Whole Bone Modeling Using Bone Whole Bone Modeling Using Bone Mineral Data Mineral Data or or Bones Are Not Amorphous Blobs Bones Are Not Amorphous Blobs Tho m as J. Beck , Sc.D. Tho m as J. Beck , Sc.D. The Johns Hopkins University The Johns Hopkins University School of Medicine School of Medicine The Fundamental problem The Fundamental problem square6 square6 Bones get less dense as we age Bones get less dense as we age square6 square6 Old people with low density bones Old people with low density bones fracture easily fracture easily square6 square6 Space Space - - flight rapidly causes bones to flight rapidly causes bones to get less dense get less dense square6 square6 Does space flight produce the same Does space flight produce the same effects on bone as aging? effects on bone as aging? The Human Femur The Human Femur Bone lo ss causes Bone lo ss causes fragility of proximal fragility of proximal (upper) end of femur (upper) end of femur Fractures are major cause Fractures are major cause of death (indirect) and of death (indirect) and disability in elderly disability in elderly Concern that space Concern that space - - flight flight might have similar might have similar conse que nces conse que nces Bone Dynamics Bone Dynamics square6 square6 Bone is a dynamic tissue and is constantly Bone is a dynamic tissue and is constantly being absorbed and rebuilt thro ugho ut life. being absorbed and rebuilt thro ugho ut life. square6 square6 Because bones get less dense with age Because bones get less dense with age physicians inte rpre t this a s an imba la nc e physicians inte rpre t this a s an imba la nc e between between resorptio n resorptio n and formation. and formation. square6 square6 Old peo p le with low density bo nes fracture Old peo p le with low density bo nes fracture easily so it is assumed that bone density is a easily so it is assumed that bone density is a measure of likelihoo d o f fracture. measure of likelihoo d o f fracture. Current Bone “Density”Measurements Current Bone “Density”Measurements DXA Scan Image of Hip DXA Scan Image of Hip Digital image with all soft tissues sub t racted and only bone mineral present Pixel valu es represent areal mass in g/cm 2 Areal mass is averaged over part of region c o ntaining bone (femoral neck region shown) Result app r oximates volumetric density and is called bone mineral de nsity (BM D ) Femoral Neck BMD Femoral Neck BMD 0 0. 2 0. 4 0. 6 0. 8 1 1. 2 1. 4 1. 6 20 40 60 80 100 A g e ( Y ea r s ) B M D ( g /cm 2 ) Looking at the details Looking at the details square6 square6 Why do bon e s g e t l e ss d e nse as we ag e? Why do bon e s g e t l e ss d e nse as we ag e? barb2ne barb2ne Does this necessarily mean that bones are Does this necessarily mean that bones are ge tting we ake r ? ge tting we ake r ? square6 square6 Why do astro n auts lose bone? Why do astro n auts lose bone? barb2ne barb2ne Are their bones getting weaker? Are their bones getting weaker? square6 square6 Wh at f a ctors are common b e t w een ag in g Wh at f a ctors are common b e t w een ag in g an d an d microgravity microgravity and how do they differ? and how do they differ? Reduced Bone Str e ngth Reduced Bone Str e ngth is an Engine ering Proble m is an Engine ering Proble m Possible reasons: Possible reasons: 1 . The ma te rial is le s s able to withs t a nd 1 . The ma te rial is le s s able to withs t a nd loading stresses loading stresses Or Or 2. The structure is altered to increase lo ading 2. The structure is altered to increase lo ading stresses stresses Structure vs. Material Properties Structure vs. Material Properties square6square6 Evidence exists that bone material strength declines Evidence exists that bone material strength declines with age but effect disappears when corrected for with age but effect disappears when corrected for porosity porosity square6square6 No good evidence that space No good evidence that space - - flight influences flight influences material properties material properties square6square6 (no reliable way to measure (no reliable way to measure in vivo in vivo anyway) anyway) square6square6 W ith ou t q u e s t ion W ith ou t q u e s t ion bo ne structure cha n ges wit h age bo ne structure cha n ges wit h age and as a result of space and as a result of space - - flight flight An engineering perspective An engineering perspective square6 square6 Long bones act as inefficient levers, Long bones act as inefficient levers, with a c tions due to musc le forc es with a c tions due to musc le forc es square6 square6 Greatest mech an ical stresses ar e in Greatest mech an ical stresses ar e in bending and torsion bending and torsion Bending Stresses in Bones Bending Stresses in Bones At a given location, stress depends on: At a given location, stress depends on: 1. 1. Properties of cross Properties of cross - - section section 2. 2. Bending Moments (moment arm Bending Moments (moment arm lengths and force magnitudes) lengths and force magnitudes) Bending stresses in cantilever beam Bending stresses in cantilever beam σσσσ = My I F y d I = Cross- sectional Moment of Inertia Compressi ve stress Tensilestress M = F x d Maximum Bending Str e ss Maximum Bending Str e ss σ max = y My I = M Z Sectio n Modul u s predict s maximum stress ( Sectio n Modul u s predict s maximum stress ( σσσσ σσσσ ) on ) on subperiosteal (outer) surface subperiosteal (outer) surface M = bending moment M = bending moment I = cross I = cross - - sectional moment of inertia sectional moment of inertia y = dista n ce from centroid y = dista n ce from centroid to surface to surface Z = secti o n modulus Z = secti o n modulus Structural Changes in Adulthood Structural Changes in Adulthood 1. 1. Bone material is continually being Bone material is continually being absorbed and reformed absorbed and reformed (remodeling). (remodeling). 