Transcript Document 7313402

Examples of Modeling and
Simulating Large-Scale
Complex Systems, Processes,
and Behaviors
Mark A. Johnson
[email protected]
Bone Fracture Healing Process
Representative Disciplines
Biochemistry
Biomechanics
Endocrinology
Bioelectricity
Medical Systems
Control
Orthopaedics
Bone Fracture Healing Model
Large Scale Systems
Physiology
Visual C++
Systems Integration
Soft Computing
Unified Modeling Language
Object Oriented
Systems Engineering
Bone Fracture Healing: Perspectives Overview
Organism
1
D iet_In
Bone mineral regulation system
1, 11
BioFunction
OrganSystem
Digestive
Type Organism
Bone Mineral
Homeostasis
D iges tiv e
U rinary
Endoc rine
Sk eletal
Cardiovascular
Urinary
Bone Mineral
Homeostasis
Cooperative/Goal
Coordinator
Reproductive
Endocrine
Fec al_Out
U rine_Out
Injec t_In
C ardiov as c ular
Serum
Skeletal
Organ
1, 206
Serum_In
Skeletal
Homeostasis
Cooperative/Goal
Coordinator
Stimulation
neR P
Bioc hem
Left/R ight Tibia
Biomec h
Bioelec t
Bones
BEP
QVC
Scapula
Tissue
Atom
Bones
Homeostasis
Cooperative/Goal
Coordinator
Strain,
Strain R ate
Serum_Out
R es onant Frequenc y ,
Youngs Modulus
Quantity of Viable C ells (QVC ), net
effec tiv e R emodeling/R egeneration
Potential (neR P)
Tibia
Tibia Homeostasis
Cooperative/Goal
Coordinator
Bioelec tric Potential (BEP) =
Steady State Potential +
Stres s Generated Potentials
R eproduc tiv e
Bone Fracture Healing
Bone mineral
Regulation
Cooperative/
Goal Coordinator
Organ System Level Bone Mineral Regulation Model
Diet_In
Digestive
Organism
homeostatic multiobjective behavioral
decision module
Urinary
Reproductive
Endocrine
Skeletal
Inject_In
Fecal_Out
Urine_Out
Cardiovascular
Skeletal Organ
System/Maintenance
Cooperative/
Goal Coordinator
Serum
Tibia Homeostasis/Bone Fracture Healing Model EOS
Serum Out
Left/Right
Left/Right Tibia
Tibia
Cooperative/
Cooperative/
GoalCoordinator
Coordinator
Goal
Reference
+
_
EOS Adaptation
Serum In
destim, dsystemic, dgoal
Controller
Plant
BEP,QVC,
neRP, RF, E
Bone Fracture Healing
OBJECTIVE
Develop an Integrated Bioelectrical, Biochemical, and Biomechanical Model of the
Bone Fracture Healing Process
Sub-Objective
Develop a Biochemical Model of the Bone Fracture Healing Process
EOS
Bioelectrical, Biochemical, and Biomechanical
Reference Model
QVC
External Osteogenic Stimulation
Adaptation Model
destim
ref_QVC
_
ref_BEP,
dmBEP
Bioelectrical Model Controller
dQVC
Bioelectrical Model Plant
BEP
+
QVC
neRP
dBEP(t) = BEP(t) - BEP(t-1)
dneRP(t) = neRP(t) - neRP(t-1)
dBEP
dneRP
QVC,
neRP
Biochemical Model Plant
Biomechanical Model Plant
Model Reference Adaptive Control Architecture
RF, E
Bone Fracture Healing
Human Tibia
Viable Cell Quantity
Bioelectric Potentials
VPE
VPTM
VMD
VDTM
VDE
Strain, Strain Rate
(future inputs)
Reference
Proximal Epiphysis (EP), Proximal to mid-diaphysis (PTM), Mid-diaphysis (MD), Distal to Mid-diaphysis (DTM) , Distal Epiphysis (DE)
Biochemical
Bone Fracture Healing Process Model
0
10
T
T

Biochemical
Homeostatic
Reference Model
S



QVC, neRP
A
2
B

0
( %

0
100

T0
200
V ia b le
dOC(t)
dOB(t)
Fuzzy Rule Base or Artificial Neural Network:
dneRP(t) = f(dOB(t), dOC(t), 
(t), 
(t))
dneRP(t)
neRP(t)
neRP(t) = neRP(t-1)+ dneRP(t)
QVC(t)
QVC(t) = QVC(t-1)+ dQVC(t)
Biochemical Model Plant Architecture
1
1
Defuzzify dneRP(t)
Rule Base:

(t), 
(t) = f(QVC(t))
1.2
H0
QVC(t)
0.8
0.8
0.6
0.6
0.4
0.4
0.2
H
dQVC(t)

