Bayesian inference of constitutive model parameters from uncertain uniaxial experiments on murine tendons

Akintunde, Akinjide R.; Miller, Kristin S.; Schiavazzi, Daniele E.

doi:10.1016/j.jmbbm.2019.04.037

Cited by 14 publications

(7 citation statements)

References 36 publications

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“…and data sources used to store the available clinical targets. For an overview of the procedures for statistical data assimilation used in this study, the interested reader is referred to [49, 50].…”

Section: Methodsmentioning

confidence: 99%

Predictive modeling of secondary pulmonary hypertension in left ventricular diastolic dysfunction

Harrod

Rogers²,

Feinstein

et al. 2020

Preprint

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Diastolic dysfunction is a common pathology occurring in about one third of patients affected by heart failure. This condition is not associated with a marked decrease in cardiac output or systemic pressure and therefore is more difficult to diagnose than its systolic counterpart. Compromised relaxation or increased stiffness of the left ventricle with or without mitral valve stenosis induces an increase in the upstream pulmonary pressures, and classified as secondary or group II (2018 Nice classification) pulmonary hypertension. This may result in an increase in the right ventricular afterload leading to right ventricular failure. Elevated pulmonary pressures are therefore an important clinical indicator of diastolic heart failure (sometimes referred to as "heart failure with preserved ejection fraction"), showing significant correlation with associated mortality. Accurate measurements of this quantity, however, are typically obtained through invasive catheterization, and after the onset of symptoms. In this study, we use the hemodynamic consistency of a differential-algebraic circulation model to predict pulmonary pressures in adult patients from other, possibly non-invasive, clinical data. We investigate several aspects of the problem, including the well posedness of a modeling approach for this type of disease, identifiability of its parameters, to the accuracy of the predicted pulmonary pressures. We also find that a classifier using the assimilated model parameters as features is free from the problem of missing data and is able to detect pulmonary hypertension with sufficiently high accuracy. For a cohort of 82 patients suffering from various degrees of heart failure severity we show that systolic, diastolic and wedge pulmonary pressures can be estimated on average within 8, 6 and 6 mmHg, respectively. We also show that, in general, increased data availability leads to improved predictions.

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Section: Methodsmentioning

confidence: 99%

Predictive modeling of secondary pulmonary hypertension in left ventricular diastolic dysfunction

Harrod

Rogers²,

Feinstein

et al. 2020

Preprint

Self Cite

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“…We also mention 17,18 for an application of MCMC to mathematical models for tumour growth. Although rare, in cardiovascular modelling, examples of studies employing MCMC to sample from multi‐modal distributions are 19 : with an application in soft tissue mechanics – constitutive modelling of tendon ligaments in mice, and 20 with an application in haemodynamic models – modelling of pulmonary hypertension with a lumped parameter model on human data.…”

Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlowith Gaussian processes for fast parameter estimation and uncertainty quantification in a1Dfluid‐dynamics model of the pulmonary circulation

Păun

Husmeier

2020

Numer Methods Biomed Eng

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The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid‐dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient‐specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed‐form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state‐of‐the‐art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long‐term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

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“…An example of a simple functions h satisfying our assumptions is h(s) = sin(2s). Now, we focus on the turning rate T given by (2). We rewrite the model in the weak form, and for simplicity we express the nonlinear weight µ[f ] (t, y, θ) as…”

Section: Asymptotic Fokker-planck Model Reductionmentioning

confidence: 99%

“…The modelling of the process of tendon healing has virtually not been addressed in the literature until recently. Some works have analysed equilibrium configurations based on macroscopic elasticity models [1,2,3]. However, the dynamics of the tendon healing process, leading to possible modelling of healing time, have not been discussed at all.…”

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confidence: 99%

Mathematical modelling of collagen fibres rearrangement during the tendon healing process

Carrillo¹,

Parisot²,

Szymańska³

2021

KRM

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Tendon injuries present a clinical challenge to modern medicine as they heal slowly and rarely is there full restoration to healthy tendon structure and mechanical strength. Moreover, the process of healing is not fully elucidated. To improve understanding of tendon function and the healing process, we propose a new model of collagen fibres rearrangement during tendon healing. The model consists of an integro-differential equation describing the dynamics of collagen fibres distribution. We further reduce the model in a suitable asymptotic regime leading to a nonlinear non-local Fokker-Planck type equation for the spatial and orientation distribution of collagen fibre bundles. Due to its simplicity, the reduced model allows for possible parameter estimation based on data. We showcase some of the qualitative properties of this model simulating its long time asymptotic behaviour and the total time for tendon fibres to align in terms of the model parameters. A possible biological interpretation of the numerical experiments performed leads us to the working hypothesis of the importance of tendon cell size in patient recovery.

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Bayesian inference of constitutive model parameters from uncertain uniaxial experiments on murine tendons

Cited by 14 publications

References 36 publications

Predictive modeling of secondary pulmonary hypertension in left ventricular diastolic dysfunction

Predictive modeling of secondary pulmonary hypertension in left ventricular diastolic dysfunction

Markov chain Monte Carlowith Gaussian processes for fast parameter estimation and uncertainty quantification in a1Dfluid‐dynamics model of the pulmonary circulation

Mathematical modelling of collagen fibres rearrangement during the tendon healing process

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