2. Method

For all calculations I used MATLAB. To demonstrate the main functions of our CPS, we use here the published data of EBPE [29]. In this study 10 healthy men participated in two cycles of controlled 7-day periods of caloric restriction (CR) and refeeding (RF) in protocol A and overfeeding (OF) and caloric restriction (CR) in protocol B at 60% energy requirement. Insulin resistance was assessed by HOMA-IR on the basis of measured serum insulin and glucose levels in the study participants. The mandatory input data to CPS is weight, fat weight, and daily energy balance values EBk. The daily weights were directly scanned in from the published graphs [29]. The fat weight data points were available only at baseline and at the end of CR, RF, and OF cycles. I used MATLAB's Piecewise Cubic Hermite Interpolating Polynomial to connect these fat data points in order to have daily fat mass estimates (see Figure 1a and b). I calculated the energy balance EBk from the difference of the metabolically utilized energy intake minus total energy expenditure.

I estimated weight-related alpha α^wk, energy density parameter for weight ϱ^ <sup>W</sup> k, Rw-ratio Rwk, and fat-burning fraction χ<sup>k</sup> from ΔWk, ΔFk, and EBk utilizing the methods described in Eqs. (1)–(19).

Figure 1. (a) Daily weight and fat weight in protocol A. (b) Daily weight and fat weight in protocol B.

Cyber-Physical System for Management and Self-Management of Cardiometabolic Health DOI: http://dx.doi.org/10.5772/intechopen.84262

For calculation of correlations between HOMA-IR and weight, fat weight, Rratio, Rw-ratio, fat-burning fraction χk, and nonprotein respiratory quotient Rnpk, I used MATLAB's corrcoef function.

For demonstration purposes, I plugged the mandatory input variables ΔWk, ΔFk, and EBk as well as the known ingested macronutrient calories CIk, FIk, and PIk into SAM-HEM algorithm with Kalman filter [1–3]. As a measure of goodness of fit of the metabolic model SAM-HEM, I calculated the predicted mean value and standard deviation of the modeling error, i.e., model-predicted value minus the known trajectory of weight, fat weight, and lean mass.

## 3. Results

One of the goals of this chapter is to demonstrate the feasibility of the concept of CPS for its main function which is to predict changes of insulin resistance and fat oxidation from serial measurements of weight and fat mass. Unfortunately, there is a paucity of published data with longitudinal observations and serial measurements of the measurable components of the energy metabolism including measuring markers of insulin resistance. A complete data set to study the insulin resistance and weight-fat weight relationship would require the following data: serial measurements of macronutrient energy intake (EI), total energy expenditure (TEE) and serial fat mass (F), and lean body mass (L) or weight (W) measurements. Very few trial data are published only with serial measurements of markers of insulin sensitivity or resistance. Nevertheless, we were able to identify a study suitable for our aim, which is to demonstrate the feasibility of our concept of CPS to track and predict SVs and markers of insulin resistance. Here we use published data from the study entitled "Effects of brief perturbation in energy balance on indices of glucose

For all calculations I used MATLAB. To demonstrate the main functions of our CPS, we use here the published data of EBPE [29]. In this study 10 healthy men participated in two cycles of controlled 7-day periods of caloric restriction (CR) and refeeding (RF) in protocol A and overfeeding (OF) and caloric restriction (CR) in protocol B at 60% energy requirement. Insulin resistance was assessed by HOMA-IR on the basis of measured serum insulin and glucose levels in the study participants. The mandatory input data to CPS is weight, fat weight, and daily energy balance values EBk. The daily weights were directly scanned in from the published graphs [29]. The fat weight data points were available only at baseline and at the end of CR, RF, and OF cycles. I used MATLAB's Piecewise Cubic Hermite Interpolating Polynomial to connect these fat data points in order to have daily fat mass estimates (see Figure 1a and b). I calculated the energy balance EBk from the difference of the metabolically utilized energy intake minus total energy

I estimated weight-related alpha α^wk, energy density parameter for weight ϱ^

Rw-ratio Rwk, and fat-burning fraction χ<sup>k</sup> from ΔWk, ΔFk, and EBk utilizing the

(a) Daily weight and fat weight in protocol A. (b) Daily weight and fat weight in protocol B.

<sup>W</sup> k,

homeostasis in healthy lean men (EBPE) [29]."

Type 2 Diabetes - From Pathophysiology to Modern Management

2. Method

expenditure.

Figure 1.

118

methods described in Eqs. (1)–(19).

The input weight and fat weight data are shown in Figure 1a for Protocol A and in Figure 1b for Protocol B. The measured data points for fat mass are connected with MATLAB's Piecewise Cubic Hermite Interpolating Polynomial. The results of Rw-ratio Rwk and fat-burning fractionation χ<sup>k</sup> for Protocols A and B are in Figure 2a and b, respectively. The measured data points for HOMA-IR are connected with MATLAB's Piecewise Cubic Hermite Interpolating Polynomial.

#### Figure 2.

(a) Daily changes of Rw-ratio, χk, and Homa-IR in protocol A. (b) Daily changes of Rw-ratio, χk, and Homa-IR in protocol B.

