Martijn van Noort, Tamara van Steeg and Joost DeJongh
LAPP
Background and Objectives:
Xenografts are used to assess treatment effects in pre-clinical oncology studies for potency and efficacy of both drug and/or radiation treatments.
Self-limiting models are applied to quantify unperturbed growth in control animals in the absence of active treatment.
Early stages of growth have often been approximated by an exponential model from which doubling time can be derived as a measure of primary xenograft cell proliferation.
The Verhulst and Gompertz model are two forms of self-limiting models for which unperturbed growth is limited by a systems parameter, the so called carrying capacity [1].
However, interpretation of systems parameters estimated from actual data differs between these models.
In practice, accurate estimation of structural and random effects for growth is also limited by data-censoring, both at the lower and the upper end of typical xenograft data ranges reported from animal studies.
The objective of this presentation is to develop a modification of the Gompertz model with parameters that can be interpreted physiologically.
Methods:
From a simulated dataset of xenograft size over time, similar to what is typically observed in control groups of pre-clinical oncology studies, it is demonstrated how censoring and model choice affects identification and interpretation of population growth model parameters.
A modification of the Gompertz model with self-limiting growth is proposed that allows direct comparison and interpretation of estimated parameters with those from the Verhulst and Gompertz models.
Three structurally different models, with two growth parameters and one boundary condition, were fitted to the same simulated xenograft growth dataset.
Results:
The three models were found to have comparable Goodness-of-Fit, as judged by Visual Predictive Checks.
Plots of model-derived auto-inhibition term versus observed xenograft size demonstrated how the three models compared in their behaviour.
It was shown that the self-limiting term in the ordinary differential equation for Gompertz growth, determining the auto-inhibition onset of xenograft growth in the host system, varied within an arbitrary range from infinity to zero.
For the Verhulst and modified Gompertz models this range was bounded between unity and zero.
A consequence of the unrestricted self-limiting term was that the growth rate constant estimated from the Gompertz model cannot directly be compared with those from other models.
Conclusions:
The modified Gompertz model was found to result in estimation of a growth rate constant comparable to the value from the Verhulst model fit, while a different growth rate parameter was found for the unmodified Gompertz model.
Furthermore, growth rates were found to depend on the observed range.
Consequently, the growth rate parameter of the Gompertz model cannot be interpreted as a physiological growth rate.
If drug or radiation treatment effects on xenograft proliferation and/or carrying capacity are inferrred by model fitting, the choice of the underlying model for unperturbed growth may affect interpretation of the treatment-specific parameters.
References:
[1] Tsoularis and Wallace. Analysis of logistic growth models. Mathematical Biosciences 179(1), 2002
Reference: PAGE () Abstr 9440 [www.page-meeting.org/?abstract=9440]
Poster: Drug/Disease Modelling - Oncology