Abstract 1103: Theoretical basis and formula for tumor-treating fields dose-response curves
Authors: Carlson Kristen 
Published: April 2023

Abstract
Radiotherapy dose-response curves are linear-quadratic (LQ), chemotherapy’s are generally semi-logarithmic or sigmoidal, and Tumor-Treating Fields’ (TTFields) resemble radiotherapy LQ, while the two modalities are presumed to have fundamentally different mechanisms of action (MoA) [1,2]. Radiotherapy produces single- or double-strand DNA breaks, while TTFields act on polarizable cellular structures. Thus, changing the incident electric field direction improves TTFields efficacy, killing 20% more tumor cells in vitro, with 90⁰ changes in the front-back/left-right (x,y) plane [1]. However, by the same logic, polarizable cell structures that are orthogonal to the (x,y) plane see 0 field strength and thus are unaffected by TTFields. The formula for TTFields effective dose with no direction change, given TTFields’ incident angle on the polarizable cell structure’s axis, is simply Deff = cos θ*Dnom, where Dnom is the electric field strength at the axis. The formulae for TTFields dose-response, given one, two, and three incident directions can be calculated (Mathematica v.12, WRI, Champaign, IL) as
n(Dnom|cosθ1|≥k) + n(Dnom|cosθ2|≥k) + n(Dnom|cosθ3|≥k)/N,
where n is the counting function, Dnom is the nominal field strength at the axis, θi the 1st, 2nd, or 3rd incident TTFields angle, k is TTFields' efficacy floor in V/cm (see below), and N is the total cell population in vivo, vitro, or silico. The formula assumes: 1) Cells are randomly-oriented in vivo [1]; 2) Polarized cell structures are straight; 3) Electric field strength is Deff not Dnom, 4) Cells are in their radiosensitive state (e.g. mitosis), 5) Reducing TTFields duty cycle/direction has no effect down to 0.25 s ([1], and unpublished data), and 6) TTFields’ minimum efficacious field strength Deff = ~0.75 V/cm for cell structures perfectly aligned with the incident TTFields angle (cf. low dose V/cm data points in MDA-MB-231, F-98, B16F1, and H1299 empirical dose-response curves [1,2]).
With feasible TTFields transducer array placements on the head or torso, it is relatively easy to achieve changes of direction in one (x,y) plane, but difficult to achieve an additional change of direction in the z-plane. For a nominal TTFields dose Dnom of 2 V/cm, only a 22⁰ change of direction off the (x,y) plane is necessary to kill the cells with Deff below the efficacy threshold, with Dnom = 1.5 V/cm, a 30⁰ change is needed, and with Dnom = 1 V/cm, a 49⁰ change is needed. In sum, we have derived TTFields’ dose-response formulae from first principles, which differentiates them from those of radiotherapy and chemotherapy, and, toward achieving 100% TTFields efficacy as a monotherapy, given motivation and guidelines for adding an additional TTFields’ change of direction per duty cycle.1.Kirson, E.D., et al., Proc Natl Acad Sci U S A, 2007.2.Moser, J.C., et al.,.Cancer Res, 2022.
Citation Format: Kristen Carlson. Theoretical basis and formula for tumor-treating fields dose-response curves [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 1103.