Extended-volume image-derived models of coronary microcirculation.

OBJECTIVE: Recent advances in tissue clearing and high-throughput imaging have enabled the acquisition of extended-volume microvasculature images at a submicron resolution. The objective of this study was to extract information from this type of images by integrating a sequence of 3D image processing steps on Terabyte scale datasets. METHODS: We acquired coronary microvasculature images throughout an entire short-axis slice of a 3-month-old Wistar-Kyoto rat heart. This dataset covered 13 × 10 × 0.6 mm at a resolution of 0.933 × 0.933 × 1.866 µm and occupied 700 Gigabytes of disk space. We used chunk-based image segmentation, combined with an efficient graph generation technique, to quantify the microvasculature in the large-scale images. Specifically, we focused on the microvasculature with a vessel diameter up to 15 µm. RESULTS: Morphological data for the complete short-axis ring were extracted within 16 h using this pipeline. From the analyses, we identified that microvessel lengths in the rat coronary microvasculature varied from 6 to 300 µm. However, their distribution was heavily skewed toward shorter lengths, with a mode of 16.5 µm. In contrast, vessel diameters ranged from 3 to 15 µm and had an approximately normal distribution of 6.5 ± 2 µm. CONCLUSION: The tools and techniques from this study will serve other investigations into the microcirculation, and the wealth of data from this study will enable the analysis of biophysical mechanisms using computer models.

Reconstruction of coronary circulation networks: A review of methods.

Building anatomically accurate models of the coronary vascular system enables potentially deeper understandings of coronary circulation. To achieve this, (a) images at different levels of vascular network-arteries, arterioles, capillaries, venules, and veins-need to be obtained through suitable imaging modalities; and (b) from images, morphological and topological information needs to be extracted using image processing techniques. While there are several modalities that enable the imaging of large vessels, microcirculation imaging-capturing vessels having diameter lesser than 100 µm-has to date been typically confined to small regions of the heart. This spatially limited microcirculatory information has often been used within cardiac models, with the potentially erroneous assumption that it is representative of the whole organ. However, with the recent advancements in imaging and image processing, it is rapidly becoming feasible to acquire, process, and quantify microcirculation data at the scale of whole organ. In this review, we summarize the progress toward this goal followed through a presentation of the current state-of-the-art imaging and image processing techniques in the context of coronary microcirculation extraction, prominently but not exclusively, from small animals.

A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes.

Experimental data from human cardiac myocytes at body temperature is crucial for a quantitative understanding of clinically relevant cardiac function and development of whole-organ computational models. However, such experimental data is currently very limited. Specifically, important measurements to characterize changes in tension development in human cardiomyocytes that occur with perturbations in cell length are not available. To address this deficiency, in this study we present an experimental data set collected from skinned human cardiac myocytes, including the passive and viscoelastic properties of isolated myocytes, the steady-state force calcium relationship at different sarcomere lengths, and changes in tension following a rapid increase or decrease in length, and after constant velocity shortening. This data set is, to our knowledge, the first characterization of length and velocity-dependence of tension generation in human skinned cardiac myocytes at body temperature. We use this data to develop a computational model of contraction and passive viscoelasticity in human myocytes. Our model includes troponin C kinetics, tropomyosin kinetics, a three-state crossbridge model that accounts for the distortion of crossbridges, and the cellular viscoelastic response. Each component is parametrized using our experimental data collected in human cardiomyocytes at body temperature. Furthermore we are able to confirm that properties of length-dependent activation at 37°C are similar to other species, with a shift in calcium sensitivity and increase in maximum tension. We revise our model of tension generation in the skinned isolated myocyte to replicate reported tension traces generated in intact muscle during isometric tension, to provide a model of human tension generation for multi-scale simulations. This process requires changes to calcium sensitivity, cooperativity, and crossbridge transition rates. We apply this model within multi-scale simulations of biventricular cardiac function and further refine the parametrization within the whole organ context, based on obtaining a healthy ejection fraction. This process reveals that crossbridge cycling rates differ between skinned myocytes and intact myocytes.

