Predicting Patient Status in Chronic Thromboembolic Pulmonary Hypertension Using a Biophysical Model

Chronic thromboembolic pulmonary hypertension (CTEPH) involves abnormally high blood pressure in the pulmonary vessels and is associated with small vessel vasculopathy and pre-capillary proximal occlusions. Management of CTEPH disease is challenging, therefore accurate diagnosis is crucial in ensuring effective treatment and improved patient outcomes. The treatment of choice for CTEPH is pulmonary endarterectomy, which is an invasive surgical intervention to remove thrombi. Following PEA, a number of patients experience poor outcomes or worse-than-expected improvements, which may indicate that they have significant small vessel disease. A method that can predict the extent of distal remodelling may provide useful clinical information to plan appropriate CTEPH patient treatment. Here, a novel biophysical modelling approach has been developed to estimate and quantify the extent of distal remodelling. This method includes a combination of mathematical modelling and computed tomography pulmonary angiography to first model the geometry of the pulmonary arteries and to identify the under-perfused regions in CTEPH. The geometric model is then used alongside haemodynamic measurements from right heart catheterisation to predict distal remodelling. In this study, the method is tested and validated using synthetically generated remodelling data. Then, a preliminary application of this technique to patient data is shown to demonstrate the potential of the approach for use in the clinical setting.Clinical relevance- Patient-specific modelling can help provide useful information regarding the extent of distal vasculopathy on a per-patient basis, which remains challenging. Physicians can be unsure of outcomes following pulmonary endarterectomy. Therefore, the predictive aspect of the patient's response to surgery can help with clinical decision-making.

An automated method for BRISQUE quantification of image quality in echocardiography

Background

Echocardiography (echo) remains the most widely used imaging modality for the assessment, monitoring, and prognostication of the heart. Despite its prevalence, standardisation efforts for echo chamber quantification are ongoing, with challenges owing to subjectivity during acquisition and analysis. Furthermore, the confidence in derived functional indices is often dependent on the quality of the acquired images. However, few studies have investigated the accuracy of echo measurements compared to a reference modality such as cardiac magnetic resonance (CMR) imaging, when stratified by image quality.

Purpose

To develop an objective and automated method to quantify echo image quality, and subsequently to investigate the relationship between image quality and patient demographics, as well as the magnitude of bias in left ventricular (LV) functional indices compared with CMR.

Methods

Transthoracic apical 2D echo (2DE) and 3D echo (3DE) data from 128 participants (72 healthy controls and 56 patients with acquired heart disease) were used to train a BRISQUE (Blind/Referenceless Image Spatial Quality Evaluator) algorithm [1]. Briefly, feature extraction was performed by fitting pixel luminances to a generalised Gaussian distribution (GGD), followed by support vector regression to correlate features (i.e., shape, variance, and mean parameters of the GGD) to quality scores (Fig. 1). Independent BRISQUE models were trained on 580 2DE images (consisting of 2-, 3-, and 4-chamber views) and 128 targeted LV 3DE acquisitions at end-diastole, each assigned a subjective perceived quality score between 1 (poor) and 9 (excellent) by a single observer. LV indices including end-diastolic volume (EDV), end-systolic volume (ESV), ejection fraction (EF), and global longitudinal strain (GLS), were assessed according to standard guidelines. Resultant BRISQUE scores were plotted against patient demographics (age, height, weight) and the measurement bias by comparison to CMR (acquired within 1 hour of echo).

Results

Several linear relationships (where P-value of slope <0.05) were observed between demographics, cardiac indices, and BRISQUE scores. Increasing patient weight (and height in 3DE) were found to be associated with poorer image quality. There was no apparent relationship between image quality and age. Of interest, EF exhibited a relationship with image quality in both 2DE and 3DE (Fig. 2), whereby higher quality images tended to overestimate EF, while lower quality images underestimated EF. For 3DE, image quality dependency was also observed for ESV and GLS biases.

Conclusions

BRISQUE can objectively quantify image quality to produce scores which correlate to those of an expert observer, with potential utility for the standardised quantification of echo image quality. Using this method, it may be possible to predict patient characteristics which adversely impact echo quality, as well as the magnitude of measurement biases for certain functional indices.

Funding Acknowledgement

Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Health Research Council (HRC) of New Zealand; National Heart Foundation (NHF) of New Zealand

Right ventricular quantification using 3D echocardiography: a comparison with CMR

Background

Volumetric and functional right ventricular (RV) indices such as ejection fraction (EF) and global strains are known independent predictors of adverse cardiovascular events. While cardiac magnetic resonance (CMR) imaging remains the reference standard for volume quantification, echocardiography is more accessible and allows for rapid ventricular assessment. Compared to conventional 2D echocardiography, 3D echocardiography (3DE) enables full volume acquisitions and the ability to circumvent geometric assumptions. Given the complexity of RV geometry and sensitivity to image plane positioning, this advantage offers the potential to obtain more accurate diagnostic measurements.

Purpose

Tools for RV analysis in 3DE have been less extensively studied compared to those for the left ventricle (LV). We sought to quantify discrepancies in RV indices derived from 3DE and CMR.

