Cancer Suppression by Compression

Abstract

Recent experiments indicate that uniformly compressing a cancer mass at its surface tends to transform many of its cells from proliferative to functional forms. Cancer cells suffer from the Warburg effect, resulting from depleted levels of cell membrane potentials. We show that the compression results in added free energy and that some of the added energy contributes distortional pressure to the cells. This excites the piezoelectric effect on the cell membranes, in particular raising the potentials on the membranes of cancer cells from their depleted levels to near-normal levels. In a sample calculation, a gain of 150 mV in is so attained. This allows the Warburg effect to be reversed. The result is at least partially regained function and accompanying increased molecular order. The transformation remains even when the pressure is turned off, suggesting a change of phase; these possibilities are briefly discussed. It is found that if the pressure is, in particular, applied adiabatically the process obeys the second law of thermodynamics, further validating the theoretical model.

Appendix: Sufficiency of and Conditions for Applying the Pressure Adiabatically

An increase in cell functional order has been predicted by the model process of Sect. 3. However, to be physically valid, it must obey the second law of thermodynamics. We show that this is obeyed if the pressure increase is adiabatic, i.e., transferred as purely the work $\Delta W$ assumed in Eq. (1). Thus, it must occur quickly enough that no heat exchange occurs. Other system constraints are also required, as enumerated. We emphasize that this is only a proof of sufficiency; other, slower pressure increases might suffice to obey the second law as well.

Consider one such cell. In being alive, it is in a generally non-equilibrium state. Only a dead cell has an entropy $S=\hbox {max}$. so that here $S\ne \hbox {max}$. How does the applied pressure affect the entropic system state of the cell? In general, adiabatic pressure leaves all probability states $p_{j}$, $j = 1,\ldots$ of the cell invariant (Binney and Skinner 2008). This leaves its entropy $S \equiv -k\sum _{j} p_{{j}}$ ln $p_{{j}}$ invariant as well, obeying $\Delta S=0$. (k is the Boltzmann constant.) This verifies that the second law of thermodynamics is obeyed by the cell compression process. It also allows the $p_{{j}}$ to remain in their original non-equilibrium state, i.e., representing a living cell.

Essential to the adiabatic approximation is that all cells are isolated from any heat flow (Sect. 6.3), and move as an ideal fluid (Binney and Skinner 2008). Such isolation from heat flow avoids particle collisions and resulting changes in states $p_{j}$ of each cell (leaving entropy change $\Delta S=0$ as required). Thus, the cells of the fluid system are assumed, as an approximation, to not collide but, rather, to flow independently. Such a fluid is the simplest non-trivial thermodynamic system (Binney and Skinner 2008). Also, under adiabatic pressure $P$, the system is compressed so quickly that no heat is transferred either to or from it.

Such fluid flow is accomplished by keeping the cells, and the medium they are in, at the same temperature (Sect. 6.3). Such heat isolation avoids the dissipatory effects of coarse graining (Frieden and Hawkins 2010) and, so, is essential to allowing the level of order to be maximal. Such maximization helps in reversing the cancer evolution back toward a state of function (Sects. 3.3 and 5.2).