Local longitudinal muscle shortening of the human esophagus from high-frequency ultrasonography

We analyzed local longitudinal shortening by combining concurrent ultrasonography and manometry with basic principles of mechanics. We applied the law of mass conservation to quantify local axial shortening of the esophageal wall from ultrasonically measured cross-sectional area concurrently with measured intraluminal pressure, from which correlations between local contraction of longitudinal and circular muscle are inferred. Two clear phases of local longitudinal shortening were observed during bolus transport. During luminal filling by bolus fluid, the muscle layer distends and the muscle thickness decreases in the absence of circular or longitudinal muscle contraction. This is followed by local contraction, first in longitudinal muscle, then in circular muscle. Maximal longitudinal shortening occurs nearly coincidently with peak intraluminal pressure. Longitudinal muscle contraction begins before and ends after circular muscle contraction. Larger longitudinal shortening is correlated with higher pressure amplitude, suggesting that circumferential contractile forces are enhanced by longitudinal muscle shortening. We conclude that a peristaltic wave of longitudinal muscle contraction envelops the wave of circular muscle contraction as it passes through the middle esophagus, with peak longitudinal contraction aligned with peak circular muscular contraction. Our results suggest that the coordination of the two waves may be a physiological response to the mechanical influence of longitudinal shortening, which increases contractile force while reducing average muscle fiber tension by increasing circular muscle fiber density locally near the bolus tail.     

Simulation studies of the role of esophageal mucosa in bolus transport

Based on a fully coupled computational model for esophageal transport, we analyzed the role of the mucosa (including the submucosa) in esophageal bolus transport and how bolus transport is affected by mucosal stiffness. Two groups of studies were conducted using a computational model. In the first group, a base case that represents normal esophageal transport and two hypothetical cases were simulated: (1) esophageal mucosa replaced by muscle and (2) esophagus without mucosa. For the base case, the geometric configuration of the esophageal wall was examined and the mechanical role of mucosa was analyzed. For the hypothetical cases, the pressure field and transport features were examined. In the second group of studies, cases with mucosa of varying stiffness were simulated. Overall transport characteristics were examined, and both pressure and geometry were analyzed. Results show that a compliant mucosa helped accommodate the incoming bolus and lubricate the moving bolus. Bolus transport was marginally achieved without mucosa or with mucosa replaced by muscle. A stiff mucosa greatly impaired bolus transport due to the lowered esophageal distensibility and increased luminal pressure. We conclude that mucosa is essential for normal esophageal transport function. Mechanically stiffened mucosa reduces the distensibility of the esophagus by obstructing luminal opening and bolus transport. Mucosal stiffening may be relevant in diseases characterized by reduced esophageal distensibility, elevated intrabolus pressure, and/or hypertensive muscle contraction such as eosinophilic esophagitis and jackhammer esophagus.     

Studies of abnormalities of the lower esophageal sphincter during esophageal emptying based on a fully coupled bolus–esophageal–gastric model

The aim of this work was to develop a fully coupled bolus–esophageal–gastric model based on the immersed boundary–finite element method to study the process of esophageal emptying across the esophagogastric junction (EGJ). The model included an esophageal segment, an ellipsoid-shaped stomach, a bolus, and a simple model of the passive and active sphincteric functions of the lower esophageal sphincter (LES). We conducted three sets of case studies: (1) the effect of a non-relaxing LES; (2) the influence of the tissue anisotropy in the form of asymmetrical right- and left-sided compliance of the LES segment; and (3) the influence of LES and gastric wall stiffness on bulge formation of the distal esophageal wall. We found that a non-relaxing LES caused sustained high wall stress along the LES segment and obstruction of bolus emptying. From the simulations of tissue anisotropy, we found that the weaker side (i.e., more compliant) of the LES segment sustained greater deformation, greater wall shear stress, and a greater high-pressure load during bolus transit. In the third set of studies, we found that a right-sided bulge in the esophageal wall tends to develop during esophageal emptying when LES stiffness was decreased or gastric wall stiffness was increased. Hence, the bulge may be partly due to the asymmetric configuration of the gastric wall with respect to the esophageal tube. Together, the observations from these simulations provide insight into the genesis of epiphrenic diverticula, a complication observed with esophageal motility disorders. Future work, with additional layers of complexity to the model, will delve into the mechanics of gastroesophageal reflux and the effects of hiatus hernia on EGJ function.     