Methods

Transthoracic real-time 3DE and cine CMR imaging were performed in 20 prospectively recruited participants (12 patients with acquired cardiac disease and 8 healthy controls), <1 hour apart. Dynamic 3D biventricular models were constructed semi-automatically from CMR by identifying fiducial landmarks, correcting in-plane breath-hold mis-registrations, and interactively fitting contours to the endocardial and epicardial borders on long- and short-axis slices. For 3DE, right ventricular endocardial models were created by fitting contours on 2D image planes resampled from the 3D volume at end-diastole and end-systole, which were subsequently tracked over one cardiac cycle (Figure 1). RV indices including end-diastolic volume (EDV), end-systolic volume (ESV), EF, global longitudinal strain (GLS), and global circumferential strain (GCS) were calculated from the 3DE- and CMR-derived 3D geometric models and compared. Paired-sample t-tests were performed to identify statistically significant differences (where P<0.05), and intraclass correlation coefficients (ICC) for absolute agreement were computed to assess the reliability for each measurement.

Results

Differences (mean ± SD) in RV indices between 3DE and CMR, with corresponding ICCs are presented in Table 1. Statistically significant differences in RV EDV, ESV, EF, and GLS were observed, with 3DE consistently underestimating volumes and overestimating function when compared to CMR. Although a statistically significant difference in RV GCS was not observed, a low ICC score indicated poor reliability.

Conclusions

Volume underestimation in RV indices between 3DE and CMR were found to be larger than those previously reported for the LV, which is likely due to the increased geometric complexity and surface area to volume ratio for the RV. Moreover, 3DE tends to overestimate RV function in terms of EF and GLS, which may impact treatment pathways if used in a clinical setting. Recognising systematic differences between modalities reinforces the need to further develop 3DE technologies for more accurate RV quantification.

Funding Acknowledgement

Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Health Research Council (HRC) of New Zealand;National Heart Foundation (NHF) of New Zealand

Leveraging CMR for 3D echocardiography: an annotated multimodality dataset for AI

Funding Acknowledgements: Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Health Research Council of New Zealand (HRC)

National Heart Foundation of New Zealand (NHF)

Segmentation of the left ventricular myocardium and cavity in 3D echocardiography (3DE) is a critical task for the quantification of systolic function in heart disease. Continuing advances in 3DE have considerably improved image quality, prompting increased clinical uptake in recent years, particularly for volumetric measurements. Nevertheless, analysis of 3DE remains a difficult problem due to inherently complex noise characteristics, anisotropic image resolution, and regions of acoustic dropout.

One of the primary challenges associated with the development of automated methods for 3DE analysis is the requirement of a sufficiently large training dataset. Historically, ground truth annotations have been difficult to obtain due to the high degree of inter- and intra-observer variability associated with manual 3DE segmentation, thus, limiting the scope of AI-based solutions. To address the lack of expert consensus, we instead used labels derived from cardiac magnetic resonance (CMR) images of the same subjects. By spatiotemporally registering CMR labels to corresponding 3DE image data on a per subject basis (Figure 1), we collated 520 annotated 3DE images from a mixed cohort of 130 human subjects (2 independent single-beat acquisitions per subject at end-diastole and end-systole) consisting of healthy controls and patients with acquired cardiac disease. Comprising images acquired across a range of patient demographics, this curated dataset exhibits variation in image quality, 3DE acquisition parameters, as well as left ventricular shape and pose within the 3D image volume.

To demonstrate the utility of such a dataset, nn-UNet, a self-configuring deep learning method for semantic segmentation was employed. An 80/20 split of the dataset was used for training and testing, respectively, and data augmentations were applied in the form of scaling, rotation, and reflection. The trained network was capable of reproducing measurements derived from CMR for end-diastolic volume, end-systolic volume, ejection fraction, and mass, while outperforming an expert human observer in terms of accuracy as well as scan-rescan reproducibility (Table I).

As part of ongoing efforts to improve the accuracy and efficiency of 3DE analysis, we have leveraged the high resolution and signal-to-noise-ratio of CMR (relative to 3DE), to create a novel, publicly available benchmark dataset for developing and evaluating 3DE labelling methods. This approach not only significantly reduces the effects of observer-specific bias and variability in training data arising from conventional manual 3DE analysis methods, but also improves the agreement between cardiac indices derived from 3DE and CMR.

Figure 1. Data annotation workflow Table I. Results

Left ventricular dimensions and mass measurement from 3D echocardiography: are we there yet?

Funding Acknowledgements

Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Health Research Council (HRC) of New Zealand and National Heart Foundation (NHF) of New Zealand

Introduction—Echocardiographic measures of left ventricular (LV) structure and size, including LV wall thickness and LV end-diastolic dimension (LVID), provide important information in the assessment of patients with heart disease. For example, LV mass is a predictor of outcome for patients with hypertension and LVID is a predictor of cardiac resynchronisation response in patients with heart failure. Advances in 3D echocardiography (3DE) have enabled full-volume acquisitions, which overcome geometric assumptions present in conventional 2D echocardiography (2DE), providing a more accurate representation of cardiac geometry. Although numerous validation studies have been performed for 3DE-derived LV volumes, comparisons of LV dimension by 3DE against established methods are limited.

Purpose—We sought to compare routine LV dimension measurements between 3DE and 2DE, with validation using cardiac magnetic resonance (CMR) imaging.

