Examples of Modeling and Simulating Large-Scale Complex Systems, Processes, and Behaviors Mark A. Johnson [email protected]

Examples of Modeling and Simulating Large-Scale

Complex Systems, Processes, and Behaviors

Mark A. Johnson

[email protected]

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


Serum Out

BEP,QVC,neRP, RF, E

+

_


Diet_In

Urinary Endocrine

Fecal_Out Urine_Out

Serum

Inject_In

Cardiovascular

Serum In







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



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


Serum Out

BEP,QVC,neRP, RF, E

+

_


Diet_In

Urinary Endocrine

Fecal_Out Urine_Out

Serum

Inject_In

Cardiovascular

Serum In







Plant

EOS Adaptation

Controller

Reference

EOS


Serum Out

BEP,QVC,neRP, RF, E

+

_


Diet_In

Urinary Endocrine

Fecal_Out Urine_Out

Serum

Inject_In

Cardiovascular

Serum In







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


Serum Out

BEP,QVC,neRP, RF, E

+

_


Diet_In

Urinary Endocrine

Fecal_Out Urine_Out

Serum

Inject_In

Cardiovascular

Serum In







Plant

EOS Adaptation

Controller

Reference

EOS


Serum Out

BEP,QVC,neRP, RF, E

+

_


Diet_In

Urinary Endocrine

Fecal_Out Urine_Out

Serum

Inject_In

Cardiovascular

Serum In







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

Documents

Examples of Modeling and Simulating Large-Scale Complex Systems, Processes, and Behaviors Mark A. Johnson [email protected]