Mechanical properties in the human gastric antrum using B-mode ultrasonography and antral distension

The aims of this study were to investigate gastric antral geometry and stress-strain properties by using transabdominal ultrasound scanning during volume-controlled distensions in the human gastric antrum. Seven healthy volunteers underwent stepwise inflation of a bag located in the antrum with volumes up to 60 ml. The stretch ratio and Cauchy stress and strain were calculated from measurements of pressure, diameter, and wall thickness. A second distension series was conducted in three volunteers during administration of the anticholinergic drug butylscopolamine. Analysis of stretch ratios demonstrated positive strain in the circumferential direction, negative strain in the radial direction, and no strain in the longitudinal direction. The stress-strain relation was exponential and did not differ without or with the administration of butylscopolamine. The wall stress was decomposed into its active and passive components. The well-known length-tension diagram from in vitro studies of smooth muscle strips was reproduced. The maximum active tension appeared at a volume of 50 ml, corresponding to a stretch ratio of 1.5. We conclude that the method provides measures of antral biomechanical wall properties and can be used to reproduce the muscle length-tension diagram in humans.     

Mapping motor neuron activity to overt behavior in the leech

As an initial step in constructing a quantitative biomechanical model of the medicinal leech (Hirudo medicinalis), we determined the passive properties of its body wall over the physiological range of dimensions. The major results of this study were:

1. The ellipsoidal cross section of resting leeches is maintained by tonic muscle activation as well as forces inherent in the structure of the body wall (i.e., residual stress).
2. The forces required for longitudinal and circumferential stretch to maximum physiological dimensions were similar in magnitude. Cutting out pieces of body wall did not affect the passive longitudinal or circumferential properties of body wall away from the edges of the cut.
3. The strain (i.e., the percentage change in dimension) of different body segments when subject to the same force was identical, despite differences in muscle crosssections.
4. Serotonin, a known modulator of tension in leech muscles, affected passive forces at all physiological muscle lengths. This suggests that the longitudinal muscle is responsible for at least part of the passive tension of the body wall.
5. We propose a simple viscoelastic model of the body wall. This model captures the dynamics of the passive responses of the leech body wall to imposed step changes in length. Using steady-state passive tensions predicted by the viscoelastic model we estimate the forces required to maintain the leech at any given length over the physiological range.

     

The mechanical advantage of local longitudinal shortening on peristaltic transport

Whereas bolus transport along the esophagus results from peristaltic contractions of the circular muscle layer, it has been suggested that local shortening of the longitudinal muscle layer concentrates circular muscle fibers in the region where the highest contractile pressures are required. Here we analyze the mechanical consequences of local longitudinal shortening (LLS) through a mathematical model based on lubrication theory. We find that local pressure and shear stress in the contraction zone are greatly reduced by the existence of LLS. In consequence, peak contractile pressure is reduced by nearly 2/3 at physiological LLS, and this reduction is greatest when peak in LLS is well aligned with peak contractile pressure. We conclude that a peristaltic wave of local longitudinal muscle contraction coordinated with the circular muscle contraction wave has both a great physiological advantage (concentrating circular muscle fibers), and a great mechanical advantage (reducing the level of contractile force required to transport the bolus), which combine to greatly reduce circular muscle tone during esophageal peristalsis.     

