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A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy
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Figures

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FIG. 1.

Androgen data interpolation, case 1. The data are taken from a clinical trial8 and interpolated using equation (13) at the beginning of each treatment cycle and using cubic hermite splines between other data points. Future androgen levels for making predictions with our model are also shown. The dashed vertical line separates the interpolated clinical data from the prediction.

Image of FIG. 2.

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FIG. 2.

Ideta model results, case 1. The clinical PSA measurements are illustrated by red circles. The AD and AI cell populations are overlaid as dashed black and gray lines to show the source of the simulated PSA concentrations. The proliferation rate, α1 p(A), and the apoptosis rate, β1 q(A), for the AD population are shown in (b). The AI population has constant proliferation and apoptosis rates. This model does not match the second and third PSA peaks well.

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FIG. 3.

Ideta model results, cases 2 – 7. Again, we see that this model has difficulty matching PSA peaks beyond the first treatment cycle.

Image of FIG. 4.

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FIG. 4.

Preliminary model results, case 1. Cell quota dependent mutation rates are shown in (b). This model has difficulty matching the low PSA levels during on-treatment periods.

Image of FIG. 5.

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FIG. 5.

Preliminary model results, cases 2 – 7. This model has difficulty matching the sharp declines in PSA levels as seen in cases 2 and 3.

Image of FIG. 6.

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FIG. 6.

Final model results, case 1. Cell quotas are shown in (b) with the minimum quotas indicated by dashed lines. In general, the PSA data is matched very accurately.

Image of FIG. 7.

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FIG. 7.

Final model results, cases 2 – 7. Again, this model matches the clinical data very accurately compared to the first two models.

Image of FIG. 8.

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FIG. 8.

Prediction of the final model, case 1. The dashed vertical line separates the clinical fit and the prediction. The PSA concentration and AI population increase significantly with another off-treatment period. However, the subsequent on-treatment period remains effective in stopping further growth.

Image of FIG. 9.

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FIG. 9.

Predictions of the final model, cases 2 – 7. The additional cycle is effective for cases 2 and 7. Cases 4, 6, and 7 experience rapid growth of the AI population during the extra off-treatment period.

Tables

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Table I.

Final model parameter ranges.

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Table II.

Comparison of model fits, including mean squared error (MSE) and Schwarz Bayesian Criterion (SBC). Lower values indicate better fits for both MSE and SBC.

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/content/aip/journal/adva/2/1/10.1063/1.3697848
2012-03-19
2014-04-19

Abstract

Prostate cancer is commonly treated by a form of hormone therapy called androgen suppression. This form of treatment, while successful at reducing the cancercell population, adversely affects quality of life and typically leads to a recurrence of the cancer in an androgen-independent form. Intermittent androgen suppression aims to alleviate some of these adverse affects by cycling the patient on and off treatment. Clinical studies have suggested that intermittent therapy is capable of maintaining androgen dependence over multiple treatment cycles while increasing quality of life during off-treatment periods. This paper presents a mathematical model of prostate cancer to study the dynamics of androgen suppression therapy and the production of prostate-specific antigen (PSA), a clinical marker for prostate cancer. Preliminary models were based on the assumption of an androgen-independent (AI) cell population with constant net growth rate. These models gave poor accuracy when fitting clinical data during simulation. The final model presented hypothesizes an AI population with increased sensitivity to low levels of androgen. It also hypothesizes that PSA production is heavily dependent on androgen. The high level of accuracy in fitting clinical data with this model appears to confirm these hypotheses, which are also consistent with biological evidence.

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Scitation: A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/1/10.1063/1.3697848
10.1063/1.3697848
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