Methods—Transthoracic echocardiography (2D and 3D) and cine CMR imaging were performed in 62 prospectively recruited participants (47 healthy controls, 9 patients with LVH, 6 patients with aortic regurgitation), <1 h apart. 2DE LV dimension measurements (interventricular septum [IVS], posterior wall thickness [PWT], and LVID) were taken at end-diastole from the parasternal long axis, and mass was calculated using the linear method based on ASE/EACVI guidelines. For 3DE, 3D geometric models of the LV were constructed by interactively fitting surfaces to the endocardium and epicardium using previously validated software, from which corresponding LV dimension measurements and mass were extracted. Measurements were obtained from CMR by a similar 3D geometric modelling process.

Results—Differences (mean ± SD) in LV dimension measurements between the three modalities and intraclass correlation coefficients (ICC) are presented in Table I. When compared with CMR, 3DE exhibited higher agreement in terms of LVID and mass than 2DE, but lower agreement in wall thickness measurements. Statistically significant differences were found between 2DE and 3DE for PWT, LVID, and mass, as well as 2DE and CMR for LVID and mass (where P < 0.01 for a paired sample t­-test, marked with an asterisk). Meanwhile, there were no statistically significant differences between 3DE and CMR for IVS, PWT, LVID, or mass.

Conclusions—Our results demonstrate that 3DE is superior to 2DE in terms of LVID and mass quantification, exhibiting good agreement with CMR. 3DE exhibited moderate and poor agreement for IVS and PWT, respectively, with both 2DE and CMR, likely due to the lower spatial resolution of 3DE. Further advances in 3DE image quality and analysis tools are therefore needed to improve accuracy of wall thickness measurements. Since 2DE imaging plane and probe positioning can result in oblique measurement and underestimation of LVID, the assessment of LVID and mass by 3DE is likely to lead to more accurate diagnostic and prognostic outcomes. Abstract Table 1

Longitudinal strain measurement by 3D modelling from cine CMR: feasibility and comparison to 2D speckle tracking echocardiography

Background

Global longitudinal strain (GLS) has emerged as a sensitive index of left ventricular (LV) systolic function with greater prognostic value than LV ejection fraction (LVEF) in a variety of cardiac disorders. While GLS is routinely derived from 2D speckle tracking echocardiography (STE) and feature tracking in cardiac magnetic resonance (CMR) imaging, calculation of strain via 3D geometric modelling enables analyses of deformation that are independent of 2D image plane constraints.

Purpose

We sought to compare longitudinal strain measurements extracted from geometric 3D analysis of CMR against values obtained from conventional 2D-STE.

Methods

Consecutive 2D-echocardiography (2D-echo) and steady-state free precession multiplanar cine CMR scans were performed in 80 prospectively recruited participants (48 healthy controls with LVEF range 53–74%, 30 patients with non-ischaemic cardiac disease with LVEF range 25–77%, and 2 heart transplant recipients with LVEF 53% and 58%), <1 hour apart. Average endocardial peak GLS from 2D-STE was calculated offline using vendor-independent clinical software from apical triplane (2, 3 and 4-chamber) images for each of the standardised LV walls (anterior, anteroseptal, inferoseptal, inferior, inferolateral, anterolateral). Dynamic 3D geometric models of the LV were reconstructed from 3 long- and 6 short-axis CMR slices over one cardiac cycle. Corresponding longitudinal strain measurements were then evaluated by extracting analogous endocardial arc lengths (apex to base of each LV wall) from the 3D LV model. Finally, an average peak GLS was calculated as the mean of the peak longitudinal strains in each LV wall.

Results

GLS measured by 2D-STE ranged between −6.5% and −27.9% for the study population. A two-way mixed-effects intraclass correlation coefficient (ICC) for absolute agreement of 0.820 (95% CI: [0.720, 0.885]) demonstrated good correlation between average GLS obtained from 2D-STE and CMR. A Bland-Altman analysis revealed a minimal bias (<1%) and 95% limits of agreement (LOA) between −6.3% and 5.5% (Fig. 1), with no apparent proportional bias. Comparatively lower correlation and wider LOA between longitudinal strains from 2D-STE and CMR were observed for each LV wall (Table I).

Conclusions

Fully automated calculation of LV GLS can be obtained from geometric 3D CMR analysis. Average peak GLS from cine CMR exhibits good agreement with 2D-STE, despite showing only moderate agreement at each LV wall. The increased discrepancy in regional longitudinal strain may be attributed to subjective plane positioning in 2D-echo, which can be expected to improve with advances in 3D-STE. The calculation of GLS by 3D geometric modelling may enhance the diagnostic value of routine cine CMR examinations for LV systolic function assessment.

Funding Acknowledgement

Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Health Research Council (HRC) of New Zealand and National Heart Foundation (NHF) of New Zealand Figure 1. Bland-Altman analysisTable I. Regional correlations

Automated analysis of 3D-echocardiography using spatially registered patient-specific CMR meshes

Funding Acknowledgements

Type of funding sources: Public grant(s) – National budget only. Main funding source(s): National Heart Foundation (NHF) of New Zealand Health Research Council (HRC) of New Zealand

Artificial intelligence shows considerable promise for automated analysis and interpretation of medical images, particularly in the domain of cardiovascular imaging. While application to cardiac magnetic resonance (CMR) has demonstrated excellent results, automated analysis of 3D echocardiography (3D-echo) remains challenging, due to the lower signal-to-noise ratio (SNR), signal dropout, and greater interobserver variability in manual annotations. As 3D-echo is becoming increasingly widespread, robust analysis methods will substantially benefit patient evaluation. 

