Model personalization requires the estimation of patient-specific tissue properties in the form of model parameters from indirect and sparse measurement data. Moreover, a low-dimensional representation of the parameter space is needed, which often has a limited ability to reveal the underlying tissue heterogeneity. As a result, significant uncertainty can be associated with the estimated values of the model parameters which, if left unquantified, will lead to unknown variability in model outputs that will hinder their reliable clinical adoption. Probabilistic estimation of model parameters, however, remains an unresolved challenge. Direct Markov Chain Monte Carlo (MCMC) sampling of the posterior distribution function (pdf) of the parameters is infeasible because it involves repeated evaluations of the computationally expensive simulation model. To accelerate this inference, one popular approach is to construct a computationally efficient surrogate and sample from this approximation. However, by sampling from an approximation, efficiency is gained at the expense of sampling accuracy. In this paper, we address this issue by integrating surrogate modeling of the posterior pdf into accelerating the Metropolis-Hastings (MH) sampling of the exact posterior pdf. It is achieved by two main components: (1) construction of a Gaussian process (GP) surrogate of the exact posterior pdf by actively selecting training points that allow for a good global approximation accuracy with a focus on the regions of high posterior probability; and (2) use of the GP surrogate to improve the proposal distribution in MH sampling, in order to improve the acceptance rate. The presented framework is evaluated in its estimation of the local tissue excitability of a cardiac electrophysiological model in both synthetic data experiments and real data experiments. In addition, the obtained posterior distributions of model parameters are interpreted in relation to the factors contributing to parameter uncertainty, including different low-dimensional representations of the parameter space, parameter non-identifiability, and parameter correlations.

To obtain a patient-specific cardiac electrophysiological (EP) model, it is important to estimate the three-dimensionally distributed tissue properties of the myocardium. Ideally, the tissue property should be estimated at the resolution of the cardiac mesh. However, such high dimensional estimation face major challenges in identifiability and computation. Most existing works reduce this dimension by partitioning the cardiac mesh into a pre-defined set of segments. The resulting low-resolution solutions have a limited ability to represent the underlying heterogeneous tissue properties of varying sizes, locations and distributions. In this paper, we present a novel framework that, going beyond a uniform low-resolution approach, is able to obtain a higher resolution estimation of tissue properties represented by spatially non-uniform resolution. This is achieved by two central elements: 1) a multi-scale coarse-to-fine optimization that facilitates higher resolution optimization using the lower resolution solution, and 2) a spatially adaptive decision criterion that retains lower resolution in homogeneous tissue regions and allows higher resolution in heterogeneous tissue regions. The presented framework is evaluated in estimating the local tissue excitability properties of a cardiac EP model on both synthetic and real data experiments. Its performance is compared with optimization using pre-defined segments. Results demonstrate the feasibility of the presented framework to estimate local parameters and to reveal heterogeneous tissue properties at a higher resolution without using a high number of unknowns.

The estimation of patient-specific tissue properties in the form of model parameters is important for personalized physiological models. However, these tissue properties are spatially varying across the underlying anatomical model, presenting a significance challenge of highdimensional (HD) optimization at the presence of limited measurement data. A common solution to reduce the dimension of the parameter space is to explicitly partition the anatomical mesh, either into a fixed small number of segments or a multi-scale hierarchy. This anatomy-based reduction of parameter space presents a fundamental bottleneck to parameter estimation, resulting in solutions that are either too low in resolution to reflect tissue heterogeneity, or too high in dimension to be reliably estimated within feasible computation. In this paper, we present a novel concept that embeds a generative variational auto-encoder (VAE) into the objective function of Bayesian optimization, providing an implicit low-dimensional (LD) search space that represents the generative code of the HD spatially-varying tissue properties. In addition, the VAE-encoded knowledge about the generative code is further used to guide the exploration of the search space. The presented method is applied to estimating tissue excitability in a cardiac electrophysiological model. Synthetic and real-data experiments demonstrate its ability to improve the accuracy of parameter estimation with more than 10x gain in efficiency.

Noninvasive reconstruction of cardiac transmembrane potential (TMP) from surface electrocardiograms (ECG) involves an ill-posed inverse problem. Model-constrained regularization is powerful for incorporating rich physiological knowledge about spatiotemporal TMP dynamics. These models are controlled by high-dimensional physical parameters which, if fixed, can introduce model errors and reduce the accuracy of TMP reconstruction. Simultaneous adaptation of these parameters during TMP reconstruction, however, is difficult due to their high dimensionality. We introduce a novel model-constrained inference framework that replaces conventional physiological models with a deep generative model trained to generate TMP sequences from low-dimensional generative factors. Using a variational auto-encoder (VAE) with long short-term memory (LSTM) networks, we train the VAE decoder to learn the conditional likelihood of TMP, while the encoder learns the prior distribution of generative factors. These two components allow us to develop an efficient algorithm to simultaneously infer the generative factors and TMP signals from ECG data. Synthetic and real-data experiments demonstrate that the presented method significantly improve the accuracy of TMP reconstruction compared with methods constrained by conventional physiological models or without physiological constraints.

Existing bias mitigation methods to reduce disparities in model outcomes across cohorts have focused on data augmentation, debiasing model embeddings, or adding fairness-based optimization objectives during training. Separately, certified word substitution robustness methods have been developed to decrease the impact of spurious features and synonym substitutions on model predictions. While their end goals are different, they both aim to encourage models to make the same prediction for certain changes in the input. In this paper, we investigate the utility of certified word substitution robustness methods to improve equality of odds and equality of opportunity on multiple text classification tasks. We observe that certified robustness methods improve fairness, and using both robustness and bias mitigation methods in training results in an improvement in both fronts.