Biomedical subjects

Graeme C Wake

Publications and source records attributed to Graeme C Wake.

7 recordsLinked to original sources

PubMed2006

Decompression schedule optimization with an isoprobabilistic risk of decompression sickness.

INTRODUCTION: Divers use decompression schedules to reduce the probability of occurrence of decompression sickness when returning to the surface at the end of a dive. The probability of decompression sickness resulting from these schedules varies across different dives and the models used to generate them. Usually the diver is unaware of this variance in risk. This paper describes an investigation into the feasibility of producing optimized iso-probabilistic decompression schedules that minimize the time it takes for a diver to reach the surface. METHODS: The decompression schedules were optimized using the sequential quadratic programming method (SQP), which minimizes the ascent time for a given probability of decompression sickness. The U.S. linear-exponential multi-gas model was used to calculate an estimate of the probability of decompression sickness for a given dive. In particular 1.3-bar oxygen in helium rebreather bounce dives to between 18 m and 81 m were considered and compared against the UK Navy QinetiQ 90 tables for a similar estimate of probability of decompression sickness. RESULTS: The SQP method reliably produced schedules with fast and stable convergence to an optimized solution. Comparison of the optimized decompression schedules with the QinetiQ 90 schedules showed similar stop times for shallow dives to 18 m. For dives with a maximum depth of 39 m to 81 m, optimizing the decompression resulted in savings in decompression time of up to 30 min. CONCLUSIONS: This paper has shown that it is feasible to produce optimized iso-probabilistic decompression tables given a reliable risk model for decompression sickness and appropriate dive trials.

Decompression↗

PubMed2005

On a functional equation model of transient cell growth.

A cell-growth model with applications to modelling the size distribution of diatoms is examined. The analytic solution to the model without dispersion is found and is shown to display periodic exponential growth rather than asynchronous (or balanced) exponential growth. It is shown that a bounding envelope (hull) of the solution to the model without dispersion takes the same shape as the limiting steady-size distribution to the dispersive case as dispersion tends to zero. The effect of variable growth rate on the shape of the hull is also discussed.

Cell Proliferation↗

PubMed2005

Adaptive bolus-based targeted glucose regulation of hyperglycaemia in critical care.

Tight regulation of blood glucose can significantly reduce mortality in critical illness. Critically ill patients are extremely diverse in the dynamics of their hyperglycaemia. Hence, responses can vary significantly, due to variations in insulin levels, effective insulin utilization, glucose absorption and other factors. Consequently, fixed protocols and sliding scales can result in error, given this large variation in patient dynamics. A two-compartment glucose-insulin system model that accounts for time-varying insulin sensitivity and endogenous glucose removal, along with two different saturation kinetics, is developed and tested in preliminary proof-of-concept clinical trials for adaptive control of blood glucose levels. The adaptive control algorithm developed in this research monitors the physiological status of a critically ill patient, allowing real-time, tight glycaemic regulation. The bolus-based insulin administration provides a safe approach to glucose level management. The ability to track changing physiological status and account for insulin transport and effect saturation enabled targeted stepwise reduction in glycaemic levels in three test cases.

Adaptation, Physiological↗

PubMed2005

Targeted glycemic reduction in critical care using closed-loop control.

BACKGROUND: Critically ill patients are often hyperglycemic and extremely diverse in their dynamics. Consequently, fixed protocols and sliding scales can result in error and poor control. Tight glucose control has been shown to significantly reduce mortality in critical care. An improved physiological system model of the glucose-insulin dynamics of a critical care patient is used to develop an adaptive tight glucose control protocol that accounts for variable patient dynamics, and is verified in limited clinical trials. METHODS: A physiologically based two-compartment system model that accounts for time-varying insulin sensitivity, time-varying endogenous glucose removal, and two saturation kinetics mechanisms is developed. A bolus-based adaptive control protocol is developed that monitors the physiological status of a critically ill patient, enabling tight glycemic regulation to preset glycemic targets. The model and protocol are verified in three, 5-h preliminary proof-of-concept clinical trials. Ethics approval was granted by the Canterbury Ethics Committee (Christchurch, New Zealand). RESULTS: Preset glycemic targets are achieved with an average absolute error of 9%, with 75% of all targets achieved within the 7% measurement error. Absolute errors greater than 7% ranged from 17% to 21%. CONCLUSIONS: Tight stepwise control was exhibited in all cases, and the adaptive system was able to match the model and observed patient dynamics. Most errors are associated with external perturbations such as drug therapies, or mismodeled parameters that can be easily adjusted with longer trials and/or more data per hour. The overall result is targeted stepwise tight glycemic regulation using insulin boluses.

Aged↗

PubMed2004

Modelling the flow [corrected] cytometric data obtained from unperturbed human tumour cell lines: parameter fitting and comparison.

In this paper we firstly present three alternative formulations of a mathematical model for human tumour cell lines unperturbed by cancer therapy. The model counts the number density of cells in each phase of the cell cycle over time where cells are differentiated by their DNA content. Data are available from the Auckland Cancer Society Research Centre, Auckland, New Zealand, in the form of DNA histograms or profiles from 11 different human tumour cell lines (i.e. in vitro) unperturbed by cancer therapy. We then apply one (computationally fast) formulation of the model and discover that although in general different combinations of parameter values give rise to very different DNA profiles it is possible that different combinations of parameter values give rise to virtually identical profiles. Experimental estimates of the rate of transition from the G1-phase (growth) to the S-phase (DNA synthesis) enable us to uniquely determine other model parameters of interest that give the least square error between the model and data. We finally apply our model to each of the 11 different cell lines and compare cell cycle phase transit times. Although the DNA histograms of each of the cell lines have similar shapes these cell lines have different combinations of transit times to each other, which could explain why they often react very differently when exposed to anti-cancer therapies during laboratory experiments. An understanding of the in vitro situation may give an insight into why some human cancer patients do not respond to cancer therapy.

Cell Cycle↗

PubMed2004

Modeling and control of the agitation-sedation cycle for critical care patients.

Agitation-sedation cycling in critically ill patients, characterized by oscillations between states of agitation and over-sedation, is damaging to patient health, and increases length of stay and healthcare costs. The mathematical model presented captures the essential dynamics of the agitation-sedation system for the first time, and is statistically validated using recorded infusion data for 37 patients. Constant patient-specific patient parameters are used, illustrating the commonality of these fundamental dynamics over a broad range of patients. The validated model serves as a basis for comparison of sedation administration methods, devices, therapeutics and protocols. Heavy derivative feedback control is shown to be an effective means of managing agitation, given consistent agitation measurement. The improved agitation management reduces the modeled mean and peak agitation levels 68.4% and 52.9% on average, respectively. Some patients showed over 90% reduction in mean agitation level through increased control gains. This improved agitation management is achieved via heavy derivative feedback control of sedation administration, which provides an essentially bolus-driven management approach, aligned with recent sedation practices.

Computer Simulation↗

PubMedDate not supplied

Modelling cell population growth with applications to cancer therapy in human tumour cell lines.

In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis (cell death) from mitosis phase (Modelling cell death in human tumour cell lines exposed to anticancer drug paclitaxel, J. Math. Biol. 2004, in press). This enabled us to compare our model to flow cytometric data of a melanoma cell line where the anticancer drug, paclitaxel, had been added. The model gives a dynamic picture of the effects of paclitaxel on the cell cycle. We hope to use the model to describe the effects of other cancer therapies on a number of different cell lines.

Antineoplastic Agents↗