Modelling the Effect of Chemotherapy on Tumour Growth

In this section we describe the model developed by Cruywagen et al. (1995) and Tracqui et al. (1995) to quantify the effect of chemotherapy on tumour growth. It is based in part on quantitative image analysis of histological sections of a human brain glioma and especially on cross-sectional area/volume measurements of serial CT images while the patient was undergoing chemotherapy. We estimated the model parameters using optimization techniques to give the best fit of the simulated tumour area to the CT scan data. We carried out numerical simulations on a two-dimensional domain, which took into account the geometry of the brain (only the ventricles and the skull) and its natural barriers to diffusion. The results were used to determine the effect of chemotherapy on the spatiotemporal growth of the tumour. (Shochat et al. (1999) have used computer-based simulations of various basic ordinary differential equation models to evaluate the efficacy of chemotherapy protocols on breast cancer.)

One of the reasons for discussing this work is that it is a somewhat different approach and it shows how the model parameters are estimated from clinical data obtained from successive computerized tomograms (CT) of a patient with an anaplastic astrocy-toma who received radiotherapy and chemotherapy. This approach is a feasible one when other methods or independent data are not available. As before the time course of the treatments was incorporated in the model, and, by using optimization techniques to fit the model response to the experimental data, an evaluation of the effectiveness of the chemotherapy was obtained by identifying parameters characterizing the rate of death of tumour cells.

Just as with the above discussions, once the feasibility of reconstructing some of the kinetic events in invasion from histological sections has been established, the hope is to be able to use such modelling to investigate other gliomas with different characteristic growth patterns and geometries and the effects of various forms of therapy using the same types of data from other patients.

Experimental Data

Since many patients with brain tumours die too soon after detection of their tumour without a sufficient number of follow-up scans, we were fortunate to be able to study one patient with an anaplastic astrocytoma who had been diagnosed and treated with X-irradiation three years previously. The tumour recurred and was re-treated chemother-apeutically with moderate success, while CT scans were taken repeatedly during the 12 months before the patient's death. From these scans one or more of the pieces of tumour were observed. The tumour area of the largest piece (piece a) was measured at three different levels (referred to as levels 1, 2 and 3; recall Figure 11.3) of the brain using a digitizing tablet and computerized area measurement technique. Since the levels at which the areas had been recorded were not always exactly the same for all the scans, some data points were obtained by linear interpolation between the neighboring upper and lower levels.

During the same terminal year, the patient received two different chemotherapies (Figure 11.28). The first one was a course of six drugs (6-thioguanine, procarbazine, di-bromodulcitol, CCNN, 5-florouracil, and hydroxyurea given over 15 days and repeated every six to eight weeks to allow for recovery of bone marrow) applied five times. The second consisted of two courses of cisplatinum given at month intervals. In addition, the patient received neutron beam irradiation during the last three weeks.

The tumour cell density was determined by image analysis of a biopsy obtained at the time of the first scan. The number of nuclei in the tumour tissue detected per mm2

Observation time (day«)

1 71 113 238 279 300 323 3S6 12 o -,-1-1 —r—T _ I -------1

Observation time (day«)

1 71 113 238 279 300 323 3S6 12 o -,-1-1 —r—T _ I -------1

6 Drugs

Cisplalinum

Neutrons

6 Drugs

Cisplalinum

Neutrons

1 20 34 72 86 118 132 170 184 225__ 267 296 339 361

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