BioSolids Exam #2 Flashcards

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Trabecular Bone Locations

Epiphyses and metaphyses
Vertebral bodies
within flat bones


Trabecular vs Cortical Bone
(Volume Fraction, Surface to Volume Ratio)

Typical bone volume fraction: 0.85-0.95 (Cortical), 0.05-0.6 (trabecular)
Surface to Volume Ratio: 2.5 (Cortical), 20 (trabecular)


Trabecular Rods and Plates

Network of Rods-open cell structure, lower density, regions of lower stress, located between condyles
Network of plates- closed cell structure, higher density, regions of high stress, located under the patellar groove, on the condyles


trabecular remodeling

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coupled bone resorption followed by bone formation at the same site



bone forming cells
synthesize and deposit unmineralized organic matrix components of bone (osteoids)
round cells with a single nucleus



bone resorbing cells
round cells with a bottom ruffled border that dissolved bone materials and removes organic components and has multiple nuclei



inactive osteoblasts surrounded by bone matrix
located in lucunae
looks similar to neuron



flat single nucleus unmineralized organic matrix components of bone that are deposited osteoblasts


mechanical properties of trabecular bone (stress-Strain)

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Compression of a bone cube is similar to a cellular solid
Initial linear portion (modulus)
Constant stress region
Final failure (consolidation)


Studies to determine mechanical properties of trabecular bone

Gibson (1985)- Compression of a bone cube is similar to a cellular solid, stress-strain curve
Goldstein review (1987)- reviewed previous studies and gave huge modulus and ultimate strengths
Ciarelli (1991)- compression bone cubes controlled experiment, gave more accurate range


compression properties of trabecular bone dependence

results of compression testing are dependent on:
Testing conditions
Location, function
Strain rate
Loading direction


wolff's law

Bone of high stiffness and strength is found in regions of high loads
Bone structure is oriented in direction of predominant loading (Trajectorial Theory)
explains anisotropy in bone (inferior/superior is higher modulus than other directions)


Fracture risk equation

Risk=expected load from and activity/(load causing failure experimentally)
risk> 1.0 High risk of failure
risk< 1.0 low risk of failure


regression analysis

Predictive power depends on strength of correlation between two variables
Least-squares approach minimizes the sum of the squared differences between original data and predicted relationship
r^2 defines the strength of the relationship (expresses the proportion of variance in the dependent variable that is explained by the independent variable
linear or non-linear


variables considered to predict fracture risk

scalar variables-density (apparent), bone volume fraction, porosity
clinical density measures- DEXA, QCT density
architectural variables- trabecular plate number, connectivity, mean intercept length

If relationship exists between stiffness/strength and variable, then it may be used to predict failure load


scalar variables to predict fracture risk

Apparent Density- Mass of bone tissue / apparent volume of space including marrow and bone
Bone Volume Fraction- Volume of bone / apparent volume
Porosity- Volume of marrow / apparent volume


clinical density measures

'bone mineral density" (BMD)
Dual-energy radiography (DEXA)
QCT Density


Dual-energy radiography (DEXA)

Reduced x-ray exposure
Limited accuracy in determining BMD
Images include cortical shell
error associated with densities due to bone thickness
correlates well with whole bone strength, since it reflects both bone size and mass
not a true volumetric density (over projected area, not volume)


QCT density

Computed tomography
Series of planar x-rays reconstructed to form 3D image
Can assess trabecular bone alone
Must be calibrated with a phantom (s piece of material with known density that is used to compare to bone)
relatively good predictor of BMD and strength


bone mineral density (BMD)

can be measured via QCT density and DEXA scans
among the strongest predictors of fracture risk
useful in the diagnosis and monitoring of treatment


operational definition of osteoporosis

BMD measured by DEXA is the refernece standard for osteoporosis diagnosis: T-score < -2.5 (2.5 SD below mean of premenopausal women)
for each SD decrease in BMD, fracture risk doubles


factors that increase the risk of fracture

low body weight
high bone turnover
lifestyle (risk of falls, smoking, excessive alcohol)
medical history (prior fracture, family history)
secondary causes (medications)


fracture prevention strategies

Applied load/ bone strength
reduce applied load (reduce fall frequency/severity, proper lifting techniques, hip protectors)
maintain or increase bone strength (exercise, diet (Ca2+, vitamin D), pharmacological intervention)


influences on bone strength

Bone mass
Bone turnover
Bone geometry
Bone architecture
Bone mineralization
Bone composition (HAP, collagen)


effects of again/osteopenia on trabecular structure

Decreases in
Bone mineral density
Number of trabeculae
Thickness of trabeculae
Number of transverse trabeculae?

