Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

Mutual-information based optimal experimental design for hyperpolarized [Formula: see text]C-pyruvate MRI

A key parameter of interest recovered from hyperpolarized (HP) MRI measurements is the apparent pyruvate-to-lactate exchange rate, [Formula: see text], for measuring tumor metabolism. This manuscript presents an information-theory-based optimal experimental design approach that minimizes the uncertainty in the rate parameter, [Formula: see text], recovered from HP-MRI measurements. Mutual information is employed to measure the information content of the HP measurements with respect to the first-order exchange kinetics of the pyruvate conversion to lactate. Flip angles of the pulse sequence acquisition are optimized with respect to the mutual information. A time-varying flip angle scheme leads to a higher parameter optimization that can further improve the quantitative value of mutual information over a constant flip angle scheme. However, the constant flip angle scheme, 35 and 28 degrees for pyruvate and lactate measurements, leads to an accuracy and precision comparable to the variable flip angle schemes obtained from our method. Combining the comparable performance and practical implementation, optimized pyruvate and lactate flip angles of 35 and 28 degrees, respectively, are recommended.

Optimal experimental design for mathematical models of haematopoiesis

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.

Designing group dose-response studies in the presence of transmission

Dose-response studies are used throughout pharmacology, toxicology and in clinical research to determine safe, effective, or hazardous doses of a substance. When involving animals, the subjects are often housed in groups; this is in fact mandatory in many countries for social animals, on ethical grounds. An issue that may consequently arise is that of unregulated between-subject dosing (transmission), where a subject may transmit the substance to another subject. Transmission will obviously impact the assessment of the dose-response relationship, and will lead to biases if not properly modelled. Here we present a method for determining the optimal design - pertaining to the size of groups, the doses, and the killing times - for such group dose-response experiments, in a Bayesian framework. Our results are of importance to minimising the number of animals required in order to accurately determine dose-response relationships. Furthermore, we additionally consider scenarios in which the estimation of the amount of transmission is also of interest. A particular motivating example is that of Campylobacter jejuni in chickens. Code is provided so that practitioners may determine the optimal design for their own studies.