Using mathematics to avoid blindness in diabetics

Abstract

Purpose: Avoid diabetic-blindness by applying five simple mathematically-inspired treatments that achieve life-long recovery from advanced diabetic retinopathy (ADR), without laser treatments or Avastin (Hoffmann-La Roche, Basel, Switzerland) injections.Methods: A mathematical model of ADR is derived; it is based on fluid leakage from abnormal ‘holes’ in small retinal blood vessels. First, the volume of a microscopic fluid droplet leaking from a single small vein-hole during a single heartbeat is derived from the Navier-Stokes flow-equations. Then, total fluid volume leaking into the retina from all M vein holes in N heartbeats is determined. Six parameters in the equations of the model with significant influence on leakage rates and leaked volumes are identified. These insights are used to design and then apply five simple, novel, and eff icient therapeutic treatments, T1 to T5, that may achieve recovery from ADR without laser surgery or Avastin injections. Daily rates, as well as total volumes, of macular fluid accumulation, removal (by eye-pumps), and leakage are calculated from optical coherence tomography (OCT)-measured macular thicknesses.Results: Ten years ago, this paper’s primary author, Arieh Helfgott (AH), suffered from ADR that no longer responded to laser surgery. After simultaneous application of treatments T1-T5, AH recovered from ADR in 42 days and has been free of ADR for over ten years, without needing Avastin injections. Leakage-volumes were shown to be very sensitive to small changes in hole diameters. In ADR, modest increases of 2.4%, 5.7%, 10.7%, 15%, and 19% in hole diameters induce impressive 10%, 25%, 50%, 75%, and 100% (volume-doubling) increases in leakage volumes, respectively. In recovery from ADR, modest decreases of −2.6%, −5.4%, −8.5%, −12%, and −15.9% in hole diameters induce equally impressive −10%, −20%, −30%, −40%, and −50% (volume-halving) decreases in leakage volumes, respectively.Conclusion: In AH’s case, mathematics helped in avoiding blindness from ADR. Simultaneous application of mathematics-inspired treatments T1-T5 resulted in reduced leakage from holes, elimination of retinal swelling (RS), and sustained recovery from ADR. With high sensitivity to hole diameters, advancing DR can easily become unmanageable, while recovery from ADR may possibly be achievable in approximately six weeks using efficient blood pressure (BP) control and small ‘repairs’ leading to reduction in hole diameters. The pumping rate of the eye is colossal; eye pumps can remove a macula-volume-equivalent in approximately 44 days. This is very helpful in recovery from ADR, and spectacular for such microscopic pumps