Compensatory and decompensatory alterations in cardiomyocyte Ca2+ dynamics in hearts with diastolic dysfunction following aortic banding.

KEY POINTS: At the cellular level cardiac hypertrophy causes remodelling, leading to changes in ionic channel, pump and exchanger densities and kinetics. Previous studies have focused on quantifying changes in channels, pumps and exchangers without quantitatively linking these changes with emergent cellular scale functionality. Two biophysical cardiac cell models were created, parameterized and validated and are able to simulate electrophysiology and calcium dynamics in myocytes from control sham operated rats and aortic-banded rats exhibiting diastolic dysfunction. The contribution of each ionic pathway to the calcium kinetics was calculated, identifying the L-type Ca2+ channel and sarco/endoplasmic reticulum Ca2+ ATPase as the principal regulators of systolic and diastolic Ca2+ , respectively. Results show that the ability to dynamically change systolic Ca2+ , through changes in expression of key Ca2+ modelling protein densities, is drastically reduced following the aortic banding procedure; however the cells are able to compensate Ca2+ homeostasis in an efficient way to minimize systolic dysfunction. ABSTRACT: Elevated left ventricular afterload leads to myocardial hypertrophy, diastolic dysfunction, cellular remodelling and compromised calcium dynamics. At the cellular scale this remodelling of the ionic channels, pumps and exchangers gives rise to changes in the Ca2+ transient. However, the relative roles of the underlying subcellular processes and the positive or negative impact of each remodelling mechanism are not fully understood. Biophysical cardiac cell models were created to simulate electrophysiology and calcium dynamics in myocytes from control rats (SHAM) and aortic-banded rats exhibiting diastolic dysfunction. The model parameters and framework were validated and the fitted parameters demonstrated to be unique for explaining our experimental data. The contribution of each ionic pathway to the calcium kinetics was calculated, identifying the L-type Ca2+ channel (LCC) and the sarco/endoplasmic reticulum Ca2+ -ATPase (SERCA) as the principal regulators of systolic and diastolic Ca2+ , respectively. In the aortic banding model, the sensitivity of systolic Ca2+ to LCC density and diastolic Ca2+ to SERCA density decreased by 16-fold and increased by 23%, respectively, relative to the SHAM model. The energy cost of ionic homeostasis is maintained across the two models. The models predict that changes in ionic pathway densities in compensated aortic banding rats maintain Ca2+ function and efficiency. The ability to dynamically alter systolic function is significantly diminished, while the capacity to maintain diastolic Ca2+ is moderately increased.

The relative role of patient physiology and device optimisation in cardiac resynchronisation therapy: A computational modelling study.

Cardiac resynchronisation therapy (CRT) is an established treatment for heart failure, however the effective selection of patients and optimisation of therapy remain controversial. While extensive research is ongoing, it remains unclear whether improvements in patient selection or therapy planning offers a greater opportunity for the improvement of clinical outcomes. This computational study investigates the impact of both physiological conditions that guide patient selection and the optimisation of pacing lead placement on CRT outcomes. A multi-scale biophysical model of cardiac electromechanics was developed and personalised to patient data in three patients. These models were separated into components representing cardiac anatomy, pacing lead location, myocardial conductivity and stiffness, afterload, active contraction and conduction block for each individual, and recombined to generate a cohort of 648 virtual patients. The effect of these components on the change in total activation time of the ventricles (ΔTAT) and acute haemodynamic response (AHR) was analysed. The pacing site location was found to have the largest effect on ΔTAT and AHR. Secondary effects on ΔTAT and AHR were found for functional conduction block and cardiac anatomy. The simulation results highlight a need for a greater emphasis on therapy optimisation in order to achieve the best outcomes for patients.

The calcium-frequency response in the rat ventricular myocyte: an experimental and modelling study.

