Effect of leptin and dieting with respect to the mean drive outside the dietary periods.

<p>Effect of leptin and dieting with respect to the mean drive outside the dietary periods.</p

History of weight fluctuations of two adult females from data presented in [15].

<p>During the period the subjects were taking part in dietary programs (dotted intervals). The dashed lines represent the weight for constant parameter values, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074997#pone-0074997-t001" target="_blank">Table 1</a>: (a) Subject A with a mean weight <i>W</i>_mean = 157.0 [lb]. (b) Subject B with <i>W</i>_mean = 140.8 [lb]. This history has been split in two sections: up to month 40 with <i>W</i>_mean = 127.4 [lb] and a second section with <i>W</i>_mean = 144.4 [lb]. From the first section all parameters are estimated. In the second section these estimates are used again except for the rate of the constant relative decrease ε of calorie expenditure which was estimated anew.</p

Mean value [cal day⁻¹] of the effect of dieting upon the drive <i>D</i>.

<p>Mean value [cal day⁻¹] of the effect of dieting upon the drive <i>D</i>.</p

Reconstruction of the drive <i>D</i> (solid line) containing dietary periods (dotted).

<p>(a) Subject A. (b) Subject B.</p

Cross-correlation <i>X</i>(<i>s</i>) of the function <i>E</i>(τ) given by (10) and the block function <i>B</i>(τ) which has the value 1 during dietary periods and 0 outside these periods.

<p>Cross-correlation <i>X</i>(<i>s</i>) of the function <i>E</i>(τ) given by (10) and the block function <i>B</i>(τ) which has the value 1 during dietary periods and 0 outside these periods.</p

Dynamics of the system of differential equations (1abc) for the (constant) parameter values given in Table 1.

<p>It is noted that the two differential equations have different time scales. Eq.(1c) has a fast time scale meaning that in the beginning <i>L</i> rapidly changes its value so that the system reaches a quasi-stationary state satisfying Next along this line the equilibrium (<i><u>C</u></i>, <i><u>L</u></i>) is slowly approached in a way prescribed by Eq.(1a) with constraint (2).</p

Proportional Insulin Infusion in Closed-Loop Control of Blood Glucose

<div><p>A differential equation model is formulated that describes the dynamics of glucose concentration in blood circulation. The model accounts for the intake of food, expenditure of calories and the control of glucose levels by insulin and glucagon. These and other hormones affect the blood glucose level in various ways. In this study only main effects are taken into consideration. Moreover, by making a quasi-steady state approximation the model is reduced to a single nonlinear differential equation of which parameters are fit to data from healthy subjects. Feedback provided by insulin plays a key role in the control of the blood glucose level. Reduced β-cell function and insulin resistance may hamper this process. With the present model it is shown how by closed-loop control these defects, in an organic way, can be compensated with continuous infusion of exogenous insulin.</p></div

Fitting the solution of differential Eq (7).

<p>The data (o) is from a meal which has rice as the main component (Fig 5 of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169135#pone.0169135.ref007" target="_blank">7</a>], ∆ Meal 1) with <i>w</i> = 280.3 mmol. The parameter estimates are given in (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169135#pone.0169135.e009" target="_blank">9</a>).</p

Peak value <i>x</i>_max as a function of the size <i>w</i> of the carbohydrate component of the meal and the parameter ω.

<p>(a) Parameter <i>w</i> is varied while the other parameters are fixed (solid line). The peak value that corresponds with the meal (<i>w</i> = 280.3) is given by (●). A linear regression (dashed line) is made after deleting the values <i>w</i> ≥ 500: <i>x</i>_max = 4.7 + 0.01 <i>w</i>. (b) Dependence of <i>x</i>_max upon ω. The value of <i>x</i>_max for (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169135#pone.0169135.e009" target="_blank">9</a>) is given by (●). For ω = 2 the peak value is 12.8 (■); this can be brought down to 9.7 by doubling ω (□), see the section on closed-loop blood glucose control.</p

Simulation run of the stationary solution of eqs (4), (5a and 5b).

<p>Given is the effect of self-control <i>S</i> (dashed) and addiction vulnerability <i>V</i> (solid) for parameter values <i>E</i> = 0.1525 and λ = 1.</p