tissue mechanics - ch3

CHAPTER 3CHAPTER 3

ANALYSIS OF BONE ANALYSIS OF BONE REMODELINGREMODELING

Remember:• Remodeling occurs throughout

entire lifetime– Rate changes with age, location,

stress/strain• Most bone tissue in adults was

produced by remodeling

Introduction

The A-R-F Sequence

• 3 major stages of a BMU as it moves through a cross-section

formation resorption

ARF

The A-R-F Sequence

• Activation - Resorption - Formation

A R F

Double BMU activation

Originating Haversian canal

Activation site

12

Activation A-R-F +

The six phases of an osteon's lifetimeActivation

ResorptionReversalFormation

MineralizationQuiescence

The A-R-F Sequence

Six phases 1. activation: bone lining cells @ point of origin

– retract from surface– attract osteoclasts

2. resorption: by osteoclasts (cutting cone)– advance ~ 40 μm/day

3. reversal: osteoblastsrecruited

– cement line formed

~200 μm

~300 μm

The A-R-F Sequence

4. formation: osteoblasts form osteoid– rapidly at first, then gradually decreasing rate– average about 1-2 μm/day

5. mineralization: hydroxyapatite– mineralization lag time ~ 10 days– primary mineralization: ~60% in few days– secondary mineralization: decreasing rate, ~6

months to complete– significance: new osteons have less mineral

than mature osteons - visible by back-scatter SEM

Osteonal “age”

shade = f(calcification) 6. quiescence: osteoblasts bone lining cells(BLC's)

– “resting”– can be reactivated– not 1o cells used to repair fractures

The A-R-F Sequence

Remodeling Cycle Duration

• Times to complete – resorption: 3 weeks– reversal: 1-2 weeks– formation: 3 months

• Frost called this cycle duration sigma (σ)• Significance: determines how fast bone

properties can be changed at a particular site

Histomorphometric Measurement of Osteonal RemodelingTechnique• "fluorochrome label"

– injected IV into living animal– binds to mineralizing bone– fluoresces in UV light

• e.g, tetracycline (common antibiotic)– label administered twice– TL = time between labels, typically 10 days

• cortical bone cross-sections ~ 100 μm thick• "undemineralized" (so labels not lost)• assumes remodeling is in steady state

Measurements1. Section area: results express per mm2 bone2. Count resorption spaces (R's), NR, #/mm2

3. Perimeters of R's, mean = SR, mm4. Count refilling BMUs (F's), NF

– have osteoid seams5. Perimeters of F's, mean = SF, μm

R

F

Measurement of Osteonal Remodeling

Measurements6. Distance between labels

– doubly labeled BMUs– mean = DL, μm

7. Mean wall thickness, tmw, μm– completed osteons (no osteoid)

8. Osteoid seam thickness, tos, μm

Never as clean in practice

F,D

C


C

C

C

CF

F,S

C

CC

C

F,D

R

R

F

F

F

R F,D

F,D F,DF,S



Calculating BMU-Level results• mineral apposition rate: MF = DL / TL (μm/day)

– "mineral" because label lies at mineralization front

– in steady state = osteoid apposition rate• mineralization lag time: Tml = tos /MF (days)

– time for osteoid to start mineralizing• BMU refilling time: TF = tmw / MF (days)

– try to measure tmw in recently-formed osteons


Calculating BMU-Level results, cont'd.• BMU activation frequency

– highly dependent on steady state condition– assume # BMUs activated/day = # starting

to refill– use a fundamental population relationship:

Population = Birthrate x Mean Lifetime– apply to refilling BMUs: NF = fa TF or

fa = NF / TF BMU’s/mm2/day


Calculating Tissue-Level results• Bone formation rate, VF

– fractional amount of new bone made per unit time

• VF = 0.365 x 10-3 MF SF NF mm2/mm2/yr– or mm3/mm3/yr (volume fraction = area

fraction)– approx. same as bone turnover rate

Example: NF = 100/mm2 SF = 200 μmTL = 10 days DL = 10 μmtos = 10 μm tmw = 100 μm

appos. rate MF = DL/TL = 10/10 = 1 μm/daymineral. lag time Tml = tos/MF = 10/1 = 10 daysrefilling time TF = tmw/MF = 100/1 = 100 daysactivation freq. fa = NF/TF = 100/100 = 1 /mm2/daybone form. rate VF = 0.365x10-3 MF SF fa

VF = 0.365x10-3 (1)(200)(1) = 0.073 mm2/mm2/yr

Measurement of Osteonal Remodeling Osteonal Remodeling Data

Table 3.1 Bone remodeling data for ribVariable Dogs Rhesus Humans

MonkeysAge, yrs 1.5-3.5 Adolescent 1-9 30-39 70-89NF, #/mm2 3.1+1.8 4.0+1.6 2.7+1.0 0.21+0.54 0.66+0.50NR, #/mm2 0.58+0.03 1.96+1.15 2.0+0.6 0.25+0.33 0.84+0.46SF, μm 120+30 200+30 280+40 250+140 300+72MF, μm/d 0.95+.26 1.3+.23 1.4+.46 1.1+.36 0.72+.20TF, d 117+ 110 54+11 54+47 73+58 109+55fa, #/yr/mm2 16+11 30+13 19+9 1.1+0.5 2.2+1.1tmw, μm 57+6 63+2 68+4 70+5 66+7VF, %/yr 11.4+9.4 36+19 38+24 1.8+0.6 4.4+1.5

FYI: REMODELING MEASUREMENTS

• ASSUMPTIONS– double fluorochrome labels, TL days apart– osteoid stained– A-R-F sequence occurs in parallel osteons– steady state!!!