KEY POINTS: In the majority of species, including humans, increased heart rate increases cardiac contractility. This change is known as the force-frequency response (FFR). The majority of mammals have a positive force-frequency relationship (FFR). In rat the FFR is controversial. We derive a species- and temperature-specific data-driven model of the rat ventricular myocyte. As a measure of the FFR, we test the effects of changes in frequency and extracellular calcium on the calcium-frequency response (CFR) in our model and three altered models. The results show a biphasic peak calcium-frequency response, due to biphasic behaviour of the ryanodine receptor and the combined effect of the rapid calmodulin buffer and the frequency-dependent increase in diastolic calcium. Alterations to the model reveal that inclusion of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated L-type channel and transient outward K(+) current activity enhances the positive magnitude calcium-frequency response, and the absence of CAMKII-mediated increase in activity of the sarco/endoplasmic reticulum Ca(2+) -ATPase induces a negative magnitude calcium-frequency response. ABSTRACT: An increase in heart rate affects the strength of cardiac contraction by altering the Ca(2+) transient as a response to physiological demands. This is described by the force-frequency response (FFR), a change in developed force with pacing frequency. The majority of mammals, including humans, have a positive FFR, and cardiac contraction strength increases with heart rate. However, the rat and mouse are exceptions, with the majority of studies reporting a negative FFR, while others report either a biphasic or a positive FFR. Understanding the differences in the FFR between humans and rats is fundamental to interpreting rat-based experimental findings in the context of human physiology. We have developed a novel model of rat ventricular electrophysiology and calcium dynamics, derived predominantly from experimental data recorded under physiological conditions. As a measure of FFR, we tested the effects of changes in stimulation frequency and extracellular calcium concentration on the simulated Ca(2+) transient characteristics and showed a biphasic peak calcium-frequency relationship, consistent with recent observations of a shift from negative to positive FFR when approaching the rat physiological frequency range. We tested the hypotheses that (1) inhibition of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated increase in sarco/endoplasmic reticulum Ca(2+) -ATPase (SERCA) activity, (2) CAMKII modulation of SERCA, L-type channel and transient outward K(+) current activity and (3) Na(+) /K(+) pump dynamics play a significant role in the rat FFR. The results reveal a major role for CAMKII modulation of SERCA in the peak Ca(2+) -frequency response, driven most significantly by the cytosolic calcium buffering system and changes in diastolic Ca(2+) .

Impact of coronary bifurcation morphology on wave propagation.

The branching pattern of the coronary vasculature is a key determinant of its function and plays a crucial role in shaping the pressure and velocity wave forms measured for clinical diagnosis. However, although multiple scaling laws have been proposed to characterize the branching pattern, the implications they have on wave propagation remain unassessed to date. To bridge this gap, we have developed a new theoretical framework by combining the mathematical formulation of scaling laws with the wave propagation theory in the pulsatile flow regime. This framework was then validated in multiple species using high-resolution cryomicrotome images of porcine, canine, and human coronary networks. Results demonstrate that the forward well-matchedness (no reflection for pressure/flow waves traveling from the coronary stem toward the microcirculation) is a salient feature in the coronary vasculature, and this result remains robust under many scenarios of the underlying pulse wave speed distribution assumed in the network. This result also implies a significant damping of the backward traveling waves, especially for smaller vessels (radius, <0.3 mm). Furthermore, the theoretical prediction of increasing area ratios (ratio between the area of the mother and daughter vessels) in more symmetric bifurcations found in the distal circulation was confirmed by experimental measurements. No differences were observed by clustering the vessel segments in terms of transmurality (from epicardium to endocardium) or perfusion territories (left anterior descending, left circumflex, and right coronary artery).

Analysis of lead placement optimization metrics in cardiac resynchronization therapy with computational modelling.

AIMS: The efficacy of cardiac resynchronization therapy (CRT) is known to vary considerably with pacing location, however the most effective set of metrics by which to select the optimal pacing site is not yet well understood. Computational modelling offers a powerful methodology to comprehensively test the effect of pacing location in silico and investigate how to best optimize therapy using clinically available metrics for the individual patient. METHODS AND RESULTS: Personalized computational models of cardiac electromechanics were used to perform an in silico left ventricle (LV) pacing site optimization study as part of biventricular CRT in three patient cases. Maps of response to therapy according to changes in total activation time (ΔTAT) and acute haemodynamic response (AHR) were generated and compared with preclinical metrics of electrical function, strain, stress, and mechanical work to assess their suitability for selecting the optimal pacing site. In all three patients, response to therapy was highly sensitive to pacing location, with laterobasal locations being optimal. ΔTAT and AHR were found to be correlated (ρ < -0.80), as were AHR and the preclinical activation time at the pacing site (ρ ≥ 0.73), however pacing in the last activated site did not result in the optimal response to therapy in all cases. CONCLUSION: This computational modelling study supports pacing in laterobasal locations, optimizing pacing site by minimizing paced QRS duration and pacing in regions activated late at sinus rhythm. Results demonstrate information content is redundant using multiple preclinical metrics. Of significance, the correlation of AHR with ΔTAT indicates that minimization of QRSd is a promising metric for optimization of lead placement.

