Mathematical Study on Palatable Diet Administration with a Reference to Diabetes Mellitus on Varying Body Frames - ANOVA Test with PFC Ratio

Abstract

A mathematical model is presented in this paper to compute the palatable prescription of chosen diet for diabetes mellitus type-II using Joselin’s principle. Two types of portions of the food as red portion and black portionare chosen for palatable diet with 1:1:1gm equivalent to 4:9:4cal.taken as Protein(P), Fat(F) and Carbohydrate(C) respectively. For the analysis, three types of body frames as Small(S), Medium(M) and Large(L) for both men and women aged 19 years and above are considered. A reference tojuvenileis introduced for the palatable diet. Differential equationsin the coupled form are definedto explain the varying glucose level and varying insulin level. Average calorie values are computed in reference to age and height for the estimation of PFC using linear regression model. ANOVA gives the comparison of results of calorie estimation for palatable diet chosen. With the administration of palatable diet, the values of PFC can be varied to meet the required glucose level of diabetes mellitus type-II.

Introduction

I. INTRODUCTION

Diabetes is the disorder of metabolism causing excessive thirst and the production of large volume of urine containing excess of sugar. Metabolic disorder is of two types:

I)Diabetes insipidus: This is the rare metabolic disorder in which the body passes large quantity of colourless urine that contains more water causing thirsty, dry hands, constipation. This is due to the failure of kidney’s function where in the water is to be reabsorbed.

II)Diabetes mellitus:This is the disorder of carbohydrate metabolism in which sugars in the body are not oxidized to produce energy due to lack of pancreatic hormone insulin. The accumulation of sugar leads to cause of hyperglycaemia in the blood. The disorder may be triggered by the various factors including physical stress, weight loss, retinopathy and hardening of the arteries (atherosclerosis). Also, due to unoxidized glucose, the cells in the lining of blood vessels and other organs may get damaged. The series of such events cause the arteries get clogged and resulting in heart attack and stroke. The systolic and diastolic blood pressure shows the increase from 4.77% to 10.35% when compared to normal values 80-120 mm Hg. As aresult the viscosity of blood decreases, the flow rate increases. But due to increase in viscosity, the flow rate decreases in the arteries. Further the micro aneurysms develop in the arteries when the cell function is disturbed. In order to regulate the proper utilization of blood glucose, administration of insulin and palatable diet distribution are necessary for varying body frames to maintain the proper utilization of insulin for the metabolic activities.

A general approach of Gatewood et.al[13] explained the effect of hormone glucose and insulin secreted by pituitary and thyroxin produced by thyroid as simplest mathematical form. Brownlee et. al[9] described glycosylation end products in tissue and the biochemical basis of diabetic complications. They also analysed the fluctuations of chemical compounds in diabetic patients. Kapur[19] presented a compartment model for diabetes mellitus taking the interaction of blood glucose with insulin at different time intervals. Bankroft et.al[5] made a comparative study of dysfunction in men with and without diabetes mellitus. Bartholovistsch et.al[8] studied the behaviour of viscosity of the blood in diabetic cases and non-diabetic cases.

Sathia [28] analysed the treatment of Alpha-Lipoic Acid (ALA) for the improvement of glucose effectiveness in lean and obese patients with type-II diabetes mellitus (non-insulin-dependent diabetes mellitus (NIDDM)). The variations were observed on whole blood viscosity, haematocrit, shear rate and the plasma viscosity. They also explained the fundus appearance in hypersensitive and diabetic, lack of exercise, a poor diet, current smoking and abstinence from alcohol use were all associated with significantly increased risk factors of diabetes. Gary et.al[12] presented the effect of body weight of a free 76 kilojoules (320 calories) daily supplement of almonds for six months. Katiyar and Basavarajappa et.al[20] analysed the diabetes mellitus under palatable composition of quantitative diet with varying body frames. Allick Gideon et.al[1] compared the effects of a caloric high carbohydrate and high fat improves glucoregulation in type- II diabetes mellitus by reducing post absorptive glycogenolysis.Venkatapuram et.al[30] explained metabolic syndrome is considered to be a metabolic precursor of type – II diabetes mellitus and is an independent risk factor in the pathogenesis of atherosclerosis. MeenaVerma et. al[22] presented the effect of increasing duration of diabetes mellitustype –II on glycated haemoglobin and insulin sensitivity. Villegas et.al[31] analysed that high intake of foods with a high glycemic index and load, especially rice, the main carbohydrate contributing food may increase the risk of type- II diabetes mellitus in Chinese women.

Keeping in view of the investigations made by various authors, the present paperconcerns the study of mathematical model for diabetes mellitus type-2. The study of palatable composition of quantitative diet using system of coupled linear differential equations is considered in the analysis. Required calorie against the height of human beings is studied as a special case using linear regression model. It is aimed at achieving the required total calorie as the ratio of Ca vs. small, Ca vs. medium and Ca vs. large body frames for men and women with age 25years and above.Studyis focused to improve the outcome of palatable composition in maintaining the blood glucose and insulin levels during fasting (pre-prandial: no caloric intake for the previous 8 hours) and after consuming the breakfast (postprandial: calorific intake in every four hours). Three types of body frames small, medium and large have been considered with an average age variation rate. The initial concentrations of blood glucose and insulin levels are documented at the time of meal-1, meal-2, mean-3 and meal-4 in a successive interval of four hours. The ratio of calorie vs height using regression equation has been computed for various PFC values for three different body frames.Palatable diet under equally divided meals will help the usage of reasonable doses to achieve the closeness of normal blood glucose levels. We have considered three different body frames with different age and height in the regression modelfor computing the total calorie of PFCusing Joslin’s principle.

References

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Copyright

Copyright © 2024 Mani K S, K S Basavarajappa, Ashwini M Rao, Ashwini. G, Shriya Anil Hardi, Srusti. S, Harsha Teja. K, Sathisha A B. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.