Post on 31-Dec-2015
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Examples of Modeling and Simulating Large-Scale
Complex Systems, Processes, and Behaviors
Mark A. Johnson
mark.a.johnson@aero.org
Bone Fracture Healing Process
Bone Fracture Healing Model
Representative Disciplines
Control
Visual C++Large Scale Systems
Soft Computing
Unified Modeling LanguageSystems Integration
Object OrientedSystems Engineering
Physiology
Bioelectricity
BiomechanicsBiochemistry
Orthopaedics
Endocrinology
Medical Systems
Organism
OrganSystem
Skeletal
Endocrine
Urinary
Digestive
1, 11
1
BioFunction Type Organism
Cardiovascular
Reproductive
Bone MineralHomeostasis
Bone MineralHomeostasisCooperative/GoalCoordinator
Organ
Tissue
Atom
Scapula
1, 206
Bones
Tibia
SkeletalHomeostasisCooperative/GoalCoordinator
Tibia HomeostasisCooperative/GoalCoordinator
BonesHomeostasisCooperative/GoalCoordinator
Bone mineral regulation system
Serum_In Stimulation
Quantity of Viable Cells (QVC), neteffective Remodeling/RegenerationPotential (neRP)
Serum_Out
BEP
Biochem Bioelect Biomech
Left/Right TibianeRP
QVC
Bioelectric Potential (BEP) =Steady State Potential +Stress Generated Potentials
Resonant Frequency,Youngs Modulus
Strain,Strain Rate
Digestive
Diet_In
Endocrine Skeletal Reproductive
Cardiovascular
Inject_InFecal_Out Urine_Out
Urinary
Serum
Bone Fracture Healing: Perspectives Overview
Bone Fracture Healing
Plant
EOS Adaptation
Controller
Reference
EOS
destim, dsystemic, dgoal
Serum Out
BEP,QVC,neRP, RF, E
+
_
SkeletalReproductiveDigestive
Diet_In
Urinary Endocrine
Fecal_Out Urine_Out
Serum
Inject_In
Cardiovascular
Serum In
Tibia Homeostasis/Bone Fracture Healing Model
Organ System Level Bone Mineral Regulation Model
Left/Right TibiaCooperative/Goal Coordinator
Skeletal OrganSystem/MaintenanceCooperative/Goal Coordinator
Bone mineralRegulationCooperative/Goal Coordinator
Organismhomeostatic multi-objective behavioraldecision module
Plant
EOS Adaptation
Controller
Reference
EOS
destim, dsystemic, dgoal
Serum Out
BEP,QVC,neRP, RF, E
+
_
SkeletalReproductiveDigestive
Diet_In
Urinary Endocrine
Fecal_Out Urine_Out
Serum
Inject_In
Cardiovascular
Serum In
Tibia Homeostasis/Bone Fracture Healing Model
Organ System Level Bone Mineral Regulation Model
Skeletal OrganSystem/MaintenanceCooperative/Goal Coordinator
Bone mineralRegulationCooperative/Goal Coordinator
Organismhomeostatic multi-objective behavioraldecision module
Left/Right TibiaCooperative/Goal Coordinator
Biochemical Model Plant
External Osteogenic StimulationAdaptation Model
Bioelectrical Model Controller
Bioelectrical, Biochemical, and BiomechanicalReference Model
EOS
ref_BEP,dmBEP
destim
dBEP(t) = BEP(t) - BEP(t-1)
BEP
+
Bioelectrical Model Plant
QVC,neRP
RF, E
QVC_
ref_QVC
dBEP
dQVC
Biomechanical Model PlantdneRP(t) = neRP(t) - neRP(t-1)dneRP
QVC
neRP