Figure 3. (a) Daily changes of Rnp and Homa-IR in protocol A. (b) Daily changes of Rnp and Homa-IR in protocol B.

In Figure 3a and b, the changes of the nonprotein respiratory quotient can be seen for Protocol A and for Protocol B. Figure 4a for Protocol A and Figure 4b for Protocol B show the results of utilized macronutrient intakes carbohydrate CI and fat FI, as well the macronutrient oxidations for carbohydrate CarbOx and fat FatOx.

4. Discussion

DOI: http://dx.doi.org/10.5772/intechopen.84262

Insulin resistance is a pathogenic factor for type 2 diabetes. Insulin resistance has a deleterious impact on glucose and lipid metabolism, blood pressure, coagulation abnormality, inflammation, oxidative stress, and endothelial dysfunction. Population studies suggest that insulin resistance is an important target to reduce CVD risk [30]. A significant proportion of apparently healthy subjects are insulin resistant. About 30–40% of subjects are afflicted with insulin resistance in affluent countries, and the total number is over 1 billion worldwide [30]. HOMA-IR-estimated insulin resistance is associated with subsequent symptomatic CVD in the general population independent of all classic and several nontraditional risk factors [30]. The main result of EPBE [29] is that it clearly demonstrates the profound effect of energy perturbation on changes of insulin resistance. Insulin resistance remained slightly impaired at the end of Protocol A (CR followed by RF) as opposed to the end of Protocol B (OF followed by CR) where the insulin resistance created by OF was normalized by CR. As it is discussed by the authors of [29], the benefit of calorie restriction in terms of improvement of insulin sensitivity is firmly established in the medical literature in various disorders like binge eating with bulimia, weight cycling, obesity, and type II diabetes. In the EPBE study, euglycemic clamp measurements were performed parallel to the HOMA-IR. Observing these in parallel, an overarching picture emerges that the sugar and insulin dynamics are strongly connected to quantifiable dynamics of body composition and the fat metabolism as

Cyber-Physical System for Management and Self-Management of Cardiometabolic Health

well as the carbohydrate- vs. fat-burning energy utilization.

icant P value for each examined variable.

metabolic health.

change ϱ^

121

Our feasibility demonstration for the main features of CPS is focused on assessing changes of insulin resistance. Using trial data from EBPE [29], we correlated HOMA-IR as a surrogate marker for insulin resistance with our surrogate markers such as R-ratio, Rw-ratio, 24 h nonprotein respiratory quotient, and fat-burning fraction. We found high correlation across the examined metabolic variables Wk, Fk, Rk, Rwk, Rnpk, and χ<sup>k</sup> with HOMA-IR along with highly signif-

The implication is that these results show strong evidence for the feasibility for our concept to a have a noninvasive long-term monitoring tool for insulin resistance for users in their natural environment. Displaying Wk, Fk, Rk, Rwk, Rnpk, and χ<sup>k</sup> on MHM and MST via our CPS can provide the needed tool to users and their providers to observe and use adaptive control strategies to improve the otherwise undetectable and invisible phenomena caused by insulin resistance and reach

A new method for metabolic research has been introduced here to extend the principles of indirect calorimetry to a broader application which considers serial measurements of changes of body composition and hydration status with no gas exchange measurements and is still able to estimate 24 h nonprotein respiratory quotient. For this purpose, a Lagrangian functional L was set up to establish the quantitative relationships between changes of fat mass, weight, and energy balance. Without calorie counting and just using the required input weight change ΔWk, fat mass change ΔFk, and energy balance EBk, the fat and nonfat energy balance can be estimated along with important semi-stable energy parameters of the metabolism including the weight-related alpha α^wk, the energy density parameter for weight

<sup>W</sup> k, the weight-related Rw-ratio Rwk, the lean mass-related alpha α^k, the

energy density parameter for lean mass change ϱ^Lk, the lean mass-related R-ratio Rk, the nonprotein respiratory quotient Rnpk, and the fat-burning fraction χk. Finding proof for the quantitative relationship between insulin resistance and Rwk, Rk, Rnpk, and χ<sup>k</sup> was difficult due to lack of previous studies [24] with the

The correlation coefficients between HOMA-IR and Wk, Fk, Rk, Rwk, Rnpk, and χ<sup>k</sup> along with their P value are shown in Table 1.

The results of goodness of fit of the SAM-HEM metabolic model to the known trajectory of weight, fat weight, and lean mass are shown in Table 2.

#### Figure 4.

(a) Daily metabolized carbohydrate and fat intake and oxidation in protocol A. (b) Daily metabolized carbohydrate and fat intake and oxidation in protocol B.


#### Table 1.

Correlation coefficients between HOMA-IR and Wk, Fk, Rk, Rwk, Rnpk, and χ<sup>k</sup>:


#### Table 2.

Goodness of fit of the SAM-HEM metabolic model to Wk, Fk, and Lk data.

Cyber-Physical System for Management and Self-Management of Cardiometabolic Health DOI: http://dx.doi.org/10.5772/intechopen.84262
