Markovian model of growth and histologic progression in prostate cancer

Models, based on bio-physical and biological considerations, may be very helpful as support tools for traditional diagnostic methodologies and interpretation of statistical data in oncology. This is particularly true when the neoplastic progression and differentiation are rather simple and regular, such as in the case of prostatic adenocarcinomas. Using clinical data as a “statistical ensemble,” we propose here a Markovian model to forecast the tumor progression. After validation with clinical data, the model is applied to the determination of the temporal evolution of the risk of metastasis.

Figure 1

Frequency of prostate adenocarcinomas in adult males derived from autopsy data [4]. For each decade, we report the percent of cases with a tumor. The solid line represents an exponential fitting.

Figure 2

Temporal evolution of the volumes of $\mathrm{WMD}$ and $\mathrm{PD}$ cells for four different realizations obtained from the same initial condition and representation of the corresponding trajectories in the volume-grade Cartesian plane.

Figure 3

Forecast of the evolution of a tumor with initial condition: $V=0.1{\mathrm{cm}}^3$ and $G=0$. Representation of the distribution of volume and grade at 5, 10, 15, 20 and 25 years after initiation (for $M=1000$ realizations) and temporal evolution of the metastasis probability.

Figure 4

Effects of the uncertainty on the initial conditions on the forecast of the evolution for three different initial conditions as reported in the text. Representation of the distribution of volume and grade at 5, 10 and 15 years after initiation.