Using mathematics to avoid blindness in diabetics

Arieh Helfgott, Ariella E.R. Helfgott, Sean Mullany


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



advanced diabetic retinopathy (ADR) treatment; blindness; blood flow; diabetic retinopathy (DR); diabetes; leaking blood vessels; macula; mathematical model; retina

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Dirani M. Out of sight. A report into diabetic eye disease in Australia. Australia: Co-published by the Baker IDI Heart and Diabetes Institute and the Centre for Eye Research; 2013. Available from:

Lee R, TY Wong, C Sabanayagam. Review: Epidemiology of diabetic retinopathy, diabetic macular edema and related vision loss. Eye Vis. 2015;2(17):1-25. doi:10.1186/s40662-015-0026-2.

Wu G. Diabetic retinopathy: The essentials. 1st ed. Philadelphia: Lippincott Williams & Wilkins; 2010.

Maturi RK, Walker JD, Chambers RB. Diabetic retinopathy for the comprehensive ophthalmologist. 2nd ed. Fort Wayne: Deluma Medical Publishers; 2015. Available from:

American Optometric Association. Diabetic Retinopathy [Internet]. St. Louis (MO); c2018 American Optometric Association. Available from:

Chan A, Duker JS, Ko TH, Fujimoto JG, Schuman JS. Normal macular thickness measurements in healthy eyes using stratus optical coherence tomography. Arch Ophthalmol. 2006;124(2):193–198.

Browning DJ. The relationship between OCT-measured central retinal thickness and visual acuity in diabetic macular edema. Ophthalmology. 2007;114 (3):525–536.

Duan XR, Liang YB, Friedman DS, et al. Normal macular thickness measurements using optical coherence tomography in healthy eyes of adult Chinese persons: the Handan Eye Study. Ophthalmology. 2010;117(8):1585-1594.

Nagra M, Gilmartin B, Thai NJ, Logan NS. Determination of retinal surface area. J Anat. 2017. doi:10.1111/joa.12641.

Caro CG, Pedley TJ, Shrouter RC, Seed WA. The mechanics of the circulation. 2nd ed. Cambridge: Cambridge University Press; 2012. Chapter 13, The systemic microcirculation.

Batchelor GK. An introduction to fluid dynamics. 3rd ed. Cambridge: Cambridge University Press;2000. Chapter 4, Flow of a uniform compressible viscous fluid.

da Silva AVB, Gouvea SA, da Silva APB, et al. Changes in retinal microvascular diameter in patients with diabetes. Int J Gen Med. 2015;8:267-273.

Tan PE, Balaratnasingam C, Xu J, et al. Quantitative comparison of retinal capillary images derived by speckle variance optical coherence tomography with histology. Invest Ophthalmol Vis Sci. 2015;56(6):3989-3996.

Wang Q, Kocaoglu OP, Cense B, et al. Imaging retinal capillaries using ultra- high-resolution optical coherence tomography and adaptive optics. Invest Ophthalmol Vis Sci. 2015;52(9):6292-6299.

Lombardo M, Parravano M, Serrao S, Ducoli P, Stirpe M, Lombardo, G. Analysis of retinal capillaries in patients with type 1 diabetes and non proliferative diabetic retinopathy using adaptive optics imaging. J Ret Vit Dis. 2013;33(8):1630-1639

Kundu PK, Cohen IM. Fluid Mechanics. Cambridge, MA: Academic Press; 2007. Chapter 17, Introduction to Biofluid Mechanics.

Munson BR, Okiishi TH, Huebsch WW, Rothmayer AP. Fluid Mechanics. 7th ed. Wiley; 2013.

Muraoka Y, Tsujikawa A, Kumagai K, et al. Age- and hypertension-dependent changes in retinal vessel diameter and wall thickness: an optical coherence tomography study. Am J Ophthalmol. 2013;156(4):706-714.

Rim TH, Choi YS, Kim SS, et al. Retinal vessel structure measurement using spectral-domain optical coherence tomography. Eye. 2016;30(1):111-119.

Thornalley PJ, Babaei-Jadidi R, Al Ali H, et al. High prevalence of low plasma thiamine concentration in diabetes linked to a marker of vascular disease. Diabetologia. 2007;50(10):2164-2170.

Rabbani N, Alam SS, Riaz S, et al. High-dose thiamine therapy for patients with type 2 diabetes and microalbuminuria: a randomised, double-blind placebo-controlled pilot study. Diabetologia. 2009;52(2):208-212.

Beltramo E, Berrone E, Tarallo S, Porta M. Effects of thiamine and benfotiamine on intracellular glucose metabolism and relevance in the prevention of diabetic complications. Acta Diabetol. 2008;45(3):131-141.

BBC NEWS Article. Diabetes Problems ‘Vitamin Link’ [Internet]; c2018 [Last updated 7 August 2007]. Available from:

Page, GL, Laight D, Cummings MH. Thiamine deficiency in diabetes mellitus and the impact of thiamine replacement on glucose metabolism and vascular disease. Int J Clin Pract. 2011;65(6):684-690.

Cinici E, Ahiskali I, Cetin N, et al. Effect of thiamine pyrophosphate on retinopathy induced by hyperglycemia in rats: A biochemical and pathological evaluation. Indian J Ophthalmol. 2016;64(6):434-439.

Hammes HP, Du X, Edelstein D, et al. Benfotiamine blocks three major pathways of hyperglycemic damage and prevents experimental diabetic retinopathy. Nat Med. 2003;9(3):294-299.

Mukherjee C, Wilcox M, Elsherbiny S. Does vitamin D deficiency affect diabetic retinopathy?: A primary care survey and literature review. EC Ophthalmol. 2016;4(1):451-458.

Payne JF, Ray R, Watson DG, et al. Vitamin D insufficiency in diabetic retinopathy. Endocr Pract. 2012;18 (2):185-103.

Millen AE, Meyers KJ, Liu Z, et al. Association between vitamin D status and age-related macular degeneration by genetic risk. JAMA Ophthalmol. 2015;133 (1):1171-1179.

Richer SP, Pizzimenti JJ. The importance of vitamin D in systemic and ocular wellness. J Optom. 2013;6(3):124-133.

Elblbesy MA, Hereba AR, Shawki MM. Effects of aspirin on rheological properties of erythrocytes in vitro. Int J Biomed Sci. 2012;8(3):188-193.

Vekasi J, Koltai K, Gaal V, Toth A, Juricskay I, Kesmarky G. The effect of aspirin on hemorheological parameters of patients with diabetic retinopathy. Clin Hemorheol Microcirc. 2008;39(1-4):385-389.

Do DV, Wang X, Vedula SS, et al. Blood pressure control for diabetic retinopathy. Cochrane Database Syst Rev. 2015;1:CD006127. doi: 10.1002/14651858.CD006127.pub2.

Sheps SG. Mayo Clinic Article. Caffeine: How does it affect blood pressure? [Internet]; [Last updated 19 Oct 2017]. Available from:


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