Therefore - degree of anisotropy may change
Fewer, thinner, longer trabeculae more prone to buckling


microarchitectural changes in osteoporosis

osteoporotic bone has a decrease in mass and number of trabeculae, and abnormalities in architecture compared to normal


architectural variables

trabecular plate number (trabeculae per unit length, always more vertical than horizontal)
connectivity- measure of branching nodes, reduced in osteoporosis
mean intercept length- measure of thickness in particular direction, quantifies anisotropy, can identify principal material directions


trajectorial theory (1866)

calculation of principal stresses in a crane, similar to orientations of trabecular bone in the proximal femur


bone structure

bone structures are "optimized" for maximum strength with minimal weight
trabeculae are aligned with principal stress directions
bone structure is regulated by cells responding to a mechanical signal


straightening long bones

abnormally curved long bones can straighten through remodeling
requires apposition on concave side (bone growth on side bent in)
requires resorption on convex side
centralized canal remains


axial loads applies to long bones(bending)

axial loading on curved bone creates:
compression on concave side- leads to bone apposition (growth)
tension on convex side- leads to bone resorption (decay)


axial loads applies to long bones(gradients)

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Axial loading on curved bone creates:
Stress gradient from tensile (positive) to less tensile (negative) on convex side
Stress gradient from less compressive (positive)to more compressive (negative) on concave side

positive gradient leads to bone resorption
negative stress gradient leads to bone formation
positive from tensile to less tensile


remodeling and repair facts

Turnover rate: ~ 5% each year
i.e. every 20 yrs almost all bone is “new”
In vitro testing of bone fatigue can’t take this into account
Disease and aging may impact remodeling rate
Age related fractures often appear to be “spontaneous”, may be damage accumulation
10% hip fractures, 50% spine fractures


methods of bone remodeling evaluation

External bone dimensions (diameter, etc.)
Bone density
Local bone apposition rate


The ‘Law of Bone Transformation’: A case of crying Wolff? Bertram & Swartz, 1991

testing to determine if mechanical influences can cause transformation of bone (Wolff's law)
confounding factors (surgical procedure, growing animal, invasive procedures)

Evidence may not reflect bone response that would occur in normal healthy adult without previous injury!


applications of remodeling theories

Ability to predict responses to
Implants (stress shielding)
Altered loading
Ability to improve and control
Corrections of deformities
Fracture healing
Age-related bone loss

Is bone density distribution “optimal” ?
Can we predict shape changes
Can we predict normal variations in bone density
Can we predict changes in bone density


bone remodeling- feedback loops, Beaupre and carter (1990)

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daily stress stimulus equation

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Daily Stress stimulus (gamma= "expected" level of stress
remodeling is driven by difference (e) between actual stress and "expected stress"
assume linear relationship between error and apposition rate (M)

n is number of cycles of “i” type of loading
m is constant (reflecting relative importance of magnitude vs. number of cycles)
sigma is some scalar value of “stress” or strain or energy
Strain energy density, Von mises stress, Hydrostatic pressure


bone density remodeling equation

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Assume linear relationship between error and apposition rate
M = c1 + c2e

Apposition may be on internal trabecular surfaces
M = apposition rate (µm/day)
Bv = bone volume
k = fraction of surfaces actively remodeling
Sv is the surface area / unit volume


bone remodeling procedure

Create starting model, apply loading conditions, material properties
Calculate stress stimulus for each element
Calculate error and change in BVF, then change in modulus
Repeat analysis with changed modulus
Continue until loads change or steady-state


remodeling simulations- Carter (1987)

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Start with arbitrary uniform modulus, then iterate until steady state
Low and high density regions are well predicted
as long as multiple loading conditions are used
“lazy zone” is needed to maintain bone with low loads


trabecular remodeling simulations- Mullender (1994)

