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DRUGDISE.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DRUGDISE
* Problem :
* *********
* This is a variant of the drug displacement problem DRUGDIS where the
* state equations have been Expanded in term of more intermediate
* functions, each one of them being less nonlinear.
* The problem is based on the kinetic model of Aarons and Rowland which
* simulates the interaction of the two drugs (warfarin and phenylnutazone)
* in a patient bloodstream. The state variable are the concentrations of
* unbound warfarin (w) and phenylbutazone (p). The problem is to control
* the rate of injection (u) of the pain-killing phenylbutazone so that both
* drugs reach a specified steady-state in minimum time and the concentration
* of warfarin does not rise above a toxicity level.
* The problem is discretized using the trapeziodal rule. It is non-convex.
* Source:
* H. Maurer and M. Wiegand,
* "Numerical solution of a drug displacement problem with bounded state
* variables",
* Optimal Control Applications and Methods 13, pp. 43-55, 1992.
* SIF input: Ph. Toint, Nov 1993.
* classification LOR2-MY-V-V
* Discretization: specify the number of interior points + 1
*IE NI 10 $-PARAMETER n=63, m=50
*IE NI 100 $-PARAMETER n=603, m=500 original value
IE NI 100 $-PARAMETER n=6003, m=5000
* Problem parameters
RE TOXIC 0.026 $-PARAMETER warfarin toxicity level
RE WSS 0.02 $-PARAMETER initial/final warfarin levels
RE UMAX 8.0 $-PARAMETER maximal injection rate
RE PSTART 0.0 $-PARAMETER initial phenybutazone level
RE PFINAL 2.0 $-PARAMETER final phenylbutazone level
RE Z 46.4 $-PARAMETER interaction coefficient
* Define useful parameters
R+ AVP PSTART PFINAL
RM AVP AVP 0.5
RM -Z Z -1.0
R* -ZZ Z -Z
IA NI-1 NI -1
RI RNI NI
RD -1/NI RNI -1.0
R* -Z/NI Z -1/NI
IE 0 0
VARIABLES
* final time
TF 'SCALE' 200.0
* warfarin concentration
DO I 0 NI
X W(I) 'SCALE' 0.02
OD I
* phenylbutazone concentration
DO I 0 NI
X P(I)
OD I
* phenylbutazone injection rate (control)
DO I 0 NI-1
X U(I)
OD I
* intermediate variables
DO I 0 NI-1
X A(I) 'SCALE' 200.0
OD I
DO I 0 NI-1
X B(I) 'SCALE' 200.0
OD I
DO I 0 NI-1
X C(I) 'SCALE' 0.0000001
OD I
GROUPS
N TFINAL TF 1.0
N TFINAL 'SCALE' 100.0
* state equations
DO I 0 NI-1
IA I+1 I 1
* warfarin concentration dynamics
XE EW(I) W(I+1) 1.0 W(I) -1.0
XE EW(I) 'SCALE' 0.02
* phenylbutazone concentration dynamics
XE EP(I) P(I+1) 1.0 P(I) -1.0
* defining equation for A
XE EA(I) A(I) 1.0
ZE EA(I) P(I) -Z
XE EA(I) 'SCALE' 200.0
* defining equation for B
XE EB(I) B(I) 1.0
ZE EB(I) W(I) -Z
XE EB(I) 'SCALE' 200.0
* defining equation for C
XE EC(I)
OD I
CONSTANTS
DO I 0 NI-1
X DRUGDISE EA(I) 232.0
X DRUGDISE EB(I) 232.0
