A mathematical model for the laser treatment of heart disease

Transmyocardial laser revascularisation (TMLR) is used to treat patients with severe coronary artery disease. A laser is used to create narrow tunnels within ischemic heart muscle in an attempt to reperfuse the area with oxygenated blood directly from the left-ventricular chamber. It has been hypothesised that initially blood flow through the patent tunnels plays an important role in the efficacy of the treatment (J. Am. College Cordiol. 25(1) (1995) 258) and Waters (J. Fluid Mech. 433 (2001) 193) developed a simple mathematical model to show that this blood flow enhances the quantity of oxygenated blood drawn into the tunnel and the subsequent delivery of oxygen to the tissue. To date, however, the optimum parameter values for this clinical technique have not been determined, e.g. the radius of the laser-drilled tunnels and their relative spacing. We present a mathematical model to determine the distribution of oxygen for a wide range of the governing parameters. Our results indicate that the tunnel radius has a significant effect on the degree of tissue reperfusion and predictions for the optimum tunnel spacing are made.