We sought to leverage the high SNR of CMR to provide training data for a convolutional neural network (CNN) capable of analysing 3D-echo. We imaged 73 participants (53 healthy volunteers, 20 patients with non-ischaemic cardiac disease) under both CMR and 3D-echo (<1 hour between scans). 3D models of the left ventricle (LV) were independently constructed from CMR and 3D-echo, and used to spatially align the image volumes using least squares fitting to a cardiac template. The resultant transformation was used to map the CMR mesh to the 3D-echo image. Alignment of mesh and image was verified through volume slicing and visual inspection (Fig. 1) for 120 paired datasets (including 47 rescans) each at end-diastole and end-systole.

100 datasets (80 for training, 20 for validation) were used to train a shallow CNN for mesh extraction from 3D-echo, optimised with a composite loss function consisting of normalised Euclidian distance (for 290 mesh points) and volume. Data augmentation was applied in the form of rotations and tilts (<15 degrees) about the long axis. The network was tested on the remaining 20 datasets (different participants) of varying image quality (Tab. I). For comparison, corresponding LV measurements from conventional manual analysis of 3D-echo and associated interobserver variability (for two observers) were also estimated.

Initial results indicate that the use of embedded CMR meshes as training data for 3D-echo analysis is a promising alternative to manual analysis, with improved accuracy and precision compared with conventional methods. Further optimisations and a larger dataset are expected to improve network performance.

(n = 20) LV EDV (ml) LV ESV (ml) LV EF (%) LV mass (g) Ground truth CMR 150.5 ± 29.5 57.9 ± 12.7 61.5 ± 3.4 128.1 ± 29.8 Algorithm error -13.3 ± 15.7 -1.4 ± 7.6 -2.8 ± 5.5 0.1 ± 20.9 Manual error -30.1 ± 21.0 -15.1 ± 12.4 3.0 ± 5.0 Not available Interobserver error 19.1 ± 14.3 14.4 ± 7.6 -6.4 ± 4.8 Not available Tab. 1. LV mass and volume differences (means ± standard deviations) for 20 test cases. Algorithm: CNN – CMR (as ground truth). Abstract Figure. Fig 1. CMR mesh registered to 3D-echo.

P4360Personalised shape models of the left ventricle from 3D echocardiography: an initial comparison to cardiac magnetic resonance imaging

Background

The heart constantly adapts to maintain cardiac output. In the longer term, this process (remodeling) can manifest as changes in ventricular volume, sphericity, and/or wall thickness, amongst several other morphological indices. Previous studies have shown the significance of remodeling in evaluations of survival, and as a determinant of the clinical course of heart failure. Yet surprisingly, diagnostic measures, typically of left ventricular (LV) mass and ejection fraction, neglect much of the shape information that is available through imaging. A recent UK Biobank study revealed that morphometric atlases show more compelling associations with cardiovascular risk factors, than do LV mass and volumes. While it has been possible to construct shape models from cardiac magnetic resonance imaging (MRI), such a framework is still under development for echocardiography (echo).

Purpose

Despite MRI being long regarded as the gold standard, it is greatly limited by high costs, long scan times and incompatibility with ferromagnetic cardiac devices. In contrast, echo has presented as a convenient alternative, whilst also offering good temporal resolution. The advancements of 3D echo now provide adequate spatial resolution and thus elicit the possibility of conducting more complex analyses on this modality. With the ability to extract LV geometry directly from 3D echo acquisitions, we sought to create dynamic, 3D patient-specific models–and subsequently compare these results to those derived from MRI.

Methods

As part of an ongoing study, 8 volunteers with no known cardiovascular problems (nor family history thereof), were recruited for non-invasive imaging. Cine MRI and 3D echo of the LV were acquired within a 2 hour session. A Siemens Avanto Fit 1.5 T MRI scanner and Siemens ACUSON SC2000 Ultrasound System with a 4Z1c Transducer were used. 3D models of the LV were generated independently from echo (EchobuildR 2.7 prototype software, Siemens Ultrasound) and MRI acquisitions (Cardiac Image Modeller v8.1), and registered to fiducial landmarks (apex, base plane, right ventricular inserts) and myocardial contours.

Results

Euclidian distances between 1682 corresponding points sampled from the surface of echo/MRI models were calculated, and used as a discrepancy measure (Figure). Across the 8 cases, we found an average root mean square deviation (RMSD) of 5.71 mm at end-systole and 6.03 mm at end-diastole. The maximum RMSD for a single model was 9.47 mm (case 8, ES).

Conclusion

We demonstrate that it is possible to create shape models from 3D echo examinations for comparison with MRI. As more cases are collected, we will devise methods to objectively quantify the mismatch that may arise between models derived from the two modalities. The establishment of such a framework would not only provide previously unavailable measures of shape and function, but in turn leverage the significantly wider clinical reach of echocardiography.

Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques

A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.

Head kinematics during shaking associated with abusive head trauma

Abusive head trauma (AHT) is a potentially fatal result of child abuse but the mechanisms of injury are controversial. To address the hypothesis that shaking alone is sufficient to elicit the injuries observed, effective computational and experimental models are necessary. This paper investigates the use of a coupled rigid-body computational modelling framework to reproduce in vivo shaking kinematics in AHT. A sagittal plane OpenSim computational model of a lamb was developed and used to interpret biomechanical data from in vivo shaking experiments. The acceleration of the head during shaking was used to provide in vivo validation of the associated computational model. Results of this study demonstrated that peak accelerations occurred when the head impacted the torso and produced acceleration magnitudes exceeding 200ms(-)(2). The computational model demonstrated good agreement with the experimental measurements and was shown to be able to reproduce the high accelerations that occur during impact. The biomechanical results obtained with the computational model demonstrate the utility of using a coupled rigid-body modelling framework to describe infant head kinematics in AHT.

