Abstract 12800: Mathematical Modeling of Myocardial Transthyretin Amyloid Deposition and Clearance

Abstract

Introduction: In vitro transthyretin amyloid (ATTR) fibrillation kinetics are well studied, however, the in vivo interplay between ATTR fibrillation and clearance causing cardiac amyloidosis (TTR-CA) is underexplored. We investigated these interactions using a mathematical model of ATTR deposition. Methods: We divided the mechanisms of ATTR deposition from tetramer to clearance by clusterin (an extracellular chaperone) into individual reactions (Fig. 1A) with 7 parameters. A system of ordinary differential equations (ODEs) describes the change in ATTR monomer, fibril, inhibitor, and complex deposition. Parameter values were determined using published experimental data and equilibrium analyses. We model an FDA-approved stabilizer, Tafamadis, by modifying S(t), the source term for production and dissociation of tetramers, as a step function downward at therapy initiation. Alternatively, a linear function S(t) models the hypothesis that senile TTR-CA is triggered by age-related wtTTR instability from oxidation. Results: The ODEs simulated a biologically meaningful model of TTR-CA. Equilibrium analyses found three phenotypes. (1) One stable, low equilibrium point representing normal myocardium (low S, high Ki). (2) Three equilibrium points, with 2 stable points (low and high) and a middle, unstable saddle point, indicating susceptibility to perturbation into a state with significant ATTR (low S/Kc2, high Ki/Kc). (3) No equilibrium points causing unbounded ATTR (high S, low Ki). In the Tafamadis model, ATTR fibril reduction was proportional to drug efficacy (Fig. 1B). Senile TTR-CA model showed rapid progression of cardiac ATTR deposition with onset dependent on slope of S (Fig. 1C). Conclusions: This mathematical model predicts physiologic ATTR clearance and pathological ATTR deposition with a limited number of parameters. It is a hypothesis generating model that can elucidate mechanisms of TTR-CA pathogenesis and investigate future therapies.