Quantifying inter-species differences in contractile function through biophysical modelling.

Animal models and measurements are frequently used to guide and evaluate clinical interventions. In this context, knowledge of inter-species differences in physiology is crucial for understanding the limitations and relevance of animal experimental assays for informing clinical applications. Extensive effort has been put into studying the structure and function of cardiac contractile proteins and how differences in these translate into the functional properties of muscles. However, integrating this knowledge into a quantitative description, formalising and highlighting inter-species differences both in the kinetics and in the regulation of physiological mechanisms, remains challenging. In this study we propose and apply a novel approach for the quantification of inter-species differences between mouse, rat and human. Assuming conservation of the fundamental physiological mechanisms underpinning contraction, biophysically based computational models are fitted to simulate experimentally recorded phenotypes from multiple species. The phenotypic differences between species are then succinctly quantified as differences in the biophysical model parameter values. This provides the potential of quantitatively establishing the human relevance of both animal-based experimental and computational models for application in a clinical context. Our results indicate that the parameters related to the sensitivity and cooperativity of calcium binding to troponin C and the activation and relaxation rates of tropomyosin/crossbridge binding kinetics differ most significantly between mouse, rat and human, while for example the reference tension, as expected, shows only minor differences between the species. Hence, while confirming expected inter-species differences in calcium sensitivity due to large differences in the observed calcium transients, our results also indicate more unexpected differences in the cooperativity mechanism. Specifically, the decrease in the unbinding rate of calcium to troponin C with increasing active tension was much lower for mouse than for rat and human. Our results also predicted crossbridge binding to be slowest in human and fastest in mouse.

Structure-based algorithms for microvessel classification.

OBJECTIVE: Recent developments in high-resolution imaging techniques have enabled digital reconstruction of three-dimensional sections of microvascular networks down to the capillary scale. To better interpret these large data sets, our goal is to distinguish branching trees of arterioles and venules from capillaries. METHODS: Two novel algorithms are presented for classifying vessels in microvascular anatomical data sets without requiring flow information. The algorithms are compared with a classification based on observed flow directions (considered the gold standard), and with an existing resistance-based method that relies only on structural data. RESULTS: The first algorithm, developed for networks with one arteriolar and one venular tree, performs well in identifying arterioles and venules and is robust to parameter changes, but incorrectly labels a significant number of capillaries as arterioles or venules. The second algorithm, developed for networks with multiple inlets and outlets, correctly identifies more arterioles and venules, but is more sensitive to parameter changes. CONCLUSIONS: The algorithms presented here can be used to classify microvessels in large microvascular data sets lacking flow information. This provides a basis for analyzing the distinct geometrical properties and modelling the functional behavior of arterioles, capillaries, and venules.

Microsphere skimming in the porcine coronary arteries: Implications for flow quantification.

Particle skimming is a phenomenon where particles suspended in fluid flowing through vessels distribute disproportionately to bulk fluid volume at junctions. Microspheres are considered a gold standard of intra-organ perfusion measurements and are used widely in studies of flow distribution and quantification. It has previously been hypothesised that skimming at arterial junctions is responsible for a systematic over-estimation of myocardial perfusion from microspheres at the subendocardium. Our objective is to integrate coronary arterial structure and microsphere distribution, imaged at high resolution, to test the hypothesis of microsphere skimming in a porcine left coronary arterial (LCA) network. A detailed network was reconstructed from cryomicrotome imaging data and a Poiseuille flow model was used to simulate flow. A statistical approach using Clopper-Pearson confidence intervals was applied to determine the prevalence of skimming at bifurcations in the LCA. Results reveal that microsphere skimming is most prevalent at bifurcations in the larger coronary arteries, namely the epicardial and transmural arteries. Bifurcations at which skimming was identified have significantly more asymmetric branching parameters. This finding suggests that when using thin transmural segments to quantify flow from microspheres, a skimming-related deposition bias may result in underestimation of perfusion in the subepicardium, and overestimation in the subendocardium.