Myocardial twitch duration and the dependence of oxygen consumption on pressure-volume area: experiments and modelling

We tested the proposition that linear length dependence of twitch duration underlies the well-characterised linear dependence of oxygen consumption (V(O(2)) ) on pressure–volume area (PVA) in the heart. By way of experimental simplification, we reduced the problem from three dimensions to one by substituting cardiac trabeculae for the classically investigated whole-heart. This allowed adoption of stress–length area (SLA) as a surrogate for PVA, and heat as a proxy for V(O(2)) . Heat and stress (force per cross-sectional area), at a range of muscle lengths and at both 1 mM and 2 mM [Ca(2+)](o), were recorded from continuously superfused rat right-ventricular trabeculae undergoing fixed-end contractions. The heat–SLA relations of trabeculae (reported here, for the first time) are linear. Twitch duration increases monotonically (but not strictly linearly) with muscle length. We probed the cellular mechanisms of this phenomenon by determining: (i) the length dependence of the duration of the Ca(2+) transient, (ii) the length dependence of the rate of force redevelopment following a length impulse (an index of Ca(2+) binding to troponin-C), (iii) the effect on the simulated time course of the twitch of progressive deletion of length and Ca(2+)-dependent mechanisms of crossbridge cooperativity, using a detailed mathematical model of the crossbridge cycle, and (iv) the conditions required to achieve these multiple length dependencies, using a greatly simplified model of twitch mechano-energetics. From the results of these four independent investigations, we infer that the linearity of the heat–SLA relation (and, by analogy, the V(O(2))–PVA relation) is remarkably robust in the face of departures from linearity of length-dependent twitch duration.

Comparison of the Gibbs and Suga formulations of cardiac energetics: the demise of "isoefficiency"

Two very different sorts of experiments have characterized the field of cardiac energetics over the past three decades. In one of these, Gibbs and colleagues measured the heat production of isolated papillary muscles undergoing isometric contractions and afterloaded isotonic contractions. The former generated roughly linear heat vs. force relationships. The latter generated enthalpy-load relationships, the peak values of which occurred at or near peak isometric force, i.e., at a relative load of unity. Contractile efficiency showed a pronounced dependence on afterload. By contrast, Suga and coworkers measured the oxygen consumption (Vo(2)) while recording the pressure-volume-time work loops of blood-perfused isolated dog hearts. From the associated (linear) end-systolic pressure-volume relations they derived a quantity labeled pressure-volume area (PVA), consisting of the sum of pressure-volume work and unspent elastic energy and showed that this was linearly correlated with Vo(2) over a wide range of conditions. This linear dependence imposed isoefficiency: constant contractile efficiency independent of afterload. Neither these data nor those of Gibbs and colleagues are in dispute. Nevertheless, despite numerous attempts over the years, no demonstration of either compatibility or incompatibility of these disparate characterizations of cardiac energetics has been forthcoming. We demonstrate that compatibility between the two formulations is thwarted by the concept of isoefficiency, the thermodynamic basis of which we show to be untenable.

Relating components of pressure-volume area in Suga's formulation of cardiac energetics to components of the stress-time integral

The concept of pressure-volume area (PVA) in whole heart studies is central to the phenomenological description of cardiac energetics proposed by Suga and colleagues (Physiol Rev 70: 247-277, 1990). PVA consists of two components: an approximately rectangular work loop (W) and an approximately triangular region of potential energy (U). In the case of isovolumic contractions, PVA consists entirely of U. The utility of Suga's description of cardiac energetics is the observation that the oxygen consumption of the heart (Vo(2)) is linearly dependent on PVA. By using isolated ventricular trabeculae, we found a basis on which to correlate the components of stress-length area (SLA; i.e., the 1-D equivalent of PVA) with specific regions of the stress-time integral (STI; i.e., the area under the force-time profile of a single twitch). In each case, proportionality obtains and is robust, independent of the type of twitch contraction (isometric or isotonic), and insensitive to changes of preload or afterload. We apply our results by examining retrospectively the interpretations reached in three independent studies published in the literature.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K⁺ current, (ii) elevated extracellular K⁺ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca²⁺ current I(Ca,L). Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.

The effect of hoof angle variations on dorsal lamellar load in the equine hoof

REASONS FOR PERFORMING STUDY

In the treatment of laminitis it is believed that reducing tension in the deep digital flexor tendon by raising the palmar angle of the hoof can reduce the load on the dorsal lamellae, allowing them to heal or prevent further damage.

OBJECTIVE

To determine the effect of alterations in hoof angle on the load in the dorsal laminar junction.

METHODS

Biomechanical finite element models of equine hooves were created with palmar angles of the distal phalanx varying from 0-15°. Tissue material relations accounting for anisotropy and the effect of moisture were used. Loading conditions simulating the stages in the stance where the vertical ground reaction force, midstance joint moment and breakover joint moment were maximal, were applied to the models. The loads were adjusted to account for the reduction in joint moment caused by increasing the palmar angle. Models were compared using the stored elastic energy, an indication of load, which was sampled in the dorsal laminar junction.

