MPC by rajabi1363

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MPC

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
 

 

MPC

    
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

  



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5

 

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 

EEG



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EEG

EEG

Evoke BIS Bispectral
EMG EEG

EEG

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BIS
  
FDA

BIS



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PID

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PID
BIS
MAP

BIS
AER SAP AER AEP

SAP HR WAVCNS

GPC
paralysis MAP MAP

PK-PD MAP
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
  

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
 




MPC



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I(t)

PK model

Ce(t)

PD model

BIS

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C2

Drug

C1

C3
Peripheral compartment
V3

I
Peripheral compartment

k21 k12

Central compartment

k31 k13

V2

V1

Muscles
Viscera

Blood Brain Liver

Fat

k10

Bones



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C (t )  V1   k31  C1 (t )   1   (k10  k12  k13 ) k 21  1  C2 (t )   k12  k 21 0 .C2 (t )  0 .I (t )          k13 0  k31  C3 (t )  0  C3 (t )          C1 (t )     ( s  k 21 ).( s  k31 ) C (s) 1 PK ( s )  1  . C p (t )  [1 0 0].C2 (t ) I ( s ) V1 ( s   ).( s   ).( s   )  C3 (t )    

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

Peripheral compartment

Central compartment

Peripheral compartment

k1e
Effect site

Pharmacodynamic

ke0

BIS

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
dCe (t )  k e0 (C1 (t )  C e (t )), dt

e Td s



 Ce ( s )  e

Td s

K e0 .C1 ( s) s  K e0

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
E  Emax 
 Ce

 EC50  Ce

BIS  BIS 0 (1 

EC50  Ce



Ce 

BIS




)


BIS (Ce (t ))  BIS ( EC50 )   BIS   BIS (Ce (t )) |Ce (t ) EC50 . (Ce (t )  EC50 )  Ce (t )

BIS0 .  . Ce (t ) 4 . EC50

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
 




MPC



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GPC




J
j  N1



N2

ˆ   j yt  j | t   wt  j  
2


j 1

Nu

  j u t  j  12



ut   K GPC w - f 
K GPC  G T G  I G T
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



1

0  u (t )  300 g

kg. min kg. min
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0  u (t )  2000 g

Extended DMC‌

gi 

y per t  i   y past t  i 



.

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Extended DMC‌
DMC 

EDMC



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GPC
GPC
 




 

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  
 

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Nominal patient #1

Nominal patient #2 100
PID GPC EDMC Set point

1
BIS

100

80

2
BIS
14

80

Set point PID GPC EDMC

60

60

40

40
0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

400

400

u (g/kg/min)

300 200 100 0

u (g/kg/min)

300 200 100 0

0

2

4

6 8 Time (min)

10

12

14

0

2

4

6 8 Time (min)

10

12

14

Nominal patient #3

Nominal patient #4

3
BIS

100

4
BIS
0 2 4 6 8 10 12 14

100

80

80

60

60

40

40

0

2

4

6

8

10

12

14

400

400

u (g/kg/min)

300 200 100 0

u (g/kg/min)

300 200 100 0

0

2

4

6 8 Time (min)

10

12

14

0

2

4

6 8 Time (min)

10

12

14

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3.5 3 2.5 2 1.5 1 0.5 0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

8 7 6 5 4 3 2 1 0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

300 250 200 150 100 50 0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

7 6

MDAPE

5 4 3 2 1 0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

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  

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‫‪PID‬‬ ‫04‬ ‫53‬ ‫03‬ ‫52‬ ‫02‬ ‫51‬ ‫01‬ ‫5‬ ‫0‬ ‫بیمار نامی گروه 1‬ ‫بیمار نامی گروه 2‬

‫‪CGPC‬‬

‫‪EDMC‬‬

‫بیمار نامی گروه 3‬

‫بیمار نامی گروه 4‬

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250 200 150 100 50 0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

35 30 25 20 15 10 5 0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

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‫‪‬‬
‫001‬ ‫09‬ ‫08‬ ‫07‬ ‫06‬ ‫05‬ ‫04‬ ‫03‬ ‫02‬ ‫01‬ ‫0‬ ‫بیماران گروه بیماران گروه بیماران گروه بیماران گروه‬ ‫1‬ ‫2‬ ‫3‬ ‫4‬

‫‪PID‬‬ ‫‪GPC‬‬ ‫‪EDMC‬‬

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
 BIS 

BIS
The hypotetical disturbance added to BIS 10 8 6
Amplitude of disturbance
20 15 10 5 0 -5 -10 -15 The hypotetical disturbance added to BIS



4 2 0 -2 -4 -6 -8 -10 0 10 20 30 Time (min) 40 50 60

Amplitude of disturbance

-20 0 10 20 30 Time (min) 40 50 60

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GPC design for Nominal patient #2 100 80 100 80

EDMC design for nominal patient #2

BIS

60 40 0 10 20 30 40 50 60

BIS
60 40 0 10 20 30 40 50 60 300 300 200

u (g/kg/min)

u (g/kg/min)
0 10 20 30 Time (min) 40 50 60

200

100

100

0

Nominal patient #2

0

0

10

20

100 80 Set point PID

30 Time (min)

40

50

60

BIS

GPC
u (g/kg/min)

60 40 0 10 20 30 40 50 60

EDMC PID
0 10 20 30 Time (min) 40 50 60

300

200

100

0

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GPC design for nominal patiant #2 100 80
100 80

EDMC design for nominal patient #2

BIS

60 40 0 10 20 30 40 50 60

BIS

60 40 0 10 20 30 40 50 60

300

300

u (g/kg/min)

200

u (g/kg/min)
0 10 20 30 Time (min) 40 50 60

200

100

100

0

0

Nominal patient #2

0

10

20

100 80 Set point PID

30 Time (min)

40

50

60

BIS

60 40 0 10 20 30 40 50 60

GPC
u (g/kg/min)

EDMC PID

300

200

100

0

0

10

20

30 Time (min)

40

50

60

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
 
 

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Nominal patient #1 100 80 60 40 4 0 2 4 Set point Constrained GPC (open loop during induction) Constrained GPC (close loop from the first)

BIS

6

8

10

12

14

Ce (g/mL)

2

0 2000

0

2

4

6

8

10

12

14

u (g/kg/min)

1000

0

0

2

4

6 8 Time (min)

10

12

14
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GIPC




GPC


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GIPC
GPC . GIPC



250

35 30 25

200

150

20 15 10

100

50

5
0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

0 Nominal patient #1 Nominal patient #2 Nominal patient #3 Nominal patient #4

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MPC
GPC design for a 40 year old patient (Weight=60 kg & EC50 = 3.6 (mg/ml) ) 5

IEEE

4

Ce (g/mL)

3 2 1 0 0 10 20 30 Time (min) 40 50 60

BIS

 

Infusion rate (mg/kg/h), BIS

100 80 60 40 20 0 0 10 20 30 Time (min) 40 50

BIS
Infusion rate BIS


60

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GPC design 5

Concentration (g/mL)

4 3 2 1 0 0 10 20 30 40 50 60

BIS, Infusion rate (mg/kg/h)

120 100 80 60 40 20 0 0 10 20 30 Time (min) 40 50 60 BIS Infusion rate

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PID EDMC GPC
GPC

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





 
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Impulse Response 0.12

0.1

0.08

Infusion

Amplitude

0.06

Bolus
0.04

0.02

0

0

100

200

300 Time (sec)

400

500

600

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