Erratum: Modeling cardiomyocyte mechanics and autoregulation of contractility by mechano-chemo-transduction feedback.

[This corrects the article DOI: 10.1016/j.isci.2022.104667.].

Modeling cardiomyocyte mechanics and autoregulation of contractility by mechano-chemo-transduction feedback.

The heart pumps blood into circulation against vascular resistance and actively regulates the contractile force to compensate for mechanical load changes. Our experimental data show that cardiomyocytes have a mechano-chemo-transduction (MCT) mechanism that increases intracellular Ca 2 + transient to enhance contractility in response to increased mechanical load. This study advances the cardiac excitation- Ca 2 + signaling-contraction (E-C) coupling model on conceptual and technical fronts. First, we developed analytical and computational models to perform 3-dimensional mechanical analysis of cardiomyocytes contracting in a viscoelastic medium under mechanical load. Next, we proposed an MCT feedback loop in the E-C coupling dynamic system to shift the feedforward paradigm of cardiac E-C coupling to an autoregulation model. Our combined modeling and experimental studies reveal that MCT enables autoregulation of E-C coupling and contractility in single cardiomyocytes, which underlies the heart's intrinsic autoregulation in compensatory response to load changes in order to maintain the stroke volume and cardiac output.

A viscoelastic Eshelby inclusion model and analysis of the Cell-in-Gel system.

We develop a viscoelastic generalization of the elastic Eshelby inclusion solution, where the inclusion and surrounding matrix are two different viscoelastic solids and the inclusion's eigenstrain is a time-periodic oscillatory input. The solution exploits the Correspondence Principle of Linear Viscoelasticity and a Discrete Fourier Transform to efficiently capture the steady-state oscillatory behavior of the 3-D mechanical fields. The approach is illustrated here in the context of the recently-developed in vitro Cell-in-Gel system, where an isolated live cardiomyocyte (the inclusion) is paced to contract periodically within a soft hydrogel (the matrix), for the purpose of studying the effect of mechanical load on biochemical signals that regulate contractility. The addition of viscoelasticity improves the fidelity of our previous elastic Eshelby inclusion analysis of the Cell-in-Gel system by accounting for the time-varying fields and the resulting hysteresis and dissipated mechanical energy. This mathematical model is used to study the parametric sensitivities of the relative stiffness of the inclusion, the inclusion's aspect ratio (slenderness), and the cross-link density of the hydrogel matrix.

On the variation in maternal birth canal in vivo viscoelastic properties and their effect on the predicted length of active second stage and levator ani tears.

The pubovisceral muscles (PVM) help form the distal maternal birth canal. It is not known why 13% of vaginal deliveries end in PVM tears, so insights are needed to better prevent them because their sequelae can lead to pelvic organ prolapse later in life. In this paper we provide the first quantification of the variation in in vivo viscoelastic properties of the intact distal birth canal in healthy nulliparous women using Fung's Quasilinear Viscoelastic Theory and a secondary analysis of data from a clinical trial of constant force birth canal dilation to 8 cm diameter in the first stage of labor in 26 nullipara. We hypothesized that no significant inter-individual variation would be found in the long time constant, τ2, which characterizes how long it takes the birth canal to be dilated by the fetal head. That hypothesis was rejected because τ2 values ranged 20-fold above and below the median value. These data were input to a biomechanical model to calculate how such variations affect the predicted length of the active second stage of labor as well as PVM tear risk. The results show there was a 100-fold change in the predicted length of active second stage for the shortest and longest τ2 values, with a noticeable increase for τ2 values over 1000 s. The correlation coefficent between predicted and observed second stage durations was 0.51. We conclude that τ2 is a strong theoretical contributor to the time a mother has to push in order to deliver a fetal head larger than her birth canal, and a weak predictor of PVM tear risk.

A constitutive model description of the in vivo material properties of lower birth canal tissue during the first stage of labor.

Remarkable changes must occur in the pelvic floor muscles and tissues comprising the birth canal to allow vaginal delivery. Despite these preparatory adaptations, approximately 13% of women who deliver vaginally for the first time (nulliparas) sustain tears near the origin of the pubovisceral muscle (PVM) which can result in pelvic organ prolapse later in life. To investigate why these tears occur, it is necessary to quantify the viscoelastic behavior of the term pregnant human birth canal. The goal of this study was to quantify the in vivo material properties of the human birth canal, in situ, during the first stage of labor and compare them to published animal data. The results show that pregnant human, ovine and squirrel monkey birth canal tissue can be characterized by the same set of constitutive relations; the interspecies differences were primarily explained by the long time constant, τ2, with its values of 555s, 1110s, and 2777s, respectively. Quantification of these viscoelastic properties should allow for improved accuracy of computer models aimed at understanding birth-related injuries.

Mechanics of muscle injury induced by lengthening contraction.

Skeletal muscle is composed of two primary structural components, contractile myofibrils and extracellular matrix (ECM). The myofibrils adhere to the surrounding endomysium through the basal lamina, sarcolemma and dystrophin, and dystrophin associated glycoprotein (DAG). In this study, a novel shear lag type model is developed to investigate the mechanics of injury to the single muscle fiber due to lengthening contractions. A single muscle fiber is considered as a composite system with reinforced by the contractile myofibrils. The lateral linkages between myofibril and endomysium is modeled as a zero thickness coating layer, that could be injured under high interfacial shear stress. The results shows that the degree of the muscle injury is correlated to the magnitude of the passive stretch during the contraction. Dystrophic muscles are more susceptible to contraction induced injury due to lack of DAG complex in lateral linkage.

Micromechanical modeling of the epimysium of the skeletal muscles.

A micromechanical model has been developed to investigate the mechanical properties of the epimysium. In the present model, the collagen fibers in the epimysium are embedded randomly in the ground substance. Two parallel wavy collagen fibers and the surrounding ground substance are used as the repeat unit (unit cell), and the epimysium is considered as an aggregate of unit cells. Each unit cell is distributed in the epimysium with some different angle to the muscle fiber direction. The model allows the progressive straightening of the collagen fiber as well as the effects of fiber reorientation. The predictions of the model compare favorably against experiment. The effects of the collagen fiber volume fraction, collagen fiber waviness at the rest length and the mechanical properties of the collagen fibers and the ground substance are analyzed. This model allows the analysis of mechanical behavior of most soft tissues if appropriate experimental data are available.

Age-related changes in the mechanical properties of the epimysium in skeletal muscles of rats.

Skeletal muscle is composed of muscle fibers and an extracellular matrix (ECM). The collagen fiber network of the ECM is a major contributor to the passive force of skeletal muscles at high strain. We investigated the effect of aging on the biomechanical and structural properties of epimysium of the tibialis anterior muscles (TBA) of rats to understand the mechanisms responsible for the age-related changes. The biomechanical properties were tested directly in vitro by uniaxial extension of epimysium. The presence of age-related changes in the arrangement and size of the collagen fibrils in the epimysium was examined by scanning electron microscopy (SEM). A mathematical model was subsequently developed based on the structure-function relationships that predicted the compliance of the epimysium. Biomechanically, the epimysium from old rats was much stiffer than that of the young rats. No differences were found in the ultrastructure and thickness of the epimysium or size of the collagen fibrils between young and old rats. The changes in the arrangement and size of the collagen fibrils do not appear to be the principal cause of the increased stiffness of the epimysium from the old rats. Other changes in the structural composition of the epimysium from old rats likely has a strong effect on the increased stiffness. The age-related increase in the stiffness of the epimysium could play an important role in the impaired lateral force transmission in the muscles of the elderly.