(t), 
(t)
Fuzzy Rule Base:
dOB(t) = f(dQVC(t))
Quantity of
Viable Cells &
Metabolic Rate
(% of normal)
100
400 (days)
( %
C
Defuzzify dQVC(t)
Fuzzy Rule Base:
dOC(t) = f(dQVC(t))
1.2
u a n tity
Fuzzy Rule Base:
dQVC(t) = f(dBEP(t))
1.4
o f
dQVC(t)
Fuzzify dBEP(t)
50
Multiple Source Derived QVC Behavior
Q
dBEP(t)
50
0
1 year
300
e lls
Model Reference Control Architecture
C
3
D
100% Stiffness or rigidity
(clinically healed)
HR(A) = 0.1%/8 days = 0.0125%/d
HR(B) = 9.9%/(91-8) days = 0.1193%/d
HR(C) = 65%/(126-91) days = 1.857%/d
HR(D) = 25%/(365-126) days = 0.1046%/d
HR = healing rate in %/day
dSSP(1) = -100%/3 days = -33.3333%/d
dSSP(2) = 0.5%/(21-3) days = 0.02777%/d
dSSP(3) = 60%/(28-21) days = 8.571%/d
dSSP(4) = 30%/(126-28) days = 0.3061%/d
dSSP(5) = 9.5%(365-126) days = 0.03975
dSSP = rate of change in %/day
0
Steady State
Potential
(% of normal)
)
Plant
(Bone Biochemical
Process Model)
dBEP
100
0.2
S ta tu s
Controller
(Biochemical Bone
Fracture Healing
Process Model)
)
+
50
100% Strength
(fully healed)
5

H0
QVC
57 (weeks)
R
: Inflamation stage
S: Soft Callus stage
H: Hard Callus stage
R: Remodeling stage
T: Transition
4
_
50
T

1
40
H
Healing (%)
100
30
e a lin g
ref_QVC
20
T0
-5
56
117 178 239
Time (days)
300
361
Epiphysis, Proximal & Distal
Transition
Mid-diaphysis
Healing Status
0
Biochemical Model Simulation Outputs
Digestive System
• Developed as part of modeling the bone fracture healing process
• Specifically as part of a bone mineral regulation model
• Uses only human organism information from open literature
• Two models are developed
• Daily and minute update interval rates
• Focus on the calcium intake-absorption-1,25 dihydroxyvitamin D3 axes
Bone mineral
Regulation
Cooperative/
Goal Coordinator
Organ System Level Bone Mineral Regulation Model
Diet_In
Digestive
Organism
homeostatic multiobjective behavioral
decision module
Urinary
Reproductive
Endocrine
Skeletal
Inject_In
Fecal_Out
Urine_Out
Cardiovascular
Skeletal Organ
System/Maintenance
Cooperative/
Goal Coordinator
Serum
Tibia Homeostasis/Bone Fracture Healing Model EOS
Serum Out
Left/Right
Left/Right Tibia
Tibia
Cooperative/
Cooperative/
GoalCoordinator
Coordinator
Goal
Reference
+
_
EOS Adaptation
Serum In
destim, dsystemic, dgoal
Controller
Plant
BEP,QVC,
neRP, RF, E
Digestive System
Dietary Input
Meal Processor #1
Meal Processor #2
…
Calcium Excretion
Accumulator
Net Calcium Excretion
Serum Input
Meal Processor #n
…
Calcium Absorption
Accumulator
Net Calcium Absorption
Digestive System
Dietary Input
Serum Input
Meal Processor #N
Model Reference:
Amount of
Calcium Input
Fuzzify VD3_In
Ca_In_T
CaP
Fuzzy Rule Base
Fuzzy Asso Mem
Defuzzify Ca_In
Ca_In
Defuzzify
Fuzzify Ca_In_T
Fuzzify Ca_In
Controller
Plant
Ca_Proc_T
Calcium Absorption (t)
Calcium Excretion (t)
Behaviors
Bone mineral
Regulation
Cooperative/
Goal Coordinator
Organ System Level Bone Mineral Regulation Model
Diet_In
Digestive
Organism
homeostatic multiobjective behavioral
decision module
Urinary
Reproductive
Endocrine
Skeletal
Inject_In
Fecal_Out
Urine_Out
Cardiovascular
Skeletal Organ
System/Maintenance
Cooperative/
Goal Coordinator
Serum
Tibia Homeostasis/Bone Fracture Healing Model EOS
Serum Out
Left/Right
Left/Right Tibia
Tibia
Cooperative/
Cooperative/
GoalCoordinator
Coordinator
Goal
Reference
+
_
EOS Adaptation
Serum In
destim, dsystemic, dgoal
Controller
Plant
BEP,QVC,
neRP, RF, E
Behaviors
Bone Mineral Homeostasis
Cooperative Coordinator
Bone Mineral Homeostasis OrganSystem
Cooperative Coordinator
Cardiovascular:
OrganSystem
Digestive:
Urinary:
Skeletal:
Reproductive:
OrganSystem OrganSystem OrganSystem OrganSystem
DigestiveOrganSystem Homeostasis
Cooperative Coordinator
DigestiveSystem:
Stomach
DigestiveSystem:
Jejunum
DigestiveSystem:
Duodenum
Behaviors
Stimulation Assessment,
and Tibia Cooperative/
Goal Coordinator
Stimulation
Stimulation and Goal
Management Inputs
ref_BEP
Reference
ref_BEP
Response and
Status Outputs
Adaptation
Adapt
QVC, Strain Rate
+
–
ΔBEP
Controller
ΔQVC
Plant
Bioelectrical Component Model Reference Adaptive
Control System Structure of the Bone Fracture
Healing/Remodeling/Regeneration Process
Model/Simulation
BEP