A minimal model of tumor growth inhibition.
The preclinical development of antitumor drugs greatly benefits from the availability of models capable of predicting tumor growth as a function of the drug administration schedule. For being of practical use, such models should be simple enough to be identifiable from standard experiments conducted on animals. In the present paper, a stochastic model is derived from a set of minimal assumptions formulated at cellular level. Tumor cells are divided in two groups: proliferating and nonproliferating. The probability that a proliferating cell generates a new cell is a function of the tumor weight. The probability that a proliferating cell becomes nonproliferating is a function of the plasma drug concentration. The time-to-death of a nonproliferating cell is a random variable whose distribution reflects the nondeterministic delay between drug action and cell death. The evolution of the expected value of tumor weight obeys two differential equations (an ordinary and a partial differential one), whereas the variance is negligible. Therefore, the tumor growth dynamics can be well approximated by the deterministic evolution of its expected value. The tumor growth inhibition model, which is a lumped parameter model that in the last few years has been successfully applied to several antitumor drugs, is shown to be a special case of the minimal model presented here.
Magni
Paolo
P
Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, I-27100 Pavia, Italy. paolo.magni@unipv.it
Germani
Massimiliano
M
De Nicolao
Giuseppe
G
Bianchini
Giulia
G
Simeoni
Monica
M
Poggesi
Italo
I
Rocchetti
Maurizio
M
D000970:Antineoplastic Agents / Q000008:administration & dosage / Q000097:blood / Q000494:pharmacology*; D002277:Carcinoma / Q000188:drug therapy / Q000473:pathology; D002452:Cell Count; D016923:Cell Death / Q000187:drug effects; D045744:Cell Line, Tumor; D049109:Cell Proliferation / Q000187:drug effects; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000188:drug therapy* / Q000473:pathology*; D016012:Poisson Distribution; D011336:Probability; D013269:Stochastic Processes; D047368:Tumor Burden / Q000187:drug effects
D000970:Antineoplastic Agents