg2+ ions. Our analysis highlights MYL1, MDH2, GLS, and TRIM28 as the primary targets of Mg2+ ions in the response of MSCs during 1-21 days phase. Our results also identify MDH2-MYL1, MDH2-RPS26, TRIM28-AK1, TRIM28-SOD2, and GLS-AK1 as the critical protein relationships affected by Mg2+ ions. By offering a comprehensive understanding of the regulatory role of Mg2+ ions on MSCs, our study contributes valuable insights into the molecular response of MSCs to Mg-based materials, thereby facilitating the development of innovative therapeutic strategies for orthopedic applications.

A homogenized constrained mixture model of cardiac growth and remodeling: analyzing mechanobiological stability and reversal.

Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extracellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.

What are the key mechanical mechanisms governing integrin-mediated cell migration in three-dimensional fiber networks?

Cell migration plays a vital role in numerous processes such as development, wound healing, or cancer. It is well known that numerous complex mechanisms are involved in cell migration. However, so far it remains poorly understood what are the key mechanisms required to produce the main characteristics of this behavior. The reason is a methodological one. In experimental studies, specific factors and mechanisms can be promoted or inhibited. However, while doing so, there can always be others in the background which play key roles but which have simply remained unattended so far. This makes it very difficult to validate any hypothesis about a minimal set of factors and mechanisms required to produce cell migration. To overcome this natural limitation of experimental studies, we developed a computational model where cells and extracellular matrix fibers are represented by discrete mechanical objects on the micrometer scale. In this model, we had exact control of the mechanisms by which cells and matrix fibers interacted with each other. This enabled us to identify the key mechanisms required to produce physiologically realistic cell migration (including advanced phenomena such as durotaxis and a biphasic relation between migration efficiency and matrix stiffness). We found that two main mechanisms are required to this end: a catch-slip bond of individual integrins and cytoskeletal actin-myosin contraction. Notably, more advanced phenomena such as cell polarization or details of mechanosensing were not necessary to qualitatively reproduce the main characteristics of cell migration observed in experiments.

Strength and ductility loss of Magnesium-Gadolinium due to corrosion in physiological environment: Experiments and modeling.

We propose a computational framework to study the effect of corrosion on the mechanical strength of magnesium (Mg) samples. Our work is motivated by the need to predict the residual strength of biomedical Mg implants after a given period of degradation in a physiological environment. To model corrosion, a mass-diffusion type model is used that accounts for localised corrosion using Weibull statistics. The overall mass loss is prescribed (e.g., based on experimental data). The mechanical behaviour of the Mg samples is modeled by a state-of-the-art Cazacu-Plunkett-Barlat plasticity model with a coupled damage model. This allowed us to study how Mg degradation in immersed samples reduces the mechanical strength over time. We performed a large number of in vitro corrosion experiments and mechanical tests to validate our computational framework. Our framework could predict both the experimentally observed loss of mechanical strength and the ductility due to corrosion for both tension and compression tests.

Role of slice thickness quantification in the 3D reconstruction of FIB tomography data of nanoporous materials.

In focused ion beam (FIB) tomography, a combination of FIB with a scanning electron microscope (SEM) is used for collecting a series of planar images of the microstructure of nanoporous materials. These planar images serve as the basis for reconstructing the three-dimensional microstructure through segmentation algorithms. However, the assumption of a constant distance between consecutively imaged sections is generally invalid due to random variations in the FIB milling process. This variation complicates the accurate reconstruction of the three-dimensional microstructure. Using synthetic FIB tomography data, we present an algorithm that repositions slices according to their actual thickness and interpolates the results using machine learning-based methods. We applied our algorithm to real datasets, comparing two standard approaches of microstructure reconstruction: on-the-fly via image processing and ruler-based via sample structuring. Our findings indicate that the ruler-based method, combined with our novel slice repositioning and interpolation algorithm, exhibits superior performance in reconstructing the microstructure.

Predicting and understanding arterial elasticity from key microstructural features by bidirectional deep learning.

Microstructural features and mechanical properties are closely related in all soft biological tissues. Both yet exhibit considerable inter-individual differences and are affected by factors such as aging and disease and its progression. Histological analysis, modern in situ imaging, and biomechanical testing have deepened our understanding of these complex interrelations, yet two key questions remain: (1) Given the specific microstructure, can one predict the macroscopic mechanical properties without mechanical testing? (2) Can one quantify individual contributions of the different microstructural features to the macroscopic mechanical properties in an automated, systematic and largely unbiased way? Here we propose a bidirectional deep learning architecture to address these two questions. Our architecture uses data from standard histological analyses, two-photon microscopy and biaxial biomechanical testing. Its capabilities are demonstrated by predicting with high accuracy (R2=0.92) the evolving mechanical properties of the murine aorta during maturation and aging. Moreover, our architecture reveals that the extracellular matrix composition and organization are the most prominent factors governing the macroscopic mechanical properties of the tissues studied herein. STATEMENT OF SIGNIFICANCE: We present a physics-informed machine learning architecture that can predict macroscopic mechanical properties of arterial tissue with high accuracy (R2=0.92) from the tissue microstructure (characterized by imaging data). For the first time, this architecture enables also a fully automatic and largely unbiased quantification of the relevance of different microstructural features (such as collagen volume fraction and fiber straightness) for the macroscopic mechanical properties. This approach opens up unprecedented ways to predictive mechanical modeling of soft biological tissues. Moreover, it provides quantitative insights into the relation between tissue microstructure and its macroscopic properties that promise to play an important role in future tissue engineering.

