arXiv subjects

Ryan J. Murphy

Publications and source records attributed to Ryan J. Murphy.

4 recordsLinked to original sources

arXiv2025

A nonparametric approach to practical identifiability of nonlinear mixed effects models

Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread adoption of this individual-based fitting, it is becoming increasingly common to take a hierarchical approach to parameter estimation, where modellers characterize the population parameter distributions, rather than considering each individual independently. This hierarchical parameter estimation is standard in pharmacometric modelling. However, many of the existing techniques for parameter identifiability do not immediately translate from the individual-based fitting to the hierarchical setting. Here, we propose a nonparametric approach to study practical identifiability within a hierarchical parameter estimation framework. We focus on the commonly used nonlinear mixed effects framework and investigate two well-studied examples from the pharmacometrics and viral dynamics literature to illustrate the potential utility of our approach.

stat.ME↗

arXiv2024

Mechanical cell interactions on curved interfaces

We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models of flat epithelia to investigate the influence of curvature for mechanical relaxation. We represent the mechanics of a cell body either by straight springs, or by curved springs that follow the curve's shape. To understand the collective dynamics of the cells, we devise an appropriate continuum limit in which the number of cells and the length of the substrate are constant but the number of springs tends to infinity. In this limit, cell density is governed by a diffusion equation in arc length coordinates, where diffusion may be linear or nonlinear depending on the choice of the spring restoring force law. Our results have important implications about modelling cells on curved geometries: (i) curved and straight springs can lead to different dynamics when there is a finite number of springs, but they both converge quadratically to the dynamics governed by the diffusion equation; (ii) in the continuum limit, the curvature of the tissue does not affect the mechanical relaxation of cells within the layer nor their tangential stress; (iii) a cell's normal stress depends on curvature due to surface tension induced by the tangential forces. Normal stress enables cells to sense substrate curvature at length scales much larger than their cell body, and could induce curvature dependences in experiments.

nlin.CG↗

arXiv2023

Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis, and prediction in the life sciences

Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis, and prediction, called Profile-Wise Analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

q-bio.QM↗

arXiv2019

Pose Estimation of Periacetabular Osteotomy Fragments with Intraoperative X-Ray Navigation

Objective: State of the art navigation systems for pelvic osteotomies use optical systems with external fiducials. We propose the use of X-Ray navigation for pose estimation of periacetabular fragments without fiducials. Methods: A 2D/3D registration pipeline was developed to recover fragment pose. This pipeline was tested through an extensive simulation study and 6 cadaveric surgeries. Using osteotomy boundaries in the fluoroscopic images, the preoperative plan is refined to more accurately match the intraoperative shape. Results: In simulation, average fragment pose errors were 1.3°/1.7 mm when the planned fragment matched the intraoperative fragment, 2.2°/2.1 mm when the plan was not updated to match the true shape, and 1.9°/2.0 mm when the fragment shape was intraoperatively estimated. In cadaver experiments, the average pose errors were 2.2°/2.2 mm, 3.8°/2.5 mm, and 3.5°/2.2 mm when registering with the actual fragment shape, a preoperative plan, and an intraoperatively refined plan, respectively. Average errors of the lateral center edge angle were less than 2° for all fragment shapes in simulation and cadaver experiments. Conclusion: The proposed pipeline is capable of accurately reporting femoral head coverage within a range clinically identified for long-term joint survivability. Significance: Human interpretation of fragment pose is challenging and usually restricted to rotation about a single anatomical axis. The proposed pipeline provides an intraoperative estimate of rigid pose with respect to all anatomical axes, is compatible with minimally invasive incisions, and has no dependence on external fiducials.

cs.CV↗