RESULTS

For all loading cases, increasing the palmar angle increased the stored elastic energy in the dorsal laminar junction. The stored elastic energy near the proximal laminar junction border for a palmar angle of 15° was between 1.3 and 3.8 times that for a palmar angle of 0°. Stored elastic energy at the distal laminar junction border was small in all cases. For the breakover case, stored elastic energy at the proximal border also increased with increasing palmar angle.

CONCLUSIONS AND POTENTIAL RELEVANCE

The models in this study predict that raising the palmar angle increases the load on the dorsal laminar junction. Therefore, hoof care interventions that raise the palmar angle in order to reduce the dorsal lamellae load may not achieve this outcome.

A finite element study of invariant-based orthotropic constitutive equations in the context of myocardial material parameter estimation

A previous study investigated a number of invariant-based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. The study was based on the assumption of a homogeneous deformation. Here, we extend the previous study by performing an inverse finite element material parameter estimation. This ensures a more realistic deformation state and material parameter estimates. The constitutive relations were compared on the basis of (i) 'goodness of fit': how well they fit a set of six shear deformation tests and (ii) 'variability': how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive relations. It was found that a specific form of the polyconvex type as well as the exponential Fung-type equations were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

Electromechanical wavebreak in a model of the human left ventricle

In the present report, we introduce an integrative three-dimensional electromechanical model of the left ventricle of the human heart. Electrical activity is represented by the ionic TP06 model for human cardiac cells, and mechanical activity is represented by the Niederer-Hunter-Smith active contractile tension model and the exponential Guccione passive elasticity model. These models were embedded into an anatomic model of the left ventricle that contains a detailed description of cardiac geometry and the fiber orientation field. We demonstrated that fiber shortening and wall thickening during normal excitation were qualitatively similar to experimental recordings. We used this model to study the effect of mechanoelectrical feedback via stretch-activated channels on the stability of reentrant wave excitation. We found that mechanoelectrical feedback can induce the deterioration of an otherwise stable spiral wave into turbulent wave patterns similar to that of ventricular fibrillation. We identified the mechanisms of this transition and studied the three-dimensional organization of this mechanically induced ventricular fibrillation.

Coupling multi-physics models to cardiac mechanics

We outline and review the mathematical framework for representing mechanical deformation and contraction of the cardiac ventricles, and how this behaviour integrates with other processes crucial for understanding and modelling heart function. Building on general conservation principles of space, mass and momentum, we introduce an arbitrary Eulerian-Lagrangian framework governing the behaviour of both fluid and solid components. Exploiting the natural alignment of cardiac mechanical properties with the tissue microstructure, finite deformation measures and myocardial constitutive relations are referred to embedded structural axes. Coupling approaches for solving this large deformation mechanics framework with three dimensional fluid flow, coronary hemodynamics and electrical activation are described. We also discuss the potential of cardiac mechanics modelling for clinical applications.

Myocardial material parameter estimation: a comparison of invariant based orthotropic constitutive equations

This study investigated a number of invariant based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. A number of orthotropic laws based on Green strain components and one microstructurally based law have previously been investigated to fit experimental measurements of stress-strain behaviour. Here we extend this investigation to include several recently proposed functional forms, i.e. invariant based orthotropic and transversely isotropic constitutive relations. These laws were compared on the basis of (i) 'goodness of fit': how well they fit a set of six shear deformation tests, (ii) 'variability': how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive laws. It was found that a specific form of the polyconvex type as well as the exponential Fung-type law from the previous study were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

A computational study of mother rotor VF in the human ventricles

Sudden cardiac death is one of the major causes of death in the industrialized world. It is most often caused by a cardiac arrhythmia called ventricular fibrillation (VF). Despite its large social and economical impact, the mechanisms for VF in the human heart yet remain to be identified. Two of the most frequently discussed mechanisms observed in experiments with animal hearts are the multiple wavelet and mother rotor hypotheses. Most recordings of VF in animal hearts are consistent with the multiple wavelet mechanism. However, in animal hearts, mother rotor fibrillation has also been observed. For both multiple wavelet and mother rotor VF, cardiac heterogeneity plays an important role. Clinical data of action potential restitution measured from the surface of human hearts have been recently published. These in vivo data show a substantial degree of spatial heterogeneity. Using these clinical restitution data, we studied the dynamics of VF in the human heart using a heterogeneous computational model of human ventricles. We hypothesized that this observed heterogeneity can serve as a substrate for mother rotor fibrillation. We found that, based on these data, mother rotor VF can occur in the human heart and that ablation of the mother rotor terminates VF. Furthermore, we found that both mother rotor and multiple wavelet VF can occur in the same heart depending on the initial conditions at the onset of VF. We studied the organization of these two types of VF in terms of filament numbers, excitation periods, and frequency domains. We conclude that mother rotor fibrillation is a possible mechanism in the human heart.