OD I
BOUNDS
* All variables are non-negative, except the C(I)
DO I 0 NI-1
XR DRUGDISE C(I)
OD I
* Impose a lower bound of 200 seconds on the phenylbutazone injection level
XL DRUGDISE TF 200.0
* Impose the bound on the toxicity level
DO I 0 NI
ZU DRUGDISE W(I) TOXIC
OD I
* Impose the bound on the maximum injection rate
DO I 0 NI-1
ZU DRUGDISE U(I) UMAX
OD I
* Fix the initial and final concentrations of warfarin and phenylbutazone
ZX DRUGDISE W(0) WSS
ZX DRUGDISE W(NI) WSS
ZX DRUGDISE P(0) PSTART
ZX DRUGDISE P(NI) PFINAL
START POINT
RM 2W/10 WSS 0.2
RM 2P/10 AVP 0.2
R+ 2(W+P)/10 2W/10 2P/10
RA D 2(W+P)/10 1.0
R* DD D D
R* ZP AVP Z
R* ZW WSS Z
R+ AA DD ZP
RA AA AA 232.0
R+ BB DD ZW
RA BB BB 232.0
R* AB AA BB
R* WP WSS AVP
R* -ZZWP WP -ZZ
R+ CD AB -ZZWP
R/ CC DD CD
DO I 0 NI-1
ZV DRUGDISE W(I) WSS
ZV DRUGDISE P(I) AVP
ZV DRUGDISE U(I) UMAX
ZV DRUGDISE A(I) AA
ZV DRUGDISE B(I) BB
ZV DRUGDISE C(I) CC
OD I
XV DRUGDISE TF 240.0
ZV DRUGDISE W(NI) WSS
ZV DRUGDISE P(NI) PFINAL
ELEMENT TYPE
EV 3S V1 V2
EV 3S V3 V4
EV 3D2 V1 V2
EV 3D2 V3 V4
EV 3D2 V5
IV 3D2 Y1 Y2
IV 3D2 Y3 Y4
EV DSQ V1 V2
IV DSQ Y
EV 3PR V1 V2
EV 3PR V3
ELEMENT USES
DO I 0 NI-1
XT WA(I) 3S
ZV WA(I) V1 TF
ZV WA(I) V2 C(I)
ZV WA(I) V3 A(I)
ZV WA(I) V4 W(I)
XT WB(I) 3D2
ZV WB(I) V1 TF
ZV WB(I) V2 C(I)
ZV WB(I) V3 W(I)
ZV WB(I) V4 U(I)
ZV WB(I) V5 P(I)
XT PA(I) 3D2
ZV PA(I) V1 TF
ZV PA(I) V2 C(I)
ZV PA(I) V3 B(I)
ZV PA(I) V4 U(I)
ZV PA(I) V5 P(I)
XT PB(I) 3S
ZV PB(I) V1 TF
ZV PB(I) V2 C(I)
ZV PB(I) V3 P(I)
ZV PB(I) V4 W(I)
XT DD(I) DSQ
ZV DD(I) V1 W(I)
ZV DD(I) V2 P(I)
XT CA(I) 3PR
ZV CA(I) V1 C(I)
ZV CA(I) V2 A(I)
ZV CA(I) V3 B(I)
XT CB(I) 3PR
ZV CB(I) V1 C(I)
ZV CB(I) V2 P(I)
ZV CB(I) V3 W(I)
OD I
GROUP USES
DO I 0 NI-1
ZE EW(I) WA(I) -1/NI
ZE EW(I) WB(I) -Z/NI
ZE EP(I) PA(I) -1/NI
ZE EP(I) PB(I) -Z/NI
XE EA(I) DD(I) -1.0
XE EB(I) DD(I) -1.0
XE EC(I) CA(I) 1.0 DD(I) -1.0
ZE EC(I) CB(I) -ZZ
OD I
OBJECT BOUND
LO DRUGDISE 200.0
* Solution
*LO SOLTN ????
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DRUGDISE
TEMPORARIES
R WSS
R WSSMV4
GLOBALS
A WSS 0.02
INDIVIDUALS
T 3S
A WSSMV4 WSS - V4
F V1 * V2 * V3 * WSSMV4
G V1 V2 * V3 * WSSMV4
G V2 V1 * V3 * WSSMV4
G V3 V1 * V2 * WSSMV4
G V4 - V1 * V2 * V3
H V1 V2 V3 * WSSMV4
H V1 V3 V2 * WSSMV4
H V1 V4 - V2 * V3
H V2 V3 V1 * WSSMV4
H V2 V4 - V1 * V3
H V3 V4 - V1 * V2
T 3D2
R Y1 V1 1.0
R Y2 V2 1.0
R Y3 V3 1.0
R Y4 V4 1.0 V5 -2.0
F Y1 * Y2 * Y3 * Y4
G Y1 Y2 * Y3 * Y4
G Y2 Y1 * Y3 * Y4
G Y3 Y1 * Y2 * Y4
G Y4 Y1 * Y2 * Y3
H Y1 Y2 Y3 * Y4
H Y1 Y3 Y2 * Y4
H Y1 Y4 Y2 * Y3
H Y2 Y3 Y1 * Y4
H Y2 Y4 Y1 * Y3
H Y3 Y4 Y1 * Y2
T DSQ
R Y V1 0.2 V2 0.2
F Y * Y
G Y Y + Y
H Y Y 2.0
T 3PR
F V1 * V2 * V3
G V1 V2 * V3
G V2 V1 * V3
G V3 V1 * V2
H V1 V2 V3
H V1 V3 V2
H V2 V3 V1
ENDATA