The mechanical basis of impaired esophageal emptying postfundoplication

Fundoplication (FP) efficacy is a trade-off between protection against reflux and postoperative dysphagia from the surgically altered mechanical balance within the esophagogastric segment. The purpose of the study was to contrast quantitatively the mechanical balance between normal and post-FP esophageal emptying. Physiological data were combined with mathematical models based on the laws of mechanics. Seven normal controls (NC) and seven post-FP patients underwent concurrent manometry and fluoroscopy. Temporal changes in geometry of the distal bolus cavity and hiatal canal, and cavity-driving pressure were quantified during emptying. Mathematical models were developed to couple cavity pressure to hiatal geometry and esophageal emptying and to determine cavity muscle tone. We found that the average length of the hiatal canal post-FP was twice that of NC; reduction of hiatal radius was not significant. All esophageal emptying events post-FP were incomplete (51% retention); there was no significant difference in the period of emptying between NC and post-FP, and average emptying rates were 40% lower post-FP. The model predicted three distinct phases during esophageal emptying: hiatal opening (phase I), a quasi-steady period (phase II), and final emptying (phase III). A rapid increase in muscle tone and driving pressure forced normal hiatal opening. Post-FP there was a severe impairment of cavity muscle tone causing deficient hiatal opening and flow and bolus retention. We conclude that impaired esophageal emptying post-FP follows from the inability of distal esophageal muscle to generate necessary tone rapidly. Immobilization of the intrinsic sphincter by the surgical procedure may contribute to this deficiency, impaired emptying, and possibly, dysphagia.     

Dynamics of intestinal propulsion

A biomechanical model and mathematical formulation of the problem of propulsion of a solid non-deformable pellet by an isolated segment of the gut are presented. The organ is modeled as a soft orthotropic cylindrical biological shell. Its wall is reinforced by transversely isotropic muscle fibers of orthogonal type of weaving embedded in a connective tissue stroma. The mechanical properties of the wall are assumed to be nonlinear, deformations are finite. The longitudinal smooth muscle syncitium possesses anisotropic and the circular muscle syncytium has anisotropic electrical properties. Their electromechanical activity is under control of a pacemaker, which is represented by interstitial cells of Cajal. The model describes the dynamics of the generation and propagation of mechanical waves of contraction-relaxation along the surface of the bioshell and propulsion of the pellet. The governing system of equations was solved numerically. The combined finite-difference and finite-element method was used. The results demonstrate that pendular movements alone provide an aboral transit, without mixing though, of the bolus. Non-propagating segmental contractions show small amplitude librations of the pellet without its visible propulsion. Only the coordinated activity of both smooth muscle layers in a form of the peristaltic reflex provides physiologically significant simultaneous propulsion and mixing of the intraluminal content (pellet).     

Cardiac sarcomere mechanics in health and disease

The sarcomere is the fundamental structural and functional unit of striated muscle and is directly responsible for most of its mechanical properties. The sarcomere generates active or contractile forces and determines the passive or elastic properties of striated muscle. In the heart, mutations in sarcomeric proteins are responsible for the majority of genetically inherited cardiomyopathies. Here, we review the major determinants of cardiac sarcomere mechanics including the key structural components that contribute to active and passive tension. We dissect the molecular and structural basis of active force generation, including sarcomere composition, structure, activation, and relaxation. We then explore the giant sarcomere-resident protein titin, the major contributor to cardiac passive tension. We discuss sarcomere dynamics exemplified by the regulation of titin-based stiffness and the titin life cycle. Finally, we provide an overview of therapeutic strategies that target the sarcomere to improve cardiac contraction and filling.     

A finite-element model for the mechanical analysis of skeletal muscles

In the present paper, a finite-element model for simulating muscle mechanics is described. Based on nonlinear continuum mechanics an algorithm is proposed that includes the contractile active and passive properties of skeletal muscle. Stress in the muscle is assumed to result from the superposition of a passive and an active part. The passive properties are described by a hyperelastic constitutive material law whereas the active part depends on the fibre length, shortening velocity and an activation function. The constraint of approximate incompressibility of the muscle element is satisfied as a property of the constitutive equations. Because of the nonlinear behaviour of the material and the highly dynamical performance an incremental procedure including iterative methods is used. The advantage of the model over previous formulations is the possibility to integrate the element into an engineering standard finite-element programme ANSYS using advanced numerical tools. The model allows simulations of muscle recruitment, calculations of stress and strain distributions and predictions of muscle shape. Other possible applications are studies of the muscle architecture, the effect of inertia and impacts. First, simple examples are presented.     

