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Introduction: Background: nutrition therapy is a complex area of healthcare systems that encompasses patient characteristics, medical decision making, nutritional formula characteristics, and costs, composing a complex ecosystem. The integration of these different domains is actualized in medical prescription in a heuristic and iterative way, taking into account patient characteristics and formulas, with a limited capacity for in-scale calculations and inclusion of factors involved in the prescription of nutritional formulas and other ecosystem elements. From a practical standpoint, depicting the four areas as equalities could provide the necessary equivalence to study dependence and consequence from left- and right-side terms. Objectives: the objective of this theoretical study is to provide a mathematical model that describes and integrates different aspects of nutrition therapy. Methods: in this theoretical study, we deducted a mathematical representation for nutrition therapy using first-grade equations and simple calculus techniques. Results: a formula that coordinates four elements of the nutrition therapy ecosystem was found: cashflow, compliance adherence, patient, and macronutrient mass, formula density and unitary cost. Conclusion: factors involving decision-making in nutrition therapy can be unified in a mathematical model. [ABSTRACT FROM AUTHOR]

Introduction: Background: nutrition therapy is a complex area of healthcare systems that encompasses patient characteristics, medical decision making, nutritional formula characteristics, and costs, composing a complex ecosystem. The integration of these different domains is actualized in medical prescription in a heuristic and iterative way, taking into account patient characteristics and formulas, with a limited capacity for in-scale calculations and inclusion of factors involved in the prescription of nutritional formulas and other ecosystem elements. From a practical standpoint, depicting the four areas as equalities could provide the necessary equivalence to study dependence and consequence from left- and right-side terms. Objectives: the objective of this theoretical study is to provide a mathematical model that describes and integrates different aspects of nutrition therapy. Methods: in this theoretical study, we deducted a mathematical representation for nutrition therapy using first-grade equations and simple calculus techniques. Results: a formula that coordinates four elements of the nutrition therapy ecosystem was found: cashflow, compliance adherence, patient, and macronutrient mass, formula density and unitary cost. Conclusion: factors involving decision-making in nutrition therapy can be unified in a mathematical model.

Introduction: Background: the planning of nutritional therapy depends restrictions defined by the prescriber, in a way that nutrients and calories levels are placed at appropriate intervals. Since industrialized formulas (IF) have fixed compositions of macro and micronutrients, there is a high risk of not meeting the set of restrictions in a given clinical scenario, i.e., attendance of the caloric, but not of the protein target. Objective: the objective of this study is to identify under what conditions it is possible an industrialized formula to meet the clinical restrictions of calories, macro and micronutrients. Methods: we deduced a mathematical relationship that must be met in order to satisfy such constraints. Using as variables: a) the necessary volume of an FI to meet the energy goal; b) the energy density of the FI; c) upper limit of calorie or nutrient; and d) the lower limit of calorie or nutrient. Results: a first degree inequality was developed that if attended allows to discriminate if a prescribed volume v of an IF meets the set of restrictions placed by the prescriber, in order to previously select viable formulas among a portfolio. Clinical vignettes are presented. Conclusion: the viability condition of an industrialized formula for the attendance of a system of constraints can be identified with the aid of a mathematical formula of the first-degree inequality type.