Abstracts

Rationale: The Ketogenic Diet (KD) is an effective treatment of refractory epilepsy, offering >50% reduction in 2/3 and cessation of seizures in about 20% of patients. The KD composition (90% fat, 7% protein, and 3% carbohydrate) forces the body to utilize fatty acid oxidation as the primary energy source and in the process a myriad of hormonal, metabolic changes lead to improved seizure control. The KD is labor intensive, requiring 50 hours of parent education and continued exact calculation of each meal to 0.1 gram in order to maximize its effect throughout the average 3-year treatment period. In this study, we aim to create a model of the KD requirements using linear algebra. By examining the information as a system of underdetermined equations we can create an application that both simplify and shorten the time for planning of KD meals.Methods: Nutritional data was gathered from the 2012 United States Department of Agriculture Nutritional Database. User selected foods are converted into a set of three linear equations with n variables and three constraints: prescribed fat content, prescribed protein content, and prescribed carbohydrate content. Each equation represents the summation of the n different food choices of one restraint category. The set of linear equations are then converted into full rank, matrix form. We normalize each column of the coefficient matrix, and different matrix manipulation techniques are applied to derive the solutions to the underdetermined system depending on the number of foods chosen (Fig 1). The Ordered Subsets Expectation Maximization (OSEM) method is the preferred method used to solve for the solutions to this system of linear equations. This method operates with an iterative nature generating solutions of underdetermined linear systems until the solution space converges. We discover that this method is not only the most efficient but also guarantees positive solutions to the system given our parameters. Results: The results are depicted in Fig. 2 using an iOS simulator to run the KD meal planning application. Fig. 2 demonstrates the application processing three food choices; peanut butter, olive oil, and celery alongside the results with added fourth food choice of mozzarella cheese. The total nutrition of both meals matches closely with the recommended KD values (prescribed by the dietician). The blue progress bar indicates that the application s constructed meal plan is within 95% precision of the KD requirements. These results show that the application is capable of handling all the different scenarios in terms of the number of food choices while generating a precise meal plan for each case.Conclusions: The algorithm for solving this model of the KD can be structured in a linear manner. This method paves the way for diet planning applications made for patients on the KD that will give suggested values for the amount of each chosen food. We believe this application will help make the KD and other dietary treatment preparations less time consuming and easier to manage.