OBJECTIVE Develop an Integrated Bioelectrical, Biochemical, and Biomechanical Model of the Bone Fracture Healing Process
Sub-ObjectiveDevelop a Biochemical Model of the Bone Fracture Healing Process
Model Reference Adaptive Control Architecture
Bone Fracture Healing
Bone Fracture Healing
Viable Cell Quantity
Strain, Strain Rate(future inputs)
Bioelectric Potentials
VDE
VDTM
VMD
VPTM
VPE
Reference
Proximal Epiphysis (EP), Proximal to mid-diaphysis (PTM), Mid-diaphysis (MD), Distal to Mid-diaphysis (DTM) , Distal Epiphysis (DE)
Human Tibia
Plant(Bone Biochemical
Process Model)
Controller(Biochemical BoneFracture HealingProcess Model)
BiochemicalHomeostaticReference Model
dBEP QVC, neRP
ref_QVC
QVC
+
_
Fuzzify dBEP(t)dBEP(t)
Fuzzy Rule Base: dQVC(t) = f( dBEP(t))
Defuzzify dneRP(t)dQVC(t)
Defuzzify dQVC(t)
Fuzzy Rule Base or Artificial Neural Network: dneRP(t) = f( dOB(t), dOC(t), (t), (t))
QVC(t) = QVC(t-1)+ dQVC(t)QVC(t)
neRP(t)
dQVC(t)
dOC(t) dOB(t)
neRP(t) = neRP(t-1)+ dneRP(t)
dneRP(t)
QVC(t)
Rule Base: (t), (t) = f(QVC(t))
Fuzzy Rule Base: dOC(t) = f( dQVC(t))
Fuzzy Rule Base: dOB(t) = f( dQVC(t))
(t), (t)
Healing (%)100
H0
50
0
T00 100 200 300 400 (days)
D
100% Stiffness or rigidity(clinically healed)
0 10 20 30 40 50 57 (weeks)
: Inflamation stageS: Soft Callus stageH: Hard Callus stageR: Remodeling stageT: Transition
S H R
T TT
A
C
B
HR(A) = 0.1%/8 days = 0.0125%/dHR(B) = 9.9%/(91-8) days = 0.1193%/dHR(C) = 65%/(126-91) days = 1.857%/dHR(D) = 25%/(365-126) days = 0.1046%/dHR = healing rate in %/day
100% Strength(fully healed)
1 year
100 0
Steady StatePotential(% of normal)
50 50
Quantity ofViable Cells &Metabolic Rate(% of normal)
0 100
dSSP(1) = -100%/3 days = -33.3333%/ddSSP(2) = 0.5%/(21-3) days = 0.02777%/ddSSP(3) = 60%/(28-21) days = 8.571%/ddSSP(4) = 30%/(126-28) days = 0.3061%/ddSSP(5) = 9.5%(365-126) days = 0.03975dSSP = rate of change in %/day
1
2
3
4
5
0.2
0.4
0.6
0.8
1
1.2
1.4
Quantity
of V
iable
Cells (
%)
0
0.2
0.4
0.6
0.8
1
1.2
Healing S
tatu
s (
%)
-5 56117178239300361Time (days)
Epiphysis, Proximal & Distal
Transition
Mid-diaphysis
Healing Status
H0
T0
Model Reference Control Architecture
Biochemical Bone Fracture Healing Process Model
Biochemical Model Plant Architecture Biochemical Model Simulation Outputs
Multiple Source Derived QVC Behavior
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
Plant
EOS Adaptation
Controller
Reference
EOS
destim, dsystemic, dgoal
Serum Out
BEP,QVC,neRP, RF, E
+
_
SkeletalReproductiveDigestive
Diet_In
Urinary Endocrine
Fecal_Out Urine_Out
Serum
Inject_In
Cardiovascular
Serum In
Tibia Homeostasis/Bone Fracture Healing Model
Organ System Level Bone Mineral Regulation Model
Left/Right TibiaCooperative/Goal Coordinator
Skeletal OrganSystem/MaintenanceCooperative/Goal Coordinator
Bone mineralRegulationCooperative/Goal Coordinator
Organismhomeostatic multi-objective behavioraldecision module
