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In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues, such as insulin Glargine, require a single daily dose. A similar procedure to the one described in the Pharmaceutical Drug Absorption case study of this chapter is used to find a model for the concentration-time evolution of plasma for insulin Glargine. For a specific patient, state-space model matrices are given by (Tarín, 2007). 0.02 0 -0.02 C = [0.0003 0 0]; D = 0 Where the state vector is given by: A = -0.435 0.209 0.268 -0.394 0.227 0 X1 X2 X3 The state variables are: X = x = insulin amount in plasma compartment x₂ = insulin amount in liver compartment x3 = insulin amount in interstitial (in body tissue) compartment The system's input is: u = external insulin flow. The system's output is: y = plasma insulin concentration. a) Find the system's transfer function. b) Verify your result using MATLAB.

In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues, such as insulin Glargine, require a single daily dose. A similar procedure to the one described in the Pharmaceutical Drug Absorption case study of this chapter is used to find a model for the concentration-time evolution of plasma for insulin Glargine. For a specific patient, state-space model matrices are given by (Tarín, 2007). 0.02 0 -0.02 C = [0.0003 0 0]; D = 0 Where the state vector is given by: A = -0.435 0.209 0.268 -0.394 0.227 0 X1 X2 X3 The state variables are: X = x = insulin amount in plasma compartment x₂ = insulin amount in liver compartment x3 = insulin amount in interstitial (in body tissue) compartment The system's input is: u = external insulin flow. The system's output is: y = plasma insulin concentration. a) Find the system's transfer function. b) Verify your result using MATLAB.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Pls solve by hand and verify it by matlab codes as requested in the question

In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues, such as insulin Glargine, require a single daily dose. A similar procedure to the one described in the Pharmaceutical Drug Absorption case study of this chapter is used to find a model for the concentration-time evolution of plasma for insulin Glargine. For a specific patient, state-space model matrices are given by (Tarín, 2007). 0.209 0.02 -0.394 0 ; B -0.02 C = [0.0003 0 0]; D = 0 Where the state vector is given by: A = -0.435 0.268 0.227 0 X = X1 X2 The state variables are: D x = insulin amount in plasma compartment • x₂ = insulin amount in liver compartment x3 = insulin amount in interstitial (in body tissue) compartment The system's input is: z = external insulin flow. The system's output is: y = plasma insulin concentration. a) Find the system's transfer function. b) Verify your result using MATLAB. Show all your workings, MATLAB codes and results. Tarin, C., Teufel, E., Picó, J., Bondia, J., and Pfleiderer, H. J. Comprehensive Pharmacokinetic Model of Insulin Glargine and Other Insulin Formulations. IEEE Transactions on Biomedical Engineering, vol. 52, no. 12, 2005, pp. 1994-2005.
Transcribed Image Text:In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues, such as insulin Glargine, require a single daily dose. A similar procedure to the one described in the Pharmaceutical Drug Absorption case study of this chapter is used to find a model for the concentration-time evolution of plasma for insulin Glargine. For a specific patient, state-space model matrices are given by (Tarín, 2007). 0.209 0.02 -0.394 0 ; B -0.02 C = [0.0003 0 0]; D = 0 Where the state vector is given by: A = -0.435 0.268 0.227 0 X = X1 X2 The state variables are: D x = insulin amount in plasma compartment • x₂ = insulin amount in liver compartment x3 = insulin amount in interstitial (in body tissue) compartment The system's input is: z = external insulin flow. The system's output is: y = plasma insulin concentration. a) Find the system's transfer function. b) Verify your result using MATLAB. Show all your workings, MATLAB codes and results. Tarin, C., Teufel, E., Picó, J., Bondia, J., and Pfleiderer, H. J. Comprehensive Pharmacokinetic Model of Insulin Glargine and Other Insulin Formulations. IEEE Transactions on Biomedical Engineering, vol. 52, no. 12, 2005, pp. 1994-2005.
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