A strategy of chemotherapeutic eradication based upon correlative variations in total cell population, growth fraction and resistance

Abstract

Having developed in previous papers the mathematical connections between growth fraction and cellular losses, and between growth fraction, doubling time, initial cell population, resistance to a given therapy and the number of courses of this therapy per doubling time, the authors examine here how these parameters are connected when eradication is to be achieved. The various calculations show that resistance must be lowered by means of combinations, well beyond the theoretical limits, in order to deal with non-dividing cells and/or large initial tumor cell populations. For a given percentage of resistance, eradication is achieved only for growth fraction above a certain limit, only for tumor cell population below a certain limit, and only for a number of courses of therapy per doubling time above a certain limit. In order to meet these requirements, it appears necessary (1) to combine the available drugs without cross-resistance; (2) to give simultaneous combinations instead of sequential ones; (3) to treat as soon as possible; (4) to find out ways of lowering toxicity in order to give as many courses as possible per doubling time; (5) to incorporate in combinations drugs effective against non-dividing cells.