Mathematical Model of Hyperbaric Oxygen Therapy Applied to Chronic Diabetic Wounds

Abstract

The failure of certain wounds to heal (including diabetic foot ulcers) is a significant socioeconomic issue for countries worldwide. There is much debate about the best way to treat these wounds and one approach that is shrouded with controversy is hyperbaric oxygen therapy (HBOT), a technique that can reduce the risk of amputation in diabetic patients.In this paper, we develop a six species mathematical model of wound healing angiogenesis and use it to investigate the effectiveness of HBOT, compare the response to different HBOT protocols and study the effect of HBOT on the healing of diabetic wounds that fail to heal for a variety of reasons. We vary the pressure level (1 atm-3 atm), percentage of oxygen inspired by the patient (21%-100%), session duration (0-180 minutes) and frequency (twice per day-once per week) and compare the simulated wound areas associated with different protocols after three weeks of treatment.We consider a variety of etiologies of wound chronicity and show that HBOT is only effective in treating certain causes of chronic wounds. For a wound that fails to heal due to excessive, oxygen-consuming bacteria, we show that intermittent HBOT can accelerate the healing of a chronic wound but that sessions should be continued until complete healing is observed. Importantly, we also demonstrate that normobaric oxygen is not a replacement for HBOT and supernormal healing is not an expected outcome. Our simulations illustrate that HBOT has little benefit for treating normal wounds, and that exposing a patient to fewer, longer sessions of oxygen is not an appropriate treatment option.

Oxygen in acute and chronic wound healing

“…Usually, 10–30 treatments are performed. HBOT has turned out to be an effective tool to increase pO 2 values in wound tissue, and the effects of HBOT on chronic wound healing have been described by a mathematical model 108,109,111 . Sheikh et al.…”

“…HBOT has turned out to be an effective tool to increase pO 2 values in wound tissue, and the effects of HBOT on chronic wound healing have been described by a mathematical model. 108,109,111 Sheikh et al 112 demonstrated increased VEGF expression in rats treated with HBOT, and Hopf et al 30 showed a stimulation of neovascularization in hypoxic tissue after HBOT. Moreover, oxygen administration has been shown to increase VEGF mRNA levels in endothelial cells and macrophages and VEGF protein expression in wound fluids in vivo.…”

Using experimental data and information criteria to guide model selection for reaction–diffusion problems in mathematical biology

“…However, the details of the models are diverse (Jin et al, 2016b;Simpson et al, 2011). The motility of cells can be modelled by: linear diffusion (Jackson et al, 2015;Maini et al, 2004;Sengers et al, 2007;Simpson et al, 2007;Swanson et al, 2003); nonlinear diffusion where the diffusivity increases with density (Bianchi et al, 2016;Flegg et al, 2009;Sengers et al, 2007), and nonlinear diffusion where the diffusivity decreases with density King and McCabe, 2003); nonlinear advection to describe directed motility, such as chemotaxis (Bianchi et al, 2016;Flegg et al, 2010), haptotaxis (Marchant et al, 2001), and cell-cell adhesion (Armstrong et al, 2009). Similarly, the proliferation of cells is often modelled using a logistic source term (Maini et al, 2004;Sengers et al, 2007;Simpson et al, 2007), but there are also many other options for modelling carrying capacity-limited proliferation (Browning et al, 2017;Gerlee, 2013;Tsoularis and Wallace, 2002).…”

Efekti primjene hiperbarične oksigenoterapije na koncentraciju glukoze, triglicerida i holesterola u serumu oboljelih od tipa 2 dijabetes melitusa

“…Antihipoksični efekat HBOT se postiže povećanjem njegove rastvorljivosti u tjelesnim tečnostima, a vjerovatno se postižu i određeni efekti preko kiseonik -vezujućih proteina u različitim tkivima. Osim poboljšanja tkivne oksigenacije, efekti HBOT mogu da uključuju i stimulaciju angiogeneze, aktivaciju fibroblasta sa stvaranjam kolagena (profibrotički efekat), povećanu fagocitoznu aktivnost makrofaga, čime se poboljšava antimikrobna zaštita tkiva, smanjenje edema tkiva, prevenciju lipidne peroksidacije i dr. [5][6][7][8][9].…”