Ultrasound Shear Wave Elasticity Imaging With Spatio-Temporal Deep Learning.

Ultrasound shear wave elasticity imaging is a valuable tool for quantifying the elastic properties of tissue. Typically, the shear wave velocity is derived and mapped to an elasticity value, which neglects information such as the shape of the propagating shear wave or push sequence characteristics. We present 3D spatio-temporal CNNs for fast local elasticity estimation from ultrasound data. This approach is based on retrieving elastic properties from shear wave propagation within small local regions. A large training data set is acquired with a robot from homogeneous gelatin phantoms ranging from 17.42 kPa to 126.05 kPa with various push locations. The results show that our approach can estimate elastic properties on a pixelwise basis with a mean absolute error of 5.01(437) kPa. Furthermore, we estimate local elasticity independent of the push location and can even perform accurate estimates inside the push region. For phantoms with embedded inclusions, we report a 53.93% lower MAE (7.50 kPa) and on the background of 85.24% (1.64 kPa) compared to a conventional shear wave method. Overall, our method offers fast local estimations of elastic properties with small spatio-temporal window sizes.

Comment on "Tensional homeostasis at different length scales" by D. Stamenovic and M. L. Smith, Soft Matter, 2021, 17, 10274-10285, DOI: 10.1039/D0SM01911A.

Many cell-types that reside within load bearing tissues appear to exhibit mechanical homeostasis, that is, a tendency to regulate particular mechanical quantities near a preferred value, often called a set-point. It is suggested here that assessing potential mechanical homeostasis requires careful attention to derivations and definitions, that is, appropriate solutions to the initial-boundary value problems that define the biophysical situation of interest and appropriate definitions of what is meant by homeostasis. Noting that this term was coined carefully, with homeo meaning "similar to" in contrast to homo meaning "the same as", one must be careful not only to identify the key mechano-regulated quantity (e.g., a stress rather than a flow or a force) but also the tolerance that defines the range of regulation, noting too that the specific target value of that variable may differ from region to region within the body while yet being regulated locally. Herein, we present a few examples to highlight specific derivations and definitions of importance when studying mechanical homeostasis across scales.

Neural network surgery: Combining training with topology optimization.

With ever increasing computational capacities, neural networks become more and more proficient at solving complex tasks. However, picking a sufficiently good network topology usually relies on expert human knowledge. Neural architecture search aims to reduce the extent of expertise that is needed. Modern architecture search techniques often rely on immense computational power, or apply trained meta-controllers for decision making. We develop a framework for a genetic algorithm that is both computationally cheap and makes decisions based on mathematical criteria rather than trained parameters. It is a hybrid approach that fuses training and topology optimization together into one process. Structural modifications that are performed include adding or removing layers of neurons, with some re-training applied to make up for any incurred change in input-output behaviour. Our ansatz is tested on several benchmark datasets with limited computational overhead compared to training only the baseline. This algorithm can achieve a significant increase in accuracy (as compared to a fully trained baseline), rescue insufficient topologies that in their current state are only able to learn to a limited extent, and dynamically reduce network size without loss in achieved accuracy. On standard ML datasets, accuracy improvements compared to baseline performance can range from 20% for well performing starting topologies to more than 40% in case of insufficient baselines, or reduce network size by almost 15%.

Unraveling the Local Relation Between Tissue Composition and Human Brain Mechanics Through Machine Learning.