• MEASUREMENTS (start with section area)1. # resorp. sp./area, NR 4. refill. perimeter, SF

2. resorp. perimeter, SR 5. inter-label dist., DL

3. # refill. BMUs/area, NF 6. wall thick., tmw

7. osteoid seam thickness, tos

• CALCULATIONS– mineral apposition rate

MF = DL/TL, [micrometers/day]– mineralization lag time

Tml = tos/MF, [days]– refilling period

TF = tmw/MF, [days]– BMU activation frequency or birth rate

NF = fa TF, fa = NF/TF, [BMU/mm2/day]


• TISSUE-LEVEL RESULTS– bone formation rate

VF = 0.365 x 10-3 MF SF NF, [mm2/mm2/yr] MF SF

– If you know the rate of change of porositydp/dt = VR - VF

then you can calc. MR fromVR = 0.365 x 10-3 MR SR NR, [mm2/mm2/yr]


• LABEL ESCAPE ERROR– some BMUs only have one label because

• they completed refilling before 2nd label was given

• they started refilling after the first label was given

– ratio of single to double labeled BMUs N1L/N2L = 2 TL / (TF - TL)

– “true” no. of refilling BMUs NF = ½ N1L + N2L


Remodeling “turns over” bone tissue• remove old bone, replace with new bone• osteonal Basic Multicellular Unit (BMU)

formation reversal resorption

Bone Turnover Remodeling Details

Activation Theories• Bone lining cells (Rodan)

− receptors -- PTH, Vit D3− change shape− expose bone− cAMP− release prostaglandins− cytologic loop

But: elegance is not evidence

Activation

Activation Theories• Hormonal – direct effect

− increased bone turnover− parathyroid hormone− glucocorticoids

− decreased bone turnover− vitamin D [1,25-(OH)2-vitamin D3]− calcitonin

− bulk of evidence from cell culture expts.− eliminates structural signals

Activation

Activation is Rate-Limiting Step

• Better correlation between bone turnover volume and activation frequency than any other factor

• Rate of remodeling cascade invariant

Resorption

Osteoclasts -- mobile, multinucleated, “cousins” of macrophages • attach• peripheral seal -- brush border• enzymatic dissolution of mineral and

collagen

Resorption

• Trabecular bone -- osteoclasts ‘roam’over an area > contact area

• Cortical bone -- tunnel straight ahead in osteons

• Reason / controlling factors unknown

Resorption

• Osteoclast speed • longitudinal -- 39 ± 14 μm/day

• indirect, from labeling expts.• radial -- ~12 μm/day

• while opening canal

Resorption

• Osteoclast lifespan difficult to determine

• evolving syncytium• nuclei enter and leave (or die) • nuclear lifespan (canine) ~11 days

Reversal

• Mononuclear phagocytes• ?? old or recycled osteoclasts • related to circulating phagocytes

• ?? inflammation-remodeling link• ?? RAP

• may form cement line, prepare walls for osteoid

Formation

also called Refilling

• Osteoblasts -- mononuclear, immobile• marrow origin• not evolved from osteoclasts• attracted by disassembled collagen• don’t survive well in bone marrow

transplants

Formation

• Osteoblasts require mechanical loading for complete differentiation

• differentiation takes time -- ~2.5 days

2.5 days x 40 μm/day = 100 μm = approx. length of reversal region

Formation

• Osteoblasts remain stationary as cutting cone moves forward

• begin cuboidal, covering 15 μm2 of bone surface

• become shorter, flatter as refilling progresses

• bone lining cells cover 300 μm2

‒ 20X surface area only 5% survive

Formation

• Single generation of osteoblasts‒ required to live for the entire

refilling period, ~3 months‒ can’t explain lamellar layers

• Multiple generations‒ ? responsible for lamellar layers‒ consistent layer thickness and

different collagen orientation unexplained

Mineralization

• Follows deposition of unmineralized matrix = osteoid

• Mineralization time lag‒ ~10 days

• Primary mineralization‒ 60% of final mineral amount‒ occurs within a few days

• Secondary mineralization‒ occurs over 6 month period

• Properties change as mineralization

Quiescence

• Inactive period‒ osteoclasts disappear ‒ osteoblasts become bone lining cells

• Indeterminate duration‒ activation is a semi-random process‒ function of time, damage

accumulation, proximate injury, metabolic activity

Long-Term Remodeling Effects

Skeletal Aging

• Activation frequency varies with age (rib ►)• Children’s bone rapidly turned over• → softer → ↑ strain → ↑turnover

Age, yr0 20 40 60 80

Act F

req,

No.

/mm

2 /yr

1

10

100


Osteonal Density

• Limited by overlap -- new osteons remove older ones

• Activation location -- assumed random• Directional control -- principal stress

and/or material properties (easiest tunnel)


Osteonal Density

• Models built upon assumptions• Increased osteonal density with age

• to a limited degree, f(osteonal size)• Age determinable by osteonal density

or percent of residual primary bone • good experimental correlation (Kerley, 1965)

• archeological significance

tissue mechanics - ch3

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