Organization of ventricular fibrillation in the human heart: experiments and models

Sudden cardiac death is a major health problem in the industrialized world. The lethal event is typically ventricular fibrillation (VF), during which the co-ordinated regular contraction of the heart is overthrown by a state of mechanical and electrical anarchy. Understanding the excitation patterns that sustain VF is important in order to identify potential therapeutic targets. In this paper, we studied the organization of human VF by combining clinical recordings of electrical excitation patterns on the epicardial surface during in vivo human VF with simulations of VF in an anatomically and electrophysiologically detailed computational model of the human ventricles. We find both in the computational studies and in the clinical recordings that epicardial surface excitation patterns during VF contain around six rotors. Based on results from the simulated three-dimensional excitation patterns during VF, which show that the total number of electrical sources is 1.4 +/- 0.12 times greater than the number of epicardial rotors, we estimate that the total number of sources present during clinically recorded VF is 9.0 +/- 2.6. This number is approximately fivefold fewer compared with that observed during VF in dog and pig hearts, which are of comparable size to human hearts. We explain this difference by considering differences in action potential duration dynamics across these species. The simpler spatial organization of human VF has important implications for treatment and prevention of this dangerous arrhythmia. Moreover, our findings underline the need for integrated research, in which human-based clinical and computational studies complement animal research.

Finite element modelling of breast biomechanics: directly calculating the reference state

Patient-specific models of the biomechanics of the breast based on finite deformation theory is potentially a valuable tool to assist clinicians in assimilating and assessing information obtained from different views of the breast, under different loading conditions and using different imaging modalities. It is anticipated that a computational model of the large deformation mechanics of the breast will also improve the accuracy of non-rigid registration techniques by restricting the deformations imposed by the algorithm to be those which are physically plausible. Accurate registration will assist clinicians in tracking suspicious regions of tissue across multiple views of the breast, which are typically taken by applying different loads on the breast during imaging. For instance, a model that can predict deformations during mammography would help to track a region of tissue between a cranio-caudal (CC) view and a medio-lateral oblique (MLO) view. Due to the nonlinear deformations imposed on the breast during different imaging techniques, the finite element reference geometry from which deformations are predicted is important. Gravity loads act on the breast during all imaging modalities. In this paper, we describe a novel modification to solving the finite element implementation of finite deformation theory, which can predict the reference state of the breast from a deformed configuration that has been derived from images of a patient placed in a single known orientation with respect to the direction of gravity.

Effect of heterogeneous APD restitution on VF organization in a model of the human ventricles

The onset of ventricular fibrillation (VF) has been associated with steep action potential duration restitution in both clinical and computational studies. Recently, detailed clinical restitution properties in cardiac patients were reported showing a substantial degree of heterogeneity in restitution slopes at the epicardium of the ventricles. The aim of the present study was to investigate the effect of heterogeneous restitution properties in a three-dimensional model of the ventricles using these clinically measured restitution data. We used a realistic model of the human ventricles, including detailed descriptions of cell electrophysiology, ventricular anatomy, and fiber direction anisotropy. We extended this model by mapping the clinically observed epicardial restitution data to our anatomic representation using a diffusion-based algorithm. Restitution properties were then fitted by regionally varying parameters of the electrophysiological model. We studied the effects of restitution heterogeneity on the organization of VF by analyzing filaments and the distributions of excitation periods. We found that the number of filaments and the excitation periods were both dependent on the extent of heterogeneity. An increased level of heterogeneity leads to a greater number of filaments and a broader distribution of excitation periods, thereby increasing the complexity and dynamics of VF. Restitution heterogeneity may play an important role in providing a substrate for cardiac arrhythmias.

Myocardial material parameter estimation: a non-homogeneous finite element study from simple shear tests

The passive material properties of myocardium play a major role in diastolic performance of the heart. In particular, the shear behaviour is thought to play an important mechanical role due to the laminar architecture of myocardium. We have previously compared a number of myocardial constitutive relations with the aim to extract their suitability for inverse material parameter estimation. The previous study assumed a homogeneous deformation. In the present study we relaxed the homogeneous assumption by implementing these laws into a finite element environment in order to obtain more realistic measures for the suitability of these laws in both their ability to fit a given set of experimental data, as well as their stability in the finite element environment. In particular, we examined five constitutive laws and compare them on the basis of (i) "goodness of fit": how well they fit a set of six shear deformation tests, (ii) "determinability": how well determined the objective function is at the optimal parameter fit, and (iii) "variability": how well determined the material parameters are over the range of experiments. Furthermore, we compared the FE results with those from the previous study.It was found that the same material law as in the previous study, the orthotropic Fung-type "Costa-Law", was the most suitable for inverse material parameter estimation for myocardium in simple shear.

Drift and breakup of spiral waves in reaction-diffusion-mechanics systems

Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction-diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD-mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD-mechanics systems for mathematics applied to life sciences.

Finite Element Modelling of Breast Biomechanics: Finding a Reference aState

Non-rigid-body registration techniques, that constrain the set of possible soft tissue deformations to be consistent with the basic laws of physics, offer a means of providing realistic and accurate estimates of breast movement under mammographic compression. Such constraints can be imposed by the use of anatomically accurate finite element models that predict soft tissue deformations. The overarching aim is to develop tools for tracking regions of interest across multiple images (different views taken at different times) for image-guided surgeries and reliable diagnostic and therapy monitoring. Due to the nonlinear deformations imposed on the breast under the various imaging modalities, the finite element reference geometry from which deformations are predicted is important. Gravity loads act on the breast in all imaging modalities. In this paper, we propose a method of identifying a stress-free reference state of the breast given a series of loaded deformed configurations that have been derived from images of a patient placed in different orientations with respect to the direction of gravity.