Species-dependent adaptation of the cardiac Na+/K+ pump kinetics to the intracellular Na+ concentration.

The Na(+)/K(+) ATPase (NKA) plays a critical role in maintaining ionic homeostasis and dynamic function in cardiac myocytes, within both the in vivo cell and in silico models. Physiological conditions differ significantly between mammalian species. However, most existing formulations of NKA used to simulate cardiac function in computational models are derived from a broad range of experimental sources spanning many animal species. The resultant inability of these models to discern species-specific features is a significant obstacle to achieving a detailed quantitative and comparative understanding of physiological behaviour in different biological contexts. Here we present a framework for characterising the steady-state NKA current using a biophysical mechanistic model specifically designed to provide a mechanistic explanation of the NKA flux supported by self-consistent species-specific data. We thus compared NKA kinetics specific to guinea- pig and rat ventricular myocytes. We observe that the apparent binding affinity for sodium in the rat is significantly lower, whereas the overall pump cycle rate is doubled, in comparison to the guinea pig. This sensitivity of NKA to its regulatory substrates compensates for the differences in Na(+) concentrations between the cell types. NKA is thereby maintained within its dynamic range over a wide range of pacing frequencies in these two species, despite significant disparities in sodium concentration. Hence, by replacing a conventional generic NKA model with our rat-specific NKA formula into a whole-cell simulation, we have, for the first time, been able to accurately reproduce the action potential duration and the steady-state sodium concentration as functions of pacing frequency.

Computational modeling of Takotsubo cardiomyopathy: effect of spatially varying ß-adrenergic stimulation in the rat left ventricle.

In Takotsubo cardiomyopathy, the left ventricle shows apical ballooning combined with basal hypercontractility. Both clinical observations in humans and recent experimental work on isolated rat ventricular myocytes suggest the dominant mechanisms of this syndrome are related to acute catecholamine overload. However, relating observed differences in single cells to the capacity of such alterations to result in the extreme changes in ventricular shape seen in Takotsubo syndrome is difficult. By using a computational model of the rat left ventricle, we investigate which mechanisms can give rise to the typical shape of the ventricle observed in this syndrome. Three potential dominant mechanisms related to effects of ß-adrenergic stimulation were considered: apical-basal variation of calcium transients due to differences in L-type and sarco(endo)plasmic reticulum Ca(2+)-ATPase activation, apical-basal variation of calcium sensitivity due to differences in troponin I phosphorylation, and apical-basal variation in maximal active tension due to, e.g., the negative inotropic effects of p38 MAPK. Furthermore, we investigated the interaction of these spatial variations in the presence of a failing Frank-Starling mechanism. We conclude that a large portion of the apex needs to be affected by severe changes in calcium regulation or contractile function to result in apical ballooning, and smooth linear variation from apex to base is unlikely to result in the typical ventricular shape observed in this syndrome. A failing Frank-Starling mechanism significantly increases apical ballooning at end systole and may be an important additional factor underpinning Takotsubo syndrome.

Aortic relative pressure components derived from four-dimensional flow cardiovascular magnetic resonance.

