Figure 3 | Scientific Reports

Figure 3

From: Constructal approach to cell membranes transport: Amending the ‘Norton-Simon’ hypothesis for cancer treatment

Figure 3

The figure represents the volumetric growth of cancer tissue under a magnetic field (50 μT, 40 Hz) in relation to the energy used by the cancer with regards to the ion involved.

The y-axis represents growth, i.e. the ratio between the volume of cancer V related to its initial value V0. The x-axis displays the ratio (in percentage) in energy consumption used for growth between a cancer cell and a normal, non-cancerous cell; here, Q is the energy used by the cancer cell while Q0 is the energy consumed by the normal cell; minus (−) and plus (+) are related to the motion of the ions in relation to the membrane’s bioelectric field; consequently, in the case of Cl inflow the cell gains energy, which in turn can be used for continued growth, while, to process Ca2+, K+ and Na+ inflow, the cell loses energy and thus growth potential as it works against the membrane potential to sustain the influx of these ions. As the tumor grows, all ion fluxes change but their percentage changes are much larger when the tumor is exposed to the magnetic field in (a), reflecting a much more pronounced consumption of ATP to process these fluxes. The inhibitory effect of the magnetic field is evident as the tumor, to achieve the same volumetric growth, is forced to consume much more energy in (a) than in (b) when it is not exposed to a magnetic field. Still, since Cl influx increases also in (a), particularly at later growth stages, this further supports the argument that magnetic field therapy may lose efficacy eventually (which is being explored in more detail in Fig. 4).

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