N.D. Evans

Structural identifiability of non-linear systems using linear/non-linear splitting

In this paper, the local state space isomorphism theorem for non-linear systems is used to analyse structural identifiability. In particular it is shown that, under certain restrictions, it is possible to perform a linear/non-linear splitting of the analysis. The relatively straightforward linear analysis then restricts the class of local diffeomorphic transformations as given by the non-linear state space isomorphism theorem. This, in turn, leads to possible simplifications to the subsequent non-linear analysis by providing an efficient means for calculating the local state diffeomorphism.

Structural identifiability of surface binding reactions involving heterogeneous analyte: Application to surface plasmon resonance experiments

Binding affinities are useful measures of target interaction and have an important role in understanding biochemical reactions that involve binding mechanisms. Surface plasmon resonance (SPR) provides convenient real-time measurement of the reaction that enables subsequent estimation of the reaction constants necessary to determine binding affinity. Three models are considered for application to SPR experiments-the well-mixed Langmuir model and two models that represent the binding reaction in the presence of transport effects. One of these models, the effective rate constant approximation, can be derived from the other by applying a quasi-steady state assumption. Uniqueness of the reaction constants with respect to SPR measurements is considered via a structural identifiability analysis. It is shown that the models are structurally unidentifiable unless the sample concentration is known. The models are also considered for analytes with heterogeneity in the binding kinetics. This heterogeneity further confounds the identifiability of key parameters necessary for reliable estimation of the binding affinity.

A coupled drug kinetics-cell cycle model to analyse the response of human cells to intervention by topotecan

A model describing the response of the growth of single human cells in the absence and presence of the anti-cancer agent topotecan (TPT) is presented. The model includes a novel coupling of both the kinetics of TPT and cell cycle responses to the agent. By linking the models in this way, rather than using separate (disjoint) approaches, it is possible to illustrate how the drug perturbs the cell cycle. The model is compared to experimental in vitro cell cycle response data (comprising single cell descriptors for molecular and behavioural events), showing good qualitative agreement for a range of TPT dose levels.

Modelling of haemodialysis in limiting serum free light chains in patients with renal failure

Abstract A mathematical model for the in vivo kinetics of free light chains is developed. The model consists of two compartments, one containing the plasma and the other the interstitial fluid. It is used to examine the effects of dialysis on myeloma, a form of cancer that results in high free light chain concentrations. The structural identifiability of the model is analysed using the Taylor series approach, and it is confirmed that the model is structurally globally identifiable provided data are collected both during dialysis and after it. The model is then used to fit clinical data from a myeloma patient suffering chronic renal failure. The data show that dialysis causes a reduction in free light chain concentrations, and this is reflected in the model responses.

Nonparametric prediction of free-light chain generation in multiple myeloma patients

Abstract Multiple Myeloma is a plasma cell cancer that produces excess Free Light Chains (FLC). Patients with this condition are treated with dialysis and chemotherapy. A previous compartmental model developed by Evans et al. [2006] described the removal of FLC through a hemodialysis membrane. In this model all rate constants were considered linear and the production of FLC a constant input function. It is known that the system rate constants and inputs are non-linear in nature due to the membrane dynamics and the use of chemotherapy to retard the production FLC producing cells. This study describes the use of maximum entropy deconvolution, in conjunction with a non-linear compartmental model, to recreate the FLC production rate in a non-parametric form, without the need for assumptions that are not supported by available data. Input functions are reconstructed from four different patients with a range of dialysis durations and FLC plasma concentrations to investigate the possible effects of chemotherapy on the underlying FLC production.

THE STRUCTURAL IDENTIFIABILITY OF A GENERAL EPIDEMIC (SIR) MODEL WITH SEASONAL FORCING

Abstract In this paper it is shown that a general SIR epidemic model, with the force of infection subject to seasonal variation, and a proportion of the number of infectives measured, is unidentifiable. This means that an uncountable number of different parameter vectors can, theoretically, give rise to the same idealised output data. Any subsequent parameter estimation from real data must be viewed with less confidence as a result. The approach is essentially that developed by Evans et al. (2002), with modifications to allow for time-variation in the effective contact rate. This approach utilises the existence of an infinitely differentiable transformation that connects the state trajectories corresponding to parameter vectors that give rise to identical output data.

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

Abstract This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of protection from maternal antibodies, and that age related empirical data are likely to be most appropriate for estimating these characteristics.

A PK-PD model of cell cycle response to topotecan

Abstract A model describing the response of the growth of single human cells in the absence and presence of the anti-cancer agent, topotecan, is presented. The model is a result of linking the pharmacokinetic (pK) and pharmacodynamic (pD) responses. By linking the models in this way, rather than using separate (static) approaches, it is possible to illustrate how the drug perturbs the cell cycle. The model is validated for a range of drug concentrations with experimental data.

Compartmental modelling to assess stability of topotecan bound to DNA

Abstract In this paper, a compartmental model is proposed for describing the in vitro kinetics of the anti-cancer agent topotecan following administration into a culture medium containing human lymphoma cells in suspension. The model extends one previously proposed by including an extra dissociation pathway, with the objective of describing the effect of DNA binding on the stability of bound topotecan. The structural identifiability and steady states of the model are analysed. The model is fitted to high performance liquid chromatography data and it is found that there is a qualitative difference between the predicted behaviour of the new model and that of the previous model.

Kinetic Modelling of Haemodialysis Removal of Myoglobin in Rhabdomyolysis Patients

Abstract A two compartment model is proposed to describe the dynamics of myoglobin in rhabdomyolysis patients undergoing dialysis. Before using clinical data to estimate the models unknown parameters, structural identifiability analysis was performed to determine the parameters uniqueness given certain clinical observations. A Taylor series expansion method was implemented which found that the model was structurally globally/uniquely identifiable for both on- and off-dialysis phases. The fitted model was then used in a predictive capacity showing that the use of Theralite High Cut-off (HCO) or HCO 1100 dialyser gave a significant reduction in myoglobin renal exposure compared to standard haemodialysis (HD).