Improved Electrical Impedance Tomography Reconstruction via a Bayesian Approach With an Anatomical Statistical Shape Model.

OBJECTIVE: electrical impedance tomography (EIT) is a promising technique for rapid and continuous bedside monitoring of lung function. Accurate and reliable EIT reconstruction of ventilation requires patient-specific shape information. However, this shape information is often not available and current EIT reconstruction methods typically have limited spatial fidelity. This study sought to develop a statistical shape model (SSM) of the torso and lungs and evaluate whether patient-specific predictions of torso and lung shape could enhance EIT reconstructions in a Bayesian framework. METHODS: torso and lung finite element surface meshes were fitted to computed tomography data from 81 participants, and a SSM was generated using principal component analysis and regression analyses. Predicted shapes were implemented in a Bayesian EIT framework and were quantitatively compared to generic reconstruction methods. RESULTS: Five principal shape modes explained 38% of the cohort variance in lung and torso geometry, and regression analysis yielded nine total anthropometrics and pulmonary function metrics that significantly predicted these shape modes. Incorporation of SSM-derived structural information enhanced the accuracy and reliability of the EIT reconstruction as compared to generic reconstructions, demonstrated by reduced relative error, total variation, and Mahalanobis distance. CONCLUSION: As compared to deterministic approaches, Bayesian EIT afforded more reliable quantitative and visual interpretation of the reconstructed ventilation distribution. However, no conclusive improvement of reconstruction performance using patient specific structural information was observed as compared to the mean shape of the SSM. SIGNIFICANCE: The presented Bayesian framework builds towards a more accurate and reliable method for ventilation monitoring via EIT.

Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models.

Stochastic individual-based mathematical models are attractive for modelling biological phenomena because they naturally capture the stochasticity and variability that is often evident in biological data. Such models also allow us to track the motion of individuals within the population of interest. Unfortunately, capturing this microscopic detail means that simulation and parameter inference can become computationally expensive. One approach for overcoming this computational limitation is to coarse-grain the stochastic model to provide an approximate continuum model that can be solved using far less computational effort. However, coarse-grained continuum models can be biased or inaccurate, particularly for certain parameter regimes. In this work, we combine stochastic and continuum mathematical models in the context of lattice-based models of two-dimensional cell biology experiments by demonstrating how to simulate two commonly used experiments: cell proliferation assays and barrier assays. Our approach involves building a simple statistical model of the discrepancy between the expensive stochastic model and the associated computationally inexpensive coarse-grained continuum model. We form this statistical model based on a limited number of expensive stochastic model evaluations at design points sampled from a user-chosen distribution, corresponding to a computer experiment design problem. With straightforward design point selection schemes, we show that using the statistical model of the discrepancy in tandem with the computationally inexpensive continuum model allows us to carry out prediction and inference while correcting for biases and inaccuracies due to the continuum approximation. We demonstrate this approach by simulating a proliferation assay, where the continuum limit model is the well-known logistic ordinary differential equation, as well as a barrier assay where the continuum limit model is closely related to the well-known Fisher-KPP partial differential equation. We construct an approximate likelihood function for parameter inference, both with and without discrepancy correction terms. Using maximum likelihood estimation, we provide point estimates of the unknown parameters, and use the profile likelihood to characterise the uncertainty in these estimates and form approximate confidence intervals. For the range of inference problems considered, working with the continuum limit model alone leads to biased parameter estimation and confidence intervals with poor coverage. In contrast, incorporating correction terms arising from the statistical model of the model discrepancy allows us to recover the parameters accurately with minimal computational overhead. The main tradeoff is that the associated confidence intervals are typically broader, reflecting the additional uncertainty introduced by the approximation process. All algorithms required to replicate the results in this work are written in the open source Julia language and are available at GitHub.