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Start with arbitrary uniform modulus, then iterate until steady state
Trabecular structure is predicted
Need to use decay function or lazy zone to prevent “checkerboarding”


remodeling cautions

Constants needed
At least 5: m, C1, C2, k, Sv, power law constants
Loading conditions are critical and simulations are very sensitive to them!
Ignoring biological response can lead to nonsensical results (Disuse will reduce, not eliminate bone; Lazy zone; Baseline biological activity; May differ between normal and healing)


bone remodeling graph

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variables whose influence you want to study
(ex. Temperature, pressure)
denoted by X1, X2



specific values given to a factor during experiments
initial limit- 2 levels
(ex. 20 degrees C, 1 Pa)
use -1, +1 to designate levels


treatment condition

one running of the experiment
ex. set T=50 degrees C, P- 1Pa and measure volume



result measured for a treatment condition
ex. measured volume
denoted by y



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calculated from responses (y1, y2)
effect of X1= (ave at +1)-(ave at -1)=(m+1)-(m-1)=y2-y1= change (delta) X1
difference in the average value at the 2 levels


degrees of freedom (DOF)

counter for information
experimental data= number of data points (y1+y2=2 DOF)
analysis- number of results
information is conserved
2^(number of factors)=responses=DOF


one at a time experiment (OAT)

change one factor at a time
ex. y1=baseline= X1=-1, X2=-1
y2= X1= +1, X2= -1
y3= X1=-1, X2= +1
choice of baseline is critical
inefficient use of data- only use part of data to calculate each effect
does not account for factors in combinations


full factorial approach

test all combinations of factors
effect of X1- averaged over both X2 levels- no baseline
all results-> all effects- use all data in each calculation= efficient use of data



number of factors in the interaction term of a factorial analysis
ex. X1X2= second order



experiments can be influenced by time related changes (ex. temperature changes over the course of the day)
randomize the order in which treatment conditions are run (reduces the chance that time related changes will be misattributed to factor effects)


continuous factor

involves something that can be quantified on a continuous scale (ex. temperature, pressure, time, voltage, etc.)


discrete factor

nominal, categorical
cannot be put on a continuous time scale
ex. supplier, country, gender, etc


advantages and disadvantages of full factorial designs

not dependent on a baseline choice
all data is used to calculate each effect ("efficient")
can measure interactions between factors
convert easily to a multi-factor model

work best with only 2 (maybe 3) levels for a factor
many DOF used to measure higher-order interactions


ANalysis Of Means (ANOM)

most basic level of analysis
which effects are largest (which factors/interactions are most important?
based off of delta (change) values (ave at level +1- ave at level -1)
magnitude of change= importance
positive change= +1 increases response, -1 decreases
negative change= -1 increases response, +1 decreases


ANalysis Of VAriance (ANOVA)

second level of analysis
which observed effects are statistically significant?
based on comparing observed effects against an estimate of error
compares delta^2 for factors and interactions with delta^2 for error
actually comparing "mean square"


replication error

Repeat (replicate) each of the treatment conditions
Independent experimental runs (not multiple measurements from the same TC)
Differences in the responses measured for identical TCs run at different times provide error
“Pure error”  not dependent on modeling assumptions
Best way to estimate error, but greatly increases effort


error- pooling of higher-order interactions

Assume that higher-order interactions are unimportant/zero
Must choose these interactions upfront (before examining results)
 these form a “pool” for error
Effects measured for pooled interactions are used to estimate error
“Error” - includes modeling error (i.e. assumptions about interactions)
Requires less experimental effort, but error estimate is not as good


replication vs pooling

"pure error"- no modeling assumptions needed
best for- small number of factors, systems with large uncertainties

assess more factors for the same effort (or same number of factors for less effort)
best for- large numbers of factors, systems with strong time/cost constraints on experimental size


anova table

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typical way of presenting ANOVA results
source- factors interactions and the error (total includes everything except m*,find error values from subtraction from total)
SS=Sum of Squares=measures the variance from each effect,factor,interaction= delta^2*(# of TC)/4
DOF= total= 1 DOF less than # of responses/TCs
MS=Mean Square= SS/DOF (SS normalized against DOF)
F=MS (effect)/MS (error) larger F, more likely the effect is "real"
p= chance that the value of F occured randomly, depends on F and DOF (effect and error)
%SS= measures "importance" of each factor/interaction- how much variance from the total does each factor attribute


judging statistical significance

if F>Fcritical (found from a table) or p>pcritical the factor/interaction is significant
alpha= the chance that an F/p value larger than the critical value could occur randomly


Treatment conditions (TC)

required number of TC is the product of levels for each factor (ex. a 2 level factor and a 3 level factor need 6 TC)
each TC has a difference set of levels (ex. TC1= +1 -1, TC2= +1 +1)


why use more than 2-levels?