A 3D active-passive numerical skeletal muscle model incorporating initial tissue strains. Validation with experimental results on rat tibialis anterior muscle

This paper presents a three-dimensional finite element model of skeletal muscle and its validation incorporating inital tissue strains. A constitutive relation was determined by using a convex free strain energy function (SEF) where active and passive response contributions were obtained fitting experimental data from the rat tibialis anterior (TA) muscle. The passive and active finite strains response was modelled within the framework of continuum mechanics by a quasi-incompressible transversely isotropic material formulation. Magnetic resonance images (MRI) were obtained to reconstruct the external geometry of the TA. This geometry includes initial strains also taken into account in the numerical model. The numerical results show excellent agreement with the experimental results when comparing reaction force-extension curves both in passive and active tests. The proposed constitutive model for the muscle is implemented in a subroutine in the commercial finite element software package ABAQUS.     

New insights into the behavior of muscle during active lengthening.

A muscle fiber was modeled as a series-connected string of sarcomeres, using an A. V. Hill type model for each sarcomere and allowing for some random variation in the properties of the sarcomeres. Applying stretches to this model led to the prediction that lengthening of active muscle on or beyond the plateau of the length tension curve will take place very nonuniformly, essentially by rapid, uncontrolled elongation of individual sarcomeres, one at a time, in order from the weakest toward the strongest. Such a "popped" sarcomere, at least in a single fiber, will be stretched to a length where there is no overlap between thick and thin filaments, and the tension is borne by passive components. This prediction allows modeling of many results that have previously been inexplicable, notably the permanent extra tension after stretch on the descending limb of the length tension curve, and the continued rise of tension during a continued stretch.     

One-dimensional steady continuum model of retraction of pseudopod in leukocytes

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.     

Modeling of the mechanical function of the human gastroesophageal junction using an anatomically realistic three-dimensional model

The aim of this study was to combine the anatomy and physiology of the human gastroesophageal junction (the junction between the esophagus and the stomach) into a unified computer model. A three-dimensional (3D) computer model of the gastroesophageal junction was created using cross-sectional images from a human cadaver. The governing equations of finite deformation elasticity were incorporated into the 3D model. The model was used to predict the intraluminal pressure values (pressure inside the junction) due to the muscle contraction of the gastroesophageal junction and the effects of the surrounding structures. The intraluminal pressure results obtained from the 3D model were consistent with experimental values available in the literature. The model was also used to examine the independent roles of each muscle layer (circular and longitudinal) of the gastroesophageal junction by contracting them separately. Results showed that the intraluminal pressure values predicted by the model were primarily due to the contraction of the circular muscle layer. If the circular muscle layer was quiescent, the contraction of the longitudinal muscle layer resulted in an expansion of the junction.In conclusion, the model provided reliable predictions of the intraluminal pressure values during the contraction of a normal gastroesophageal junction. The model also provided a framework to examine the role of each muscle layer during the contraction of the gastroesophageal junction.     

Assessment of intraluminal impedance for the detection of pharyngeal bolus flow during swallowing in healthy adults

Intraluminal impedance, a nonradiological method for assessing bolus flow within the gut, may be suitable for investigating pharyngeal disorders. This study evaluated an impedance technique for the detection of pharyngeal bolus flow during swallowing. Patterns of pharyngoesophageal pressure and impedance were simultaneously recorded with videofluoroscopy in 10 healthy volunteers during swallowing of liquid, semisolid, and solid boluses. The timing of bolus head and tail passage recorded by fluoroscopy was correlated with the timing of impedance drop and recovery at each recording site. Bolus swallowing produced a drop in impedance from baseline followed by a recovery to at least 50% of baseline. The timing of the pharyngeal and esophageal impedance drop correlated with the timing of the arrival of the bolus head. In the pharynx, the timing of impedance recovery was delayed relative to the timing of clearance of the bolus tail. In contrast, in the upper esophageal sphincter (UES) and proximal esophagus, the timing of impedance recovery correlated well with the timing of clearance of the bolus tail. Impedance-based estimates of pharyngoesophageal bolus clearance time correlated with true pharyngoesophageal bolus clearance time. Patterns of intraluminal impedance recorded in the pharynx during bolus swallowing are therefore more complex than those in the esophagus. During swallowing, mucosal contact between the tongue base and posterior pharyngeal wall prolongs the duration of pharyngeal impedance drop, leading to overestimation of bolus tail timing. Therefore, we conclude that intraluminal impedance measurement does not accurately reflect the bolus transit in the pharynx but does accurately reflect bolus transit across the UES and below.     