Plant
EOS Adaptation
Controller
Reference
EOS
destim, dsystemic, dgoal
Serum Out
BEP,QVC,neRP, RF, E
+
_
SkeletalReproductiveDigestive
Diet_In
Urinary Endocrine
Fecal_Out Urine_Out
Serum
Inject_In
Cardiovascular
Serum In
Tibia Homeostasis/Bone Fracture Healing Model
Organ System Level Bone Mineral Regulation Model
Skeletal OrganSystem/MaintenanceCooperative/Goal Coordinator
Bone mineralRegulationCooperative/Goal Coordinator
Organismhomeostatic multi-objective behavioraldecision module
Left/Right TibiaCooperative/Goal Coordinator
Meal Processor #1 Meal Processor #2 Meal Processor #n
Dietary Input Serum Input
Calcium Excretion
Accumulator
Calcium AbsorptionAccumulator
… …
Net Calcium AbsorptionNet Calcium Excretion
Digestive System
Model Reference:Amount of Calcium Input
Meal Processor #N
Dietary Input Serum Input
Calcium Absorption (t) Calcium Excretion (t)
ControllerPlant
Ca_In_T
Ca_Proc_T
CaP
Ca_InFuzzify Ca_In
Fuzzify VD3_In
Fuzzy Rule Base
Defuzzify
Fuzzify Ca_In_T
Defuzzify Ca_In
Fuzzy Asso Mem
Digestive System
Behaviors
Plant
EOS Adaptation
Controller
Reference
EOS
destim, dsystemic, dgoal
Serum Out
BEP,QVC,neRP, RF, E
+
_
SkeletalReproductiveDigestive
Diet_In
Urinary Endocrine
Fecal_Out Urine_Out
Serum
Inject_In
Cardiovascular
Serum In
Tibia Homeostasis/Bone Fracture Healing Model
Organ System Level Bone Mineral Regulation Model
Left/Right TibiaCooperative/Goal Coordinator
Skeletal OrganSystem/MaintenanceCooperative/Goal Coordinator
Bone mineralRegulationCooperative/Goal Coordinator
Organismhomeostatic multi-objective behavioraldecision module
Plant
EOS Adaptation
Controller
Reference
EOS
destim, dsystemic, dgoal
Serum Out
BEP,QVC,neRP, RF, E
+
_
SkeletalReproductiveDigestive
Diet_In
Urinary Endocrine
Fecal_Out Urine_Out
Serum
Inject_In
Cardiovascular
Serum In
Tibia Homeostasis/Bone Fracture Healing Model
Organ System Level Bone Mineral Regulation Model
Skeletal OrganSystem/MaintenanceCooperative/Goal Coordinator
Bone mineralRegulationCooperative/Goal Coordinator
Organismhomeostatic multi-objective behavioraldecision module
Left/Right TibiaCooperative/Goal Coordinator
Digestive:OrganSystem
Bone Mineral HomeostasisCooperative Coordinator
Urinary:OrganSystem
Skeletal:OrganSystem
Reproductive:OrganSystem
Cardiovascular:OrganSystem
DigestiveSystem:Jejunum
DigestiveSystem:Duodenum
DigestiveSystem:Stomach
DigestiveOrganSystem HomeostasisCooperative Coordinator
Bone Mineral Homeostasis OrganSystemCooperative Coordinator
Behaviors
Bioelectrical Component Model Reference Adaptive Control System Structure of the Bone Fracture
Healing/Remodeling/Regeneration Process Model/Simulation
Adaptation
Controller Plant
Stimulation Assessment,and Tibia Cooperative/Goal Coordinator
ΔQVC
Adapt
Reference
ΔBEPBEP
ref_BEPref_BEP
Stimulation
QVC, Strain Rate
–
+
Response andStatus Outputs
Stimulation and GoalManagement Inputs
Behaviors