A model of infection and immune response to low dose radiation

Low dose radiation therapy (LDRT) using doses in the range of 30-150 cGy has been proposed as a means of mitigating the pneumonia associated with COVID-19. However, preliminary results from ongoing clinical trials have been mixed. The aim of this work is to develop a mathematical model of the viral infection and associated systemic inflammation in a patient based on the time evolution of the viral load. The model further proposes an immunomodulatory response to LDRT based on available data. Inflammation kinetics are then explored and compared to clinical results.

The time evolution of a viral infection, inflammatory signaling factors, and inflammatory response are modeled by a set of coupled differential equations. Adjustable parameters are taken from the literature where available and otherwise iteratively adjusted to fit relevant data. Simple functions modeling both the suppression of pro-inflammatory signal factors and the enhancement of anti-inflammatory factors in response to low doses of radiation are developed. The inflammation response is benchmarked against C-reactive protein (CRP) levels measured for cohorts of patients with severe COVID-19.

The model fit the time-evolution of viral load data, cytokine data, and inflammation (CRP) data. When LDRT was applied early, the model predicted a reduction in peak inflammation consistent with the difference between the non-surviving and surviving cohorts. This reduction of peak inflammation diminished as the application of LDRT was delayed.

The model tracks the available data on viral load, cytokine levels, and inflammatory biomarkers well. An LDRT effect is large enough in principle to provide a life-saving immunomodulatory effect, though patients treated with LDRT already near the peak of their inflammation trajectory are unlikely to see drastic reductions in that peak. This result potentially explains some discrepancies in the preliminary clinical trial data.