Physiology of the esophageal pressure transition zone: separate contraction waves above and below

Manometrically measured peristaltic pressure amplitude displays a well-defined trough in the upper esophagus. Whereas this manometric "transition zone" (TZ) has been associated with striated-to-smooth muscle fiber transition, the underlying physiology of the TZ and its role in bolus transport are unclear. A computer model study of bolus retention in the TZ showed discoordinated distinct contraction waves above and below. Our aim was to test the hypothesis that distinct upper/lower contraction waves above/below the manometric TZ are normal physiology and to quantify space-time coordination between tone and bolus transport through the TZ. Eighteen normal barium swallows were analyzed in 6 subjects with concurrent 21-channel high-resolution manometry and digital fluoroscopy. From manometry, the TZ center (nadir pressure amplitude) and the upper/lower margins of the pressure trough were objectively quantified. Using fluoroscopy, we quantified space-time trajectories of the bolus tail and bolus tail pressures and maximum intraluminal pressures proximal to the tail with their space-time trajectories. In every swallow, the bolus tail followed distinct trajectories above/below the TZ, separated by a well-defined spatial "jump" that terminated an upper contraction wave and initiated a lower contraction wave (3.32 +/- 1.63 cm, P = 0.0004). An "indentation wave" always formed within the TZ distal to the upper wave, increasing in amplitude until the lower wave was initiated. As the upper contraction wave tail entered the TZ, it slowed and the tail pressure reduced rapidly, while indentation wave pressure increased to normal tail pressure values at the initiation of the lower wave. The TZ was a special zone of segmental contraction. The TZ is, physiologically, the transition from an upper contraction wave originating in the proximal striated esophagus to a lower contraction wave that moves into the distal smooth muscle esophagus. Complete bolus transport requires coordination of upper/lower waves and sufficient segmental squeeze to fully clear the bolus from the TZ during the transition period.     

Shape and tension distribution of the active canine diaphragm

Both diaphragm shape and tension contribute to transdiaphragmatic pressure, but of the three variables, tension is most difficult to measure. We measured transdiaphragmatic pressure and the global shape of the in vivo canine diaphragm and used principles of mechanics to compute the tension distribution. Our hypotheses were that 1) tension in the active diaphragm is nonuniform with greater tension in the central tendon than in the muscular regions; 2) maximum tension is essentially oriented in the muscle fiber direction, whereas minimum tension is orthogonal to the fiber direction; and 3) during submaximal activation change in the in vivo global shape is small. Metallic markers, each 2 mm in length, were implanted surgically on the peritoneal surface of the diaphragm at 1.5- to 2.0-cm intervals along the muscle bundles at the midline, ventral, middle, and dorsal regions of the left costal diaphragm and along a muscle bundle of the crural diaphragm. Postsurgery, a biplane videofluoroscopic system was used to determine the in vivo three-dimensional coordinates of the markers at end expiration and end inspiration during quiet breathing as well as at end-inspiratory efforts against an occluded airway at lung volumes of functional residual capacity and at one-third maximum inspiratory capacity increments in volume to total lung capacity. A surface was fit to the marker locations using a two-dimensional spline algorithm. Diaphragm surface was modeled as a pressurized membrane, and tension distribution in the active diaphragm was computed using the ANSYS finite element program. We showed that the peak of the diaphragm dome was closer to the ventral surface than to the dorsal surface and that there was a depression or valley in the crural region. In the supine position, during inspiratory efforts, the caudal displacement of the dorsal region of the diaphragm was greater than that of the dome, and the valley along the crural diaphragm was accentuated. In contrast, at lower lung volumes in the prone posture, the caudal displacement of the dome was greater than that of the crural region. At end of inspiration, transdiaphragmatic pressure was approximately 6.5 cmH2O, and tensions were nonuniform in the diaphragm. Maximum principal stress sigma(1) of central tendon was found to be greater than sigma(1) of the costal region, and that was greater than sigma(1) of the crural region, with values of 14-34, 14-29, and 4-14 g/cm, respectively. The corresponding data of the minimum principal stress sigma(2) were 9-18, 3-9, and 0-1.5 g/cm, respectively. Maximum principal tension was approximately parallel to the muscle fibers, whereas minimum tension was essentially orthogonal to the longitudinal direction of the muscle fibers. In the muscular region, sigma(1) was approximately 3-fold sigma(2), whereas in the central tendon, sigma(1) was only approximately 1.5-fold sigma(2.).     