PURPOSE: To describe the assessment of the spatiotemporal distribution of relative aortic pressure quantifying the magnitude of its three major components. METHODS: Nine healthy volunteers and three patients with aortic disease (bicuspid aortic valve, dissection, and Marfan syndrome) underwent 4D-flow CMR. Spatiotemporal pressure maps were computed from the CMR flow fields solving the pressure Poisson equation. The individual components of pressure were separated into time-varying inertial ("transient"), spatially varying inertial ("convective"), and viscous components. RESULTS: Relative aortic pressure is primarily caused by transient effects followed by the convective and small viscous contributions (64.5, 13.6, and 0.3 mmHg/m, respectively, in healthy subjects), although regional analysis revealed prevalent convective effects in specific contexts, e.g., Sinus of Valsalva and aortic arch at instants of peak velocity. Patients showed differences in peak transient values and duration, and localized abrupt convective changes explained by abnormalities in aortic geometry, including the presence of an aneurysm, a pseudo-coarctation, the inlet of a dissection, or by complex flow patterns. CONCLUSION: The evaluation of the three components of relative pressure enables the quantification of mechanistic information for understanding and stratifying aortic disease, with potential future implications for guiding therapy.

A displacement-based finite element formulation for incompressible and nearly-incompressible cardiac mechanics.

The Lagrange Multiplier (LM) and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics. In this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed Perturbed Lagrangian formulation, which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of LM techniques. A modified Shamanskii-Newton-Raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and, exploiting its equivalence, modifications are developed for the penalty form. Focusing on accuracy, we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics. Our results illustrate the well-known influence of locking phenomena on the penalty approach (particularly for lower order schemes) and its effect on accuracy for whole-cycle mechanics. Additionally, we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable. Combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics, the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics.

Beta-adrenergic stimulation maintains cardiac function in Serca2 knockout mice.

Previous studies on Serca2 knockout (KO) mice showed that cardiac function is sustained in vivo for several weeks after knockout, whereas SERCA protein levels decrease and calcium dynamics are significantly impaired. In this study, we reconcile observed cellular and organ level contractile function using a cardiac multiscale model. We identified and quantified the changes in cellular function that are both consistent with observations and able to compensate for the decrease in SERCA. Calcium transients were used as input for multiscale computational simulations to predict whole-organ response. Although this response matched experimental pressure-volume (PV) measurements in healthy mice, the reduced magnitude calcium transients observed in KO cells were insufficient to trigger ventricular ejection. To replicate the effects of elevated catecholamine levels observed in vivo, cells were treated with isoproterenol. Incorporation of the resulting measured ß-adrenergically stimulated calcium transients into the model resulted in a close match with experimental PV loops. Changes in myofilament properties, when considered in isolation, were not able to increase tension development to levels consistent with measurements, further confirming the necessity of a high ß-adrenergic state. Modeling additionally indicated that increased venous return observed in the KO mice helps maintain a high ejection fraction via the Frank-Starling effect. Our study shows that increased ß-adrenergic stimulation is a potentially highly significant compensatory mechanism by which cardiac function is maintained in Serca2 KO mice, producing the increases in both systolic and diastolic calcium, consistent with the observed contractile function observed in experimental PV measurements.

Parameters in dynamic models of complex traits are containers of missing heritability.

Polymorphisms identified in genome-wide association studies of human traits rarely explain more than a small proportion of the heritable variation, and improving this situation within the current paradigm appears daunting. Given a well-validated dynamic model of a complex physiological trait, a substantial part of the underlying genetic variation must manifest as variation in model parameters. These parameters are themselves phenotypic traits. By linking whole-cell phenotypic variation to genetic variation in a computational model of a single heart cell, incorporating genotype-to-parameter maps, we show that genome-wide association studies on parameters reveal much more genetic variation than when using higher-level cellular phenotypes. The results suggest that letting such studies be guided by computational physiology may facilitate a causal understanding of the genotype-to-phenotype map of complex traits, with strong implications for the development of phenomics technology.

Personalized surgical planning for coronary bypass graft configurations using patient-specific computational modeling to avoid flow competition in arterial grafts.

