26.05 Exponential Decay Modeling Can Define Parameters of the Weight Loss Trajectory After Gastric Bypass

E. S. Wise^1,2, J. Felton¹, M. D. Kligman^{1  1}University Of Maryland Medical Center,Department Of Surgery,Baltimore, MD, USA ²Vanderbilt University Medical Center,Department Of Surgery,Nashville, TN, USA

Introduction:

Laparoscopic Roux-en-Y gastric bypass (LRYGB) is a well-described operation that produces durable and clinically significant weight loss. While factors influencing future weight loss have been studied, temporal patterns of weight loss are less well described. We test the hypotheses that postoperative weight loss may conform to exponential decay, and subsequently, that three-month weight loss can help characterize a patient’s weight loss trajectory.

Methods:

A retrospective analysis of 1,097 consecutive LRYGB patients at a single institution over a ten year period provided the data necessary to generate postoperative weight loss curves. Using pre- and postoperative BMI data, the mean and standard deviation of postoperative BMI as a function of time was obtained, with multiple linear and nonlinear fits tested for optimal conformity. The highest and poorest performing patients at three month follow-up were stratified based on their cumulative rate of weight loss into two strata: <0.3% EBMIL/day (n = 102) and >0.5% EBMIL/d (n = 191). Exponential decay rate constants (λ) were generated for each group, allowing for optimized estimation of time until half of the weight loss is complete (t_1/2) as well as plateau BMI (BMI_f). Linear regression analysis was used to interrogate the association of λ, calculated at three months and normalized using a BMI_f of 25 kg/m² (λ_{n, 3 mo.}), to %EBMIL at 2-3 years, a surrogate for actual BMI_f.

Results:

For the entire cohort, one-phase exponential decay provided the best fit for the weight loss function over time (n = 1,097, r = .43, λ (x 10³) = 7.3, t_1/2 = 95 days, BMI_f = 31.4). Patients who performed poorly at three months (<0.3% EBMIL/d, n = 102, r = .49, lambda(x 10³) = 6.4, t_1/2 = 108 days, BMI_f = 38.9) had a smaller λ and a higher BMI_f than those who performed optimally (>0.5% EBMIL/d, n = 191, r = .62, λ (x 10³) = 9.4, t_1/2 = 74 days, BMI_f = 26.6; Figure 1A). Normalized rate constants calculated from three-month weight loss (λ_{n,3 mo.}) demonstrated a significant correlation with %EBMIL_{2-3 years} (n = 428, P < .001, r = .28, B = -4.1 %EBMIL per unit increase in normalized lambda; Figure 1B).

Conclusion:

We demonstrate that weight loss after LRYGB conforms to exponential decay. This finding necessarily submits that weight loss trajectory is governed by a patient-specific rate constant and a plateau BMI. Further studies are necessary to characterize the patient and institution-specific factors that contribute to these parameters. However, we find that patient performance at three months, as suggested by λ_{n,3 mo}, is a significant predictor of long term weight loss in accordance with our hypothesis.