Circumferential,not longitudinal,colonic stretch increases synaptic input to mouse prevertebral ganglion neurons

The relationship between longitudinal and circular muscle tension in the mouse colon and mechanosensory excitatory synaptic input to neurons in the superior mesenteric ganglion (SMG) was investigated in vitro. Electrical activity was recorded intracellularly from SMG neurons, and muscle tension was simultaneously monitored in the longitudinal, circumferential, or both axes. Colonic intraluminal pressure and volume changes were also monitored simultaneously with muscle tension changes. The results showed that the frequency of fast excitatory postsynaptic potentials (fEPSPs) in SMG neurons increased when colonic muscle tension decreased, when the colon relaxed and refilled with fluid after contraction, and during receptive relaxation preceding spontaneous colonic contractions. In contrast, fEPSP frequency decreased when colonic muscle tension increased during spontaneous colonic contraction and emptying. Manual stretch of the colon wall to 10-15% beyond resting length in the circumferential axis of flat sheet preparations increased fEPSP frequency in SMG neurons, but stretch in the longitudinal axis to 15% beyond resting length in the same preparations did not. There was no increase in synaptic input when tubular colon segments were stretched in their long axes up to 20% beyond their resting length. The circumferential stretch-sensitive increase in the frequency of synaptic input to SMG neurons persisted when the colonic muscles were relaxed pharmacologically by nifedipine (2 microM) or nicardipine (3 microM). These results suggest that colonic mechanosensory afferent nerves projecting to the SMG function as length or stretch detectors in parallel to the circular muscle layer.     

Intestinal propulsion of a solid non-deformable bolus

A mathematical model of a segment of the gut with an enclosed pellet is constructed. The gut is represented as a thin deformable soft biological shell with the pellet modeled as a non-deformable solid. Mechanical properties of the gut wall were represented as longitudinal and circular smooth muscle layers embedded in stroma that satisfies the general type of nonlinear orthotropy. Deformations of the wall are finite. Bolus propulsion is numerically simulated by generation and propagation of an electromechanical wave along the syncytia. Pharmacological manipulation is applied to model 5-HT type 3 antagonist (Lotronex, GlaxoSmithKline) and 5-HT type 4 agonist (Zelnorm, Novartis, AB) drugs on the dynamics of bolus progression. The results lead to new quantitative insights into the complex spatio-temporal patterns of gastrointestinal transit. It is demonstrated that the reciprocal relationship in contraction of the longitudinal and circular smooth muscle syncytia is necessary to provide the "mixing" type of movements during the preparatory phase of propulsion. Strong simultaneous contractions of the both smooth muscle layers are required to expel the "mixed" pellet from the segment. The model is implemented as an interactive software system, Gut Discovery(www.aincompany.com), and accurately predicts the effects of drugs on gut motility.     

Sarcomere length changes in a 3D mathematical model of the pig ventricles

Measurements of the geometry and fibrous-sheet structure of the left and right ventricles of the pig heart are fitted with a finite element model. Mechanical changes during the heart cycle are computed by solving the equations of motion under specified ventricular boundary conditions and using experimentally defined constitutive laws for the active and passive material properties of myocardial tissue. The resulting patterns of deformation, such as axial torsion and changes in wall thickness and base-apex length, are consistent with experimental observations. The model can therefore be used to predict sarcomere length changes and other strain patterns throughout the myocardium and throughout the cardiac cycle. Here we present sarcomere length changes at a limited number of material points within the wall. Sarcomere length typically varies by 10% above and below the unloaded length; although under the boundary conditions imposed in the current model the midwall circumferentially oriented sarcomere lengths increased by up to 20% at end diastole. We provide web-access details for a downloadable software program designed to provide more extensive information on mechanical deformation, such as the principal strains and muscle fibre cross-sectional area changes during the cardiac cycle.