Biexponential model for predicting weight loss after gastric surgery for obesity

Background. Following gastric restrictive surgery, morbidly obese patients rarely achieve their ideal body weight defined by Metropolitan Life tables. The final body weight will depend on the initial body composition because there will be greater weight loss from fat than lean body mass. The purpose of this study was to develop a mathematical model that accurately estimates the rate and extent of weight loss following gastric bypass surgery. Methods. Patients underwent gastric bypass followed by intensive medical therapy and serial bioelectrical impedance analysis (BIA) body composition measurements. Differential equations were derived to model weight loss. Results. Weight loss in the fat and lean body compartments followed monoexponential decay kinetics with differing rate constants. Total body weight loss (W_T) at time t was W_T = k_f/(k_f - k₁) (W_foe^-kft + W_loe^-k1t), where W_fo and W_lo are the initial fat and lean body masses determined by BIA and k_f and k_l are the rate constants for the fat and lean compartments, respectively. Following surgically induced weight loss, k_f = 7.61 ± 1.27 × 10^-2, and k_l = -0.93 ± 0.13 × 10^-2, with the ratio of residual sum of the squares to the total sum of the squares of 98.8%. Conclusion. Accurate prediction of weight loss depends on the initial fat and lean compartment mass since each of these loses weight at a different rate and to a different extent. When these effects are accounted for, the total body weight loss can be accurately predicted for any given time following surgery.