Objectives: Flow competition between coronary artery bypass grafts (CABG) and native coronary arteries is a significant problem affecting arterial graft patency. The objectives of this study were to compare the predictive hemodynamic flow resulting from various total arterial grafting configurations and to evaluate whether the use of computational fluid dynamics (CFD) models capable of predicting flow can assist surgeons to make better decisions for individual patients by avoiding poorly functioning grafts. Methods: Sixteen cardiac surgeons declared their preferred CABG configuration using bilateral internal mammary and radial arteries for each of 5 patients who had differing degrees of severe triple vessel coronary disease. Surgeons selected both a preferred 'aortic' strategy, with at least one graft arising from the ascending aorta, and a preferred "anaortic" strategy which could be performed as a "no-aortic touch" operation. CT coronary angiograms of the 5 patients were coupled to CFD models using a novel flow solver "COMCAB." Twelve different CABG configurations were compared for each patient of which 4 were "aortic" and 8 were "anaortic." Surgeons then selected their preferred grafting configurations after being shown predictive hemodynamic metrics including functional assessment of stenoses (instantaneous wave-free ratio; fractional flow reserve), transit time flowmetry graft parameters (mean graft flow; pulsatility index) and myocardial perfusion. Results: A total of 87.5% (7/8) of "anaortic" configurations compared to 25% (1/4) of "aortic" configurations led to unsatisfactory grafts in at least 1 of the 5 patients (P = 0.038). The use of the computational models led to a significant decrease in the selection of unsatisfactory grafting configurations when surgeons employed "anaortic" (21.25% (17/80) vs. 1.25% (1/80), P < 0.001) but not "aortic" techniques (5% (4/80) vs. 0% (0/80), P = 0.64). Similarly, there was an increase in the selection of ideal configurations for "anaortic" (6.25% (5/80) vs. 28.75% (23/80), P < 0.001) but not "aortic" techniques (65% (52/80) vs. 61.25% (49/80), P = 0.74). Furthermore, surgeons who planned to use more than one unique "anaortic" configuration across all 5 patients increased (12.5% (2/16) vs. 87.5% (14/16), P<0.001). Conclusions: "COMCAB" is a promising tool to improve personalized surgical planning particularly for CABG configurations involving composite or sequential grafts which are used more frequently in anaortic operations.

Sodium accumulation in SERCA knockout-induced heart failure.

In cardiomyocytes, a major decrease in the level of sarco/endoplasmic reticulum Ca(2+) ATPase (SERCA) can severely impair systolic and diastolic functions. In mice with cardiomyocyte-specific conditional excision of the Serca2 gene (SERCA2 KO), end-stage heart failure developed between four and seven weeks after gene deletion combined with [Na(+)](i) elevation and intracellular acidosis. In this study, to investigate the underpinning changes in Ca(2+) dynamics and metabolic homeostasis, we developed data-driven mathematical models of Ca(2+) dynamics in the ventricular myocytes of the control, four-week, and seven-week SERCA2 knockout (KO) mice. The seven-week KO model showed that elevated [Na(+)](i) was due to increased Na(+) influxes through the Na(+)/Ca(2+) exchanger (NCX) and the Na(+)/H(+) exchanger, with the latter exacerbated by intracellular acidosis. Furthermore, NCX upregulation in the seven-week KO model resulted in increased ATP consumption for ion transport. Na(+) accumulation in the SERCA KO due to NCX upregulation and intracellular acidosis potentially play a role in the development of heart failure, by initiating a reinforcing cycle involving: a mismatch between ATP demand and supply; an increasingly compromised metabolism; a decreased pH(i); and, finally, an even greater [Na(+)](i) elevation.

An analysis of deformation-dependent electromechanical coupling in the mouse heart.

To investigate the effects of the coupling between excitation and contraction on whole-organ function, we have developed a novel biophysically based multiscale electromechanical model of the murine heart. Through comparison with a comprehensive in vivo experimental data set, we show good agreement with pressure and volume measurements at both physiological temperatures and physiological pacing frequencies. This whole-organ model was used to investigate the effects of material and haemodynamic properties introduced at the tissue level, as well as emergent function of our novel cell contraction model. Through a comprehensive sensitivity analysis at both the cellular and whole organ level, we demonstrate the sensitivity of the model's results to its parameters and the constraining effect of experimental data. These results demonstrate the fundamental importance of length- and velocity-dependent feedback to the cellular scale for whole-organ function, and we show that a strong velocity dependence of tension is essential for explaining the differences between measured single cell tension and whole-organ pressure transients.