continuous factor- test non-linear effects
discrete factor- test more than 2 possibilities (DOF= # levels- 1 in 3+ levels)
continuous vs. discrete- effect analysis


fractional factorials

"fractions" of full factorials (2 level designs: 1/2 or 1/4 the # of TC)
smaller experiment, but with the same number of effects
effects are "confounded" with each other and cannot be separated
use sparsity of effects- assume interaction terms are zero


design of fractional factorials

must preserve symmetry of design
can produce different confounding patterns
"resolution" is one measure of the severity of confounding


resolution in fractional factorials

higher values indicate less severe confounding
one measure of the severity of confounding
III is the lowest (worst) level
in practive III, IV, and V resolutions are common


model verification

"solving the equations right"
numerically accurate


model validation

"solving the right equations"
accurately predicts the physical phenomenon it was designed to replicate


validation/verification requirements for theoretical use

Requirements for numerical studies for theoretical use:
define model selection (relevant geometry, physics, boundary conditions, material properties)
verification (mesh refinement, code validation, non-linear convergence)
proper parameter identification (able to be duplicated, reasonably unique)


validation/verification requirements for "applied biomechanics" use

Requirements for numerical studies for "applied biomechanics" use:
Sensitivity study to understand uncertainty in inputs-Define range for comparison to experiments, Show how uncertainty impacts conclusions
Inter-subject variability assessment- May be parameterized, Perhaps several subjects, rather than single model


validation/verification requirements for clinical use

Requirements for numerical studies for clinical use:
Validation against in vitro experiments
Risk-benefit analysis- Collaboration with clinical researchers
Retrospective studies- Provide sensitivity and specificity
Prospective studies


types of fractures

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closed fracture- crack/break through bones but they stay in place
open fracture- bones break through the skin (soft tissue damage)
transverse fracture- caused by tension
greenstick- due to bending and mostly occurs in children because their bones are more ductile and will bend more before fracture (can occur in adults if it is at low speed)
comminuted fracture- bone broken into small fragments


what determines the type of fracture?

type of loads (tension, compression, bending, torsion)
energy of impact


healing process

hematoma (bringing in blood supple, bruising)
soft callus- either intramembranous formation (bone growth within membranous tissue at the periosteum and endosteum) or endrochondral ossification (cartilage formation, bone is formed on top, cartilage is replaced)
hard callus- mineralization of bone that begins away from the fracture and changes the diameter an material properties of the bone and affects rigidity


"Ilizarov type" external fracture fixation

metal external splint with wires and rods to hold the bone in place and can gradually straighten the bone with screws
can also length the bone if the fracture is stretched on both sides to allow for more soft callus formation
useful for comminuted fractures


things that change external fixator stiffness

screw length
screw diameter
number of screws or wires
distance of screws from fracture
size of the connecting bar
number of connecting bars
distance between connecting bars


intramedullary pins

insertion of a pin through the intramedullary space in the center of the bone
reamed options (drilling through the canal) may rely on friction
unreamed pins may require screw fixation
may have a lot of movement if the pin is too narrow for the canal


compression plates

Plate provides compression across transverse fracture or fragments
May use a tension device or specially designed holes to pull ends together as plate is tightened in place
Contact of plate with bone may be critical in altering blood supply and therefore healing


biomechanics of fracture healing

Interfragmentary movement
Small movements stimulate healing
Too much movement leads to non-union
Detection of movements can also characterize healing process

Blood supply is critical
Unstable fixation may disrupt vascular supply
High hydrostatic pressure may limit vascularization (ex. cartilage)


bone fatigue behavior

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S-N curve (left)
failure occurs instantly if ultimate stress is applied
"theoretical endurance limit"- theoretical stress that can always be applied and the bone will never fail
right graph- if the same stress is causing greater strains over time then the modulus must be decreasing


Miner-Palmgren's Rule

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combines stress states for multiple cycles of multiple types of loading
Dmp = Damage according to Miner-Palmgren Rule
Ni = # of cycles at a particular load level
Nfi = # of cycles to failure at particular load level i
m = different load levels considered

For a linear model, Dmp = 1.0 at failure


mechanisms of fractures and crack initiators in bone

loading -> crack initiation (with repair prevents fatigue)-> crack growth -> failure

crack initiators- haversian canals, lacunae, canaliculi
crack initiation increase= decrease in crack growth