The Cardiac Physiome Project

Preserving multi-dimensional information: A hypersphere method for parameter space analysis

Background

Physiological modelling often involves models described by large numbers of variables and significant volumes of clinical data. Mathematical interpretation of such models frequently necessitates analysing data points in high-dimensional spaces. Existing algorithms for analysing high-dimensional points either lose important dimensionality or do not describe the full position of points. Hence, there is a need for an algorithm which preserves this information.

Methods

The most-distant uncovered point (MDUP) hypersphere method is a binary classification approach which defines a collection of equidistant N-dimensional points as the union of hyperspheres. The method iteratively generates hyperspheres at the most distant point in the interest region not yet contained within any hypersphere, until the entire region of interest is defined by the union of all generated hyperspheres. This method is tested on a 7-dimensional space with up to 35.8 million points representing feasible and infeasible spaces of model parameters for a clinically validated cardiovascular system model.

Results

For different numbers of input points, the MDUP hypersphere method tends to generate large spheres away from the boundary of feasible and infeasible points, but generates the greatest number of relatively much smaller spheres around the boundary of the region of interest to fill this space. Runtime scales quadratically, in part because the current MDUP implementation is not parallelised.

Conclusions

The MDUP hypersphere method can define points in a space of any dimension using only a collection of centre points and associated radii, making the results easily interpretable. It can identify large continuous regions, and in many cases capture the general structure of a region in only a relative few hyperspheres. The MDUP method also shows promise for initialising optimisation algorithm starting conditions within pre-defined feasible regions of model parameter spaces, which could improve model identifiability and the quality of optimisation results.

Finite velocity of ECG signal propagation: preliminary theory, results of a pilot experiment and consequences for medical diagnosis

A satisfactory model of the biopotentials propagating through the human body is essential for medical diagnostics, particularly for cardiovascular diseases. In our study, we develop the theory, that the propagation of biopotential of cardiac origin (ECG signal) may be treated as the propagation of low-frequency endogenous electromagnetic wave through the human body. We show that within this approach, the velocity of the ECG signal can be theoretically estimated, like for any other wave and physical medium, from the refraction index of the tissue in an appropriate frequency range. We confirm the theoretical predictions by the comparison with a direct measurement of the ECG signal propagation velocity and obtain mean velocity as low as v=1500 m/s. The results shed new light on our understanding of biopotential propagation through living tissue. This propagation depends on the frequency band of the signal and the transmittance of the tissue. This finding may improve the interpretation of the electric measurements, such as ECG and EEG when the frequency dependence of conductance and the phase shift introduced by the tissue is considered. We have shown, that the ECG propagation modifies the amplitude and phase of signal to a considerable extent. It may also improve the convergence of inverse problem in electrocardiographic imaging.

Modelling patient specific cardiopulmonary interactions

Mechanical ventilation is well known for having detrimental effects on the cardiovascular system, particularly when using high positive end-expiratory pressure. High positive end-expiratory pressure levels cause a decrease in stroke volume, which, under normal conditions, usually bring about a decrease in stressed blood volume. Stressed blood volume, defined as the total pressure generating volume of the cardiovascular system, has been shown to be a potential index of fluid responsiveness, making it a potentially important diagnostic tool. Generally, respiratory and haemodynamic care are provided independently of one another. However, that positive end-expiratory pressure alters both stroke volume and stressed blood volume suggests both the pulmonary and cardiovascular state should be conjointly optimised and used to guide positive end-expiratory pressure. However, the complex and patient-specific nature of cardiopulmonary interactions which occur during mechanical ventilation presents a challenge for accurate modelling of respiratory and cardiovascular interactions required to better optimise care. Previous models attempting to incorporate cardiopulmonary interactions have suffered from poor reliability at higher PEEP levels, largely due to an exaggerated effect of intrathoracic pressure on the cardiovascular system. A new parameter, alpha, is added to a previously validated cardiopulmonary model, to modulate the percentage of intrathoracic pressure applied to the vena cava and left ventricle. The new parameter aims to increase reliability under high PEEP conditions as well as provide a patient specific solution to modelling cardiopulmonary interactions. The results from the identified optimal alpha are compared to the original model to investigate how this new parameter may be used to create a more patient-specific cardiopulmonary model, which would be better suited for guidance of care in the ICU.

Spatially resolved transcriptomics in immersive environments

Spatially resolved transcriptomics is an emerging class of high-throughput technologies that enable biologists to systematically investigate the expression of genes along with spatial information. Upon data acquisition, one major hurdle is the subsequent interpretation and visualization of the datasets acquired. To address this challenge, VR-Cardiomics is presented, which is a novel data visualization system with interactive functionalities designed to help biologists interpret spatially resolved transcriptomic datasets. By implementing the system in two separate immersive environments, fish tank virtual reality (FTVR) and head-mounted display virtual reality (HMD-VR), biologists can interact with the data in novel ways not previously possible, such as visually exploring the gene expression patterns of an organ, and comparing genes based on their 3D expression profiles. Further, a biologist-driven use-case is presented, in which immersive environments facilitate biologists to explore and compare the heart expression profiles of different genes.

In silico trials: Verification, validation and uncertainty quantification of predictive models used in the regulatory evaluation of biomedical products

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Regulators now consider also evidences produced in silico.

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We need accepted methods to evaluate the credibility of models.

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In this paper we describe the use of the ASME V&V-40 technical standard.

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We also discuss its application to various types of modelling methods.

Historically, the evidences of safety and efficacy that companies provide to regulatory agencies as support to the request for marketing authorization of a new medical product have been produced experimentally, either in vitro or in vivo. More recently, regulatory agencies started receiving and accepting evidences obtained in silico, i.e. through modelling and simulation. However, before any method (experimental or computational) can be acceptable for regulatory submission, the method itself must be considered “qualified” by the regulatory agency. This involves the assessment of the overall “credibility” that such a method has in providing specific evidence for a given regulatory procedure. In this paper, we describe a methodological framework for the credibility assessment of computational models built using mechanistic knowledge of physical and chemical phenomena, in addition to available biological and physiological knowledge; these are sometimes referred to as “biophysical” models. Using guiding examples, we explore the definition of the context of use, the risk analysis for the definition of the acceptability thresholds, and the various steps of a comprehensive verification, validation and uncertainty quantification process, to conclude with considerations on the credibility of a prediction for a specific context of use. While this paper does not provide a guideline for the formal qualification process, which only the regulatory agencies can provide, we expect it to help researchers to better appreciate the extent of scrutiny required, which should be considered early on in the development/use of any (new) in silico evidence.