Evolving Improved Sampling Protocols for Dose-Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric.

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Partial differential equation models for invasive species spread in the presence of spatial heterogeneity.

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread which appear qualitatively similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions and must be considered when designing models of invasive species spread.

Sensor Selection for Tidal Volume Determination via Linear Regression-Impact of Lasso versus Ridge Regression.

The measurement of respiratory volume based on upper body movements by means of a smart shirt is increasingly requested in medical applications. This research used upper body surface motions obtained by a motion capture system, and two regression methods to determine the optimal selection and placement of sensors on a smart shirt to recover respiratory parameters from benchmark spirometry values. The results of the two regression methods (Ridge regression and the least absolute shrinkage and selection operator (Lasso)) were compared. This work shows that the Lasso method offers advantages compared to the Ridge regression, as it provides sparse solutions and is more robust to outliers. However, both methods can be used in this application since they lead to a similar sensor subset with lower computational demand (from exponential effort for full exhaustive search down to the order of O (n2)). A smart shirt for respiratory volume estimation could replace spirometry in some cases and would allow for a more convenient measurement of respiratory parameters in home care or hospital settings.

The Effects of Additional Local-Mixing Compartments in the DISST Model-Based Assessment of Insulin Sensitivity.

BACKGROUND: The identification of insulin sensitivity in glycemic modelling can be heavily obstructed by the presence of outlying data or unmodelled effects. The effect of data indicative of local mixing is especially problematic with models assuming rapid mixing of compartments. Methods such as manual removal of data and outlier detection methods have been used to improve parameter ID in these cases, but modelling data with more compartments is another potential approach. METHODS: This research compares a mixing model with local depot site compartments with an existing, clinically validated insulin sensitivity test model. The Levenberg-Marquardt (LM) parameter identification method was implemented alongside a modified version (aLM) capable of operator-independent omission of outlier data in accordance with the 3 standard deviation rule. Three cases were tested: LM where data points suspected to be affected by incomplete mixing at the depot site were removed, aLM, and LM with the more complex mixing model. RESULTS: While insulin parameters identified in the mixing model differed greatly from those in the DISST model, there were strong Spearman correlations of approximately 0.93 for the insulin sensitivity values identified across all 3 methods. The 2 models also showed comparable identification stability in insulin sensitivity estimation through a Monte Carlo analysis. However, the mixing model required modifications to the identification process to improve convergence, and still failed to converge to feasible parameters on 5 of the 212 trials. CONCLUSIONS: The mixing compartment model effectively captured the dynamics of mixing behavior, but with no significant improvement in insulin sensitivity identification.

The dimensional reduction method for identification of parameters that trade-off due to similar model roles.

Parameter identification is an important and widely used process across the field of biomedical engineering. However, it is susceptible to a number of potential difficulties, such as parameter trade-off, causing premature convergence at non-optimal parameter values. The proposed Dimensional Reduction Method (DRM) addresses this issue by iteratively reducing the dimension of hyperplanes where trade off occurs, and running subsequent identification processes within these hyperplanes. The DRM was validated using clinical data to optimize 4 parameters of the widely used Bergman Minimal Model of glucose and insulin kinetics, as well as in-silico data to optimize 5 parameters of the Pulmonary Recruitment (PR) Model. Results were compared with the popular Levenberg-Marquardt (LMQ) Algorithm using a Monte-Carlo methodology, with both methods afforded equivalent computational resources. The DRM converged to a lower or equal residual value in all tests run using the Bergman Minimal Model and actual patient data. For the PR model, the DRM attained significantly lower overall median parameter error values and lower residuals in the vast majority of tests. This shows the DRM has potential to provide better resolution of optimum parameter values for the variety of biomedical models in which significant levels of parameter trade-off occur.

Information on biotic interactions improves transferability of distribution models.

Predicting changes in species' distributions is a crucial problem in ecology, with leading methods relying on information about species' putative climatic requirements. Empirical support for this approach relies on our ability to use observations of a species' distribution in one region to predict its range in other regions (model transferability). On the basis of this observation, ecologists have hypothesized that climate is the strongest determinant of species' distributions at large spatial scales. However, it is difficult to reconcile this claim with the pervasive effects of biotic interactions. Here, we resolve this apparent paradox by demonstrating how biotic interactions can affect species' range margins yet still be compatible with model transferability. We also identify situations where small changes in species' interactions dramatically shift range margins.

Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension.

We describe a fast and accurate method to compute the pressure and equilibrium states for maps of the interval T:[0,1]-->[0,1] with respect to potentials phi:[0,1]-->R. An approximate Ruelle-Perron-Frobenius operator is constructed and the pressure read off as the logarithm of the leading eigenvalue of this operator. By setting phi identical with 0, we recover the topological entropy. The conformal measure and the equilibrium state are computed as eigenvectors. Our approach is extremely efficient and very simple to implement. Rigorous convergence results are stated for piecewise expanding maps.

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