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estimate of ^zk�<sup>1</sup> at time k � 1 can be updated at the arrival of the new measured variables yk and xk. This method allows us to estimate α^wk when ΔWk, ΔFk, and Fk

Type 2 Diabetes - From Pathophysiology to Modern Management

Once all parameters of the energy balance Eq. (4) are known, the nonfat energy balance and fat energy balance can be calculated as in Eqs. (11) and (12),

Here φ<sup>k</sup> designates fat intake fraction as defined in Eq. (13), and χ<sup>k</sup> denotes the

<sup>φ</sup><sup>k</sup> <sup>¼</sup> FIk MEIk

<sup>χ</sup><sup>k</sup> <sup>¼</sup> FOk TEEk

ϱWk � Rwk þ ϱ<sup>F</sup>

ϱWk � Rwk þ ϱ<sup>F</sup>

ϱWk � Rwk þ ϱ<sup>F</sup>

Important properties of Eqs. (15) and (16) are that they add up to the total energy balance equation as in Eq. (3). It can be seen in this pair of equations that with decreasing insulin resistance, i.e., decreasing HOMA-IR and concomitantly increasing Rw-ratio Rwk, the fat-burning fraction χ<sup>k</sup> increases, and the carbohydrate burning fraction 1 � χ<sup>k</sup> would decrease. Similarly, with increasing insulin resistance, i.e., increasing HOMA-IR and concomitantly decreasing Rw-ratio Rwk, the fat-burning fraction χ<sup>k</sup> decreases, and carbohydrate burning fraction 1 � χ<sup>k</sup>

Accordingly, the carbohydrate burning fraction 1 � χ<sup>k</sup> and the fat-burning frac-

<sup>¼</sup> COk COk þ FOk

<sup>¼</sup> FOk COk þ FOk

In Eq. (13), FIk represents fat intake, and in Eq. (14), FOk stands for oxidized fat

We made an important observation in [2, 3, 26] that the R-ratio Rk strongly and negatively correlates with HOMA-IR. Building on this observation and using Rwratio Rwk, we introduce here a possible modeling of the connection between insulin resistance and substrate fractionation. At assumed steady state, the fat-burning fraction χ<sup>k</sup> approximates food fraction φ<sup>k</sup> according to [31], and they become quasi equal. Under this condition the nonfat and fat energy balance can be written in a

<sup>W</sup> <sup>k</sup> can be estimated when a new set of ΔWk, ΔFk, and EBk

ϱWk � ΔWk ¼ 1 � φ<sup>k</sup> ð Þ� MEIk � 1 � χ<sup>k</sup> ð Þ� TEEk, (11)

ϱ<sup>F</sup> � ΔFk ¼ φ<sup>k</sup> � MEIk � χ<sup>k</sup> � TEEk: (12)

, (13)

: (14)

� ð Þ MEIk � TEEk , (15)

� ð Þ MEIk � TEEk : (16)

, (17)

: (18)

are available. Similarly, ϱ^

fat-burning fraction as in Eq. (14).

simplified form as in Eqs. (15) and (16):

tion χ<sup>k</sup> can be written as in Eqs. (17) and (18):

would increase as demonstrated in Figure 2a and b.

<sup>ϱ</sup>Wk � <sup>Δ</sup>Wk <sup>¼</sup> <sup>ϱ</sup><sup>F</sup>

<sup>ϱ</sup><sup>F</sup> � <sup>Δ</sup>Fk <sup>¼</sup> <sup>ϱ</sup>Wk � Rwk

<sup>1</sup> � <sup>χ</sup><sup>k</sup> <sup>¼</sup> <sup>ϱ</sup><sup>F</sup>

<sup>χ</sup><sup>k</sup> <sup>¼</sup> <sup>ϱ</sup>Wk � Rwk ϱWk � Rwk þ ϱ<sup>F</sup>

are available.

respectively:

and

128

calories of day k:

Zsolt Peter Ori Ori Diagnostic Instruments, LLC, Durham, NC, USA

\*Address all correspondence to: zsolt.ori56@gmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