A biomechanical model of mammographic compressions

A number of biomechanical models have been proposed to improve nonrigid registration techniques for multimodal breast image alignment. A deformable breast model may also be useful for overcoming difficulties in interpreting 2D X-ray projections (mammograms) of 3D volumes (breast tissues). If a deformable model could accurately predict the shape changes that breasts undergo during mammography, then the model could serve to localize suspicious masses (visible in mammograms) in the unloaded state, or in any other deformed state required for further investigations (such as biopsy or other medical imaging modalities). In this paper, we present a validation study that was conducted in order to develop a biomechanical model based on the well-established theory of continuum mechanics (finite elasticity theory with contact mechanics) and demonstrate its use for this application. Experimental studies using gel phantoms were conducted to test the accuracy in predicting mammographic-like deformations. The material properties of the gel phantom were estimated using a nonlinear optimization process, which minimized the errors between the experimental and the model-predicted surface data by adjusting the parameter associated with the neo-Hookean constitutive relation. Two compressions (the equivalent of cranio-caudal and medio-lateral mammograms) were performed on the phantom, and the corresponding deformations were recorded using a MRI scanner. Finite element simulations were performed to mimic the experiments using the estimated material properties with appropriate boundary conditions. The simulation results matched the experimental recordings of the deformed phantom, with a sub-millimeter root-mean-square error for each compression state. Having now validated our finite element model of breast compression, the next stage is to apply the model to clinical images.

A Computationally Efficient Optimization Kernel for Material Parameter Estimation Procedures

Estimating material parameters is an important part in the study of soft tissue mechanics. Computational time can easily run to days, especially when all available experimental data are taken into account. The material parameter estimation procedure is examplified on a set of homogeneous simple shear experiments to estimate the orthotropic constitutive parameters of myocardium. The modification consists of changing the traditional least-squares approach to a weighted least-squares. This objective function resembles a L2-norm type integral which is approximated using Gaussian quadrature. This reduces the computational time of the material parameter estimation by two orders of magnitude.

Myocardial Material Parameter Estimation—A Comparative Study for Simple Shear

The study of ventricular mechanics—analyzing the distribution of strain and stress in myocardium throughout the cardiac cycle—is crucially dependent on the accuracy of the constitutive law chosen to represent the highly nonlinear and anisotropic properties of passive cardiac muscle. A number of such laws have been proposed and fitted to experimental measurements of stress-strain behavior. Here we examine five of these laws and compare them on the basis of (i) “goodness of fit:” How well they fit a set of six shear deformation tests, (ii) “determinability:” How well determined the objective function is at the optimal parameter fit, and (iii) “variability:” How well determined the material parameters are over the range of experiments. These criteria are utilized to discuss the advantages and disadvantages of the constitutive laws.

Self-organized pacemakers in a coupled reaction-diffusion-mechanics system

Using a computational model of a coupled reaction-diffusion-mechanics system, we find that mechanical deformation can induce automatic pacemaking activity. Pacemaking is shown to occur after a single electrical or mechanical stimulus in an otherwise nonoscillatory medium. We study the mechanisms underpinning this effect and conditions for its existence. We show that self-organized pacemakers drift throughout the medium to approach attractors with locations that depend on the size of the medium, and on the location of the initial stimulus.

Noninvasive electrical imaging of the heart: theory and model development

The aim of this work is to begin quantifying the performance of a recently developed activation imaging algorithm of Huiskamp and Greensite [IEEE Trans. Biomed. Eng. 44:433-446]. We present here the modeling and computational issues associated with this process. First, we present a practical construction of the appropriate transfer matrix relating an activation sequence to body surface potentials from a general boundary value problem point of view. This approach makes explicit the role of different Green's functions and elucidates features (such as the anisotropic versus isotropic distinction) not readily apparent from alternative formulations. A new analytic solution is then developed to test the numerical implementation associated with the transfer matrix formulation presented here and convergence results for both potentials and normal currents are given. Next, details of the construction of a generic porcine model using a nontraditional data-fitting procedure are presented. The computational performance of this model is carefully examined to obtain a mesh of an appropriate resolution to use in inverse calculations. Finally, as a test of the entire approach, we illustrate the activation inverse procedure by reconstructing a known activation sequence from simulated data. For the example presented, which involved two ectopic focii with large amounts of Gaussian noise (100 microV rms) present in the torso signals, the reconstructed activation sequence had a similarity index of 0.880 when compared to the input source.

Ventricular activation during sympathetic imbalance and its computational reconstruction

We characterized the epicardial activation sequence during a norepinephrine (NE)-induced ventricular arrhythmia in anesthetized pigs and studied factors that modulated it. Subepicardial NE infusion caused the QRS complex to invert within a single beat (n = 35 animals, 101 observations), and the earliest epicardial activation consistently shifted to the randomly located infusion site (n = 14). This preceded right atrial activation, whereas the total ventricular epicardial activation time increased from 20 +/- 4 to 50 +/- 9 ms (P < 0.01). These events were accompanied by a ventricular tachycardia and a drop in left ventricular pressure, which were fully reversed after the infusion was stopped. Epicardial pacing at the infusion site mimicked all electrical and hemodynamic changes induced by NE. The arrhythmia was prevented by propranolol and abolished by cardiac sympathetic or vagal nerve stimulation. Focal automaticity was computationally reconstructed using a two-dimensional sheet of 256 x 256 resistively coupled ventricular cells, where calcium handling was abnormally high in the central region. We conclude that adrenergic stimulation to a small region of the ventricle elicits triggered automaticity and that computational reconstruction implicates calcium overload. Interventions that reduce spatial inhomogeneities of intracellular calcium may prevent this type of arrhythmia.