Compartmental OED - Revision history

RobertLampel: /* Mathematical formulation */

2026-03-26T10:18:55Z

Mathematical formulation

← Older revision		Revision as of 10:18, 26 March 2026
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	For the three-dimensional parameter <math>p = (\theta_1, \theta_2, \theta_3)</math> the original initial value problem is given by		For the three-dimensional parameter <math>p = (\theta_1, \theta_2, \theta_3)</math> the original initial value problem is given by
	<math>		<math>
	\dot{y}(t) =: f(t, p) = \theta_3 \cdot (-\theta_1 \cdot \exp(-\theta_1 \cdot t) + \theta_2 \cdot \exp(-\theta_2 \cdot t)), \quad y(0) = 0.		\dot{y}(t) = f(t, p) = \theta_3 \cdot (-\theta_1 \cdot \exp(-\theta_1 \cdot t) + \theta_2 \cdot \exp(-\theta_2 \cdot t)), \quad y(0) = 0.
	</math>		</math>

RobertLampel at 13:41, 13 February 2026

2026-02-13T13:41:26Z

← Older revision		Revision as of 13:41, 13 February 2026
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	}}		}}

	The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a three parameters in a one-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the single state. The following description is taken from [[#compartmental\| [1]]].		The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine three parameters in a one-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the single state. The following description is taken from [[#compartmental\| [1]]].

	Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.		Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.

RobertLampel at 13:41, 13 February 2026

2026-02-13T13:41:14Z

← Older revision		Revision as of 13:41, 13 February 2026
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	}}		}}

	The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a three parameters in a ~~three~~-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the ~~three states~~. The following description is taken from [[#compartmental\| [1]]].		The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a three parameters in a one-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the single state. The following description is taken from [[#compartmental\| [1]]].

	Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.		Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.

RobertLampel at 13:40, 13 February 2026

2026-02-13T13:40:41Z

← Older revision		Revision as of 13:40, 13 February 2026
Line 5:		Line 5:
	}}		}}

	The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a ~~single parameter~~ in a three-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the three states. The following description is taken from [[#compartmental\| [1]]].		The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a three parameters in a three-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the three states. The following description is taken from [[#compartmental\| [1]]].

	Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.		Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.

RobertLampel at 13:40, 13 February 2026

2026-02-13T13:40:18Z

← Older revision		Revision as of 13:40, 13 February 2026
Line 5:		Line 5:
	}}		}}

	The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a single parameter in a ~~one~~-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the ~~single state~~. The following description is taken from [[#compartmental\| [1]]].		The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a single parameter in a three-dimensional [[:Category:ODE model\|ODE model]], where we can directly measure the three states. The following description is taken from [[#compartmental\| [1]]].

	Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.		Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 1979) to the results of an experiment in which six horses each received 15 mg/kg of theophylline as aminophylline by intragastric administration.

RobertLampel: /* Reference Solutions */

2025-11-28T10:44:25Z

Reference Solutions

← Older revision		Revision as of 10:44, 28 November 2025
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	Here is one local solution to the above control problem.		Here is one local solution to the above control problem.

	<gallery caption="Reference solution plots" widths="~~180px~~" heights="~~140px~~" perrow="1">		<gallery caption="Reference solution plots" widths="500px" heights="300px" perrow="1">
	Image:Compartmental OED.png\| Sensitivities and measurement control for <math>\theta=(0.05884, 4.298, 21.80)</math>.		Image:Compartmental OED.png\| Sensitivities and measurement control for <math>\theta=(0.05884, 4.298, 21.80)</math>.
	</gallery>		</gallery>

RobertLampel: /* Parameters */

2025-10-10T09:51:03Z

Parameters

← Older revision		Revision as of 09:51, 10 October 2025
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	<p>		<p>
	<math>		<math>
	t_f = 40; \quad \mathcal{W} = [0,1]; \quad M = 5; \quad p = (0.05884,4.298,21.80)		y_0 = 0; \quad t_f = 40; \quad \mathcal{W} = [0,1]; \quad M = 5; \quad p = (0.05884,4.298,21.80)
	</math>		</math>
	</p>		</p>

RobertLampel: /* Mathematical formulation */

2025-10-10T09:50:38Z

Mathematical formulation

← Older revision		Revision as of 09:50, 10 October 2025
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	For the three-dimensional parameter <math>p = (\theta_1, \theta_2, \theta_3)</math> the original initial value problem is given by		For the three-dimensional parameter <math>p = (\theta_1, \theta_2, \theta_3)</math> the original initial value problem is given by
	<math>		<math>
	\dot{x}(t) =: f(t, p) = \theta_3 \cdot (-\theta_1 \cdot \exp(-\theta_1 \cdot t) + \theta_2 \cdot \exp(-\theta_2 \cdot t)), \quad x(0) = 0.		\dot{y}(t) =: f(t, p) = \theta_3 \cdot (-\theta_1 \cdot \exp(-\theta_1 \cdot t) + \theta_2 \cdot \exp(-\theta_2 \cdot t)), \quad y(0) = 0.
	</math>		</math>

RobertLampel: /* References */

2025-10-09T11:06:14Z

References

← Older revision		Revision as of 11:06, 9 October 2025
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	== References ==		== References ==
	<span id="compartmental">[1]</span> Optimum Experimental Designs for Properties of a Compartmental Model, A. Atkinson, K. Chaloner, A. Herzberg, https://www.jstor.org/stable/pdf/2532547.pdf<br>		<span id="compartmental">[1]</span> Optimum Experimental Designs for Properties of a Compartmental Model, A. Atkinson, K. Chaloner, A. Herzberg, J. Juritz, https://www.jstor.org/stable/pdf/2532547.pdf<br>

RobertLampel: /* References */

2025-10-09T07:39:58Z

References

← Older revision		Revision as of 07:39, 9 October 2025
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	== References ==		== References ==
	<span id="compartmental">[1]</span> Optimum Experimental Designs for Properties of a Compartmental Model, A. Atkinson, K. Chaloner, A. ~~Herzbert~~, https://www.jstor.org/stable/pdf/2532547.pdf<br>		<span id="compartmental">[1]</span> Optimum Experimental Designs for Properties of a Compartmental Model, A. Atkinson, K. Chaloner, A. Herzberg, https://www.jstor.org/stable/pdf/2532547.pdf<br>