The regional mechanical properties of brain tissue are not only key in the context of brain injury and its vulnerability towards mechanical loads, but also affect the behavior and functionality of brain cells. Due to the extremely soft nature of brain tissue, its mechanical characterization is challenging. The response to loading depends on length and time scales and is characterized by nonlinearity, compression-tension asymmetry, conditioning, and stress relaxation. In addition, the regional heterogeneity-both in mechanics and microstructure-complicates the comprehensive understanding of local tissue properties and its relation to the underlying microstructure. Here, we combine large-strain biomechanical tests with enzyme-linked immunosorbent assays (ELISA) and develop an extended type of constitutive artificial neural networks (CANNs) that can account for viscoelastic effects. We show that our viscoelastic constitutive artificial neural network is able to describe the tissue response in different brain regions and quantify the relevance of different cellular and extracellular components for time-independent (nonlinearity, compression-tension-asymmetry) and time-dependent (hysteresis, conditioning, stress relaxation) tissue mechanics, respectively. Our results suggest that the content of the extracellular matrix protein fibronectin is highly relevant for both the quasi-elastic behavior and viscoelastic effects of brain tissue. While the quasi-elastic response seems to be largely controlled by extracellular matrix proteins from the basement membrane, cellular components have a higher relevance for the viscoelastic response. Our findings advance our understanding of microstructure - mechanics relations in human brain tissue and are valuable to further advance predictive material models for finite element simulations or to design biomaterials for tissue engineering and 3D printing applications.

Predictive constitutive modelling of arteries by deep learning.

The constitutive modelling of soft biological tissues has rapidly gained attention over the last 20 years. Current constitutive models can describe the mechanical properties of arterial tissue. Predicting these properties from microstructural information, however, remains an elusive goal. To address this challenge, we are introducing a novel hybrid modelling framework that combines advanced theoretical concepts with deep learning. It uses data from mechanical tests, histological analysis and images from second-harmonic generation. In this first proof of concept study, our hybrid modelling framework is trained with data from 27 tissue samples only. Even such a small amount of data is sufficient to be able to predict the stress-stretch curves of tissue samples with a median coefficient of determination of R2 = 0.97 from microstructural information, as long as one limits the scope to tissue samples whose mechanical properties remain in the range commonly encountered. This finding suggests that deep learning could have a transformative impact on the way we model the constitutive properties of soft biological tissues.

What do cells regulate in soft tissues on short time scales?

Cells within living soft biological tissues seem to promote the maintenance of a mechanical state within a defined range near a so-called set-point. This mechanobiological process is often referred to as mechanical homeostasis. During this process, cells interact with the fibers of the surrounding extracellular matrix (ECM). It remains poorly understood, however, what individual cells actually regulate during these interactions, and how these micromechanical regulations are translated to the tissue-level to lead to what we observe as biomaterial properties. Herein, we examine this question by a combination of experiments, theoretical analysis, and computational modeling. We demonstrate that on short time scales (hours) - during which deposition and degradation of ECM fibers can largely be neglected - cells appear to not regulate the stress / strain in the ECM or their own shape, but rather only the contractile forces that they exert on the surrounding ECM. STATEMENT OF SIGNIFICANCE: Cells in soft biological tissues sense and regulate the mechanical state of the extracellular matrix to ensure structural integrity and functionality. This so-called mechanical homeostasis plays an important role in the natural history of various diseases such as aneurysms in the cardiovascular system or cancer. Yet, it remains poorly understood to date which target quantity cells regulate on the mircroscale and how it translates to the macroscale. In this paper, we combine experiments, computer simulations, and theoretical analysis to compare different hypotheses about this target quantity. This allows us to identify a likely candidate for it at least on short time scales and in the simplified environment of tissue equivalents.

A computational framework for modeling cell-matrix interactions in soft biological tissues.

Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

Mechanical homeostasis in tissue equivalents: a review.

There is substantial evidence that growth and remodeling of load bearing soft biological tissues is to a large extent controlled by mechanical factors. Mechanical homeostasis, which describes the natural tendency of such tissues to establish, maintain, or restore a preferred mechanical state, is thought to be one mechanism by which such control is achieved across multiple scales. Yet, many questions remain regarding what promotes or prevents homeostasis. Tissue equivalents, such as collagen gels seeded with living cells, have become an important tool to address these open questions under well-defined, though limited, conditions. This article briefly reviews the current state of research in this area. It summarizes, categorizes, and compares experimental observations from the literature that focus on the development of tension in tissue equivalents. It focuses primarily on uniaxial and biaxial experimental studies, which are well-suited for quantifying interactions between mechanics and biology. The article concludes with a brief discussion of key questions for future research in this field.

Growth and remodelling of living tissues: perspectives, challenges and opportunities.

One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.

Anisotropic stiffness and tensional homeostasis induce a natural anisotropy of volumetric growth and remodeling in soft biological tissues.

Growth in soft biological tissues in general results in anisotropic changes of the tissue geometry. It remains a key challenge in biomechanics to understand, quantify, and predict this anisotropy. In this paper, we demonstrate that anisotropic tissue stiffness and the well-known mechanism of tensional homeostasis induce a natural anisotropy of the geometric changes resulting from volumetric growth in soft biological tissues. As a rule of thumb, this natural anisotropy makes differential tissue volume elements dilate mainly in the direction(s) of lowest stiffness. This simple principle is shown to explain the experimentally observed growth behavior in a host of different soft biological tissues without relying on any additional heuristic assumptions or quantities (such as ad hoc defined growth tensors).