2. 2. Bones adapt to changes in Bones adapt to changes in mechanical loading through life mechanical loading through life (modeling). (modeling). The Mechanism: The Mechanism: Skeletal Loa d ing a nd Str a in Stimuli Skeletal Loa d ing a nd Str a in Stimuli square6 square6 Stresses cause loaded bones to distort slig htly Stresses cause loaded bones to distort slig htly square6 square6 These minut e chang e s in sh ap e or dim e nsion These minut e chang e s in sh ap e or dim e nsion a r e s t ra ins a r e s t ra ins square6 square6 Strains are detected at the cellular level Strains are detected at the cellular level square6 square6 Bone is adapted to maintain a specific level Bone is adapted to maintain a specific level and frequency of daily strain and frequency of daily strain Frost’s Frost’s Mechanostat Mechanostat square6 square6 Bone ad ap ts to keep av erag e daily str a i n s w i t h i n Bone ad ap ts to keep av erag e daily str a i n s w i t h i n a “norm a l ” r a ng e. a “norm a l ” r a ng e. square6 square6 Strains abov e rang e cause new bone fo rmatio n Strains abov e rang e cause new bone fo rmatio n — — (modeling) to stimulate bones to get stronger. (modeling) to stimulate bones to get stronger. square6 square6 Strains below rang e cause bo ne to be lost Strains below rang e cause bo ne to be lost – – (increased rates of remodeling) to stimulate (increased rates of remodeling) to stimulate bon e s t o get w e ak er. bon e s t o get w e ak er. Bone Bone Remodeling Remodeling square6 square6 Occurs mainly on Occurs mainly on internal internal bone surfaces bone surfaces throughout life throughout life square6 square6 Rates are influenced by hormones and Rates are influenced by hormones and by skeletal loading by skeletal loading barb2ne barb2ne Increased loading Increased loading suppresses suppresses remodeling remodeling barb2ne barb2ne Decr eased lo ad i n g Decr eased lo ad i n g stimulates stimulates remodeling remodeling Bone Bone remodeling remodeling square6 square6 Sk el et al lo ad ing is dimi nished i n t h e Sk el et al lo ad ing is dimi nished i n t h e e l de rly re la tive to when the y were stronge r e l de rly re la tive to when the y were stronge r an d more act i v e an d more act i v e square6 square6 Space Space - - flight removes skeletal loading from flight removes skeletal loading from most of th e b o d y ( excep t u p p e r extremi t i es) most of th e b o d y ( excep t u p p e r extremi t i es) square6 square6 Expect remodeling o n internal bone Expect remodeling o n internal bone surfaces to be stimulated in both cases surfaces to be stimulated in both cases Remodeling Remodeling in presence of load in presence of load Mechanical Mechanical Load Load square6square6 Bone is temporarily removed Bone is temporarily removed from internal surfaces from internal surfaces square6square6 Bendi ng strains i n crease on Bendi ng strains i n crease on external external surfaces surfaces square6square6 New bo ne is added to external New bo ne is added to external surfaces (modeli n g) surfaces (modeli n g) square6square6 Bone diameter increases to Bone diameter increases to compensate internal bone loss compensate internal bone loss Effects of normal modeling on bone density Effects of normal modeling on bone density square6 square6 Le ss bone ne eds to be adde d to e x te rnal Le ss bone ne eds to be adde d to e x te rnal surface than removed from internal surface surface than removed from internal surface square6 square6 Bone gets less dense because it is bigg er in Bone gets less dense because it is bigg er in diameter and because less bo ne needed to diameter and because less bo ne needed to maintain sectio n modulus maintain sectio n modulus Bone Modeling and Changing Load Bone Modeling and Changing Load square6 square6 New bo ne formation resulting from New bo ne formation resulting from increased strain stimuli increased strain stimuli square6 square6 Because long bo nes are mainly loading Because long bo nes are mainly loading in bending, maximum strains are on in bending, maximum strains are on the the outer outer surface surface square6 square6 New bone formation (modeling) New bone formation (modeling) occurs o n t h e occurs o n t h e outer outer surface of bo ne surface of bo ne Adaptation to Increased Loading Adaptation to Increased Loading square6 square6 Strains throug hout the bone should increase. Strains throug hout the bone should increase. square6 square6 Rates of remodeling sho u ld decrease Rates of remodeling sho u ld decrease square6 square6 May expect bo ne to g e t bigg er and cortex May expect bo ne to g e t bigg er and cortex thicker. thicker. square6 square6 Sectio n modulus sho u ld increase Sectio n modulus sho u ld increase square6 square6 Density may or may not increase depending Density may or may not increase depending on details of changes. on details of changes. Adaptation to Decreased Load Adaptation to Decreased Load square6 square6 Strains decrease throug h bo ne Strains decrease throug h bo ne square6 square6 Remod e lin g i n creases from int e rnal Remod e lin g i n creases from int e rnal surfaces surfaces square6 square6 Bone s h ould be los t from inte rnal Bone s h ould be los t from inte rnal surfaces and cor tices sh oul d g e t surfaces and cor tices sh oul d g e t thinner thinner square6 square6 Both sectio n modulus and density Both sectio n modulus and density shou ld decr ease shou ld decr ease Space Space - - Flight Effects Flight Effects square6 square6 All loading will be absent (except that All loading will be absent (except that due to exercise countermeasures) due to exercise countermeasures) square6 square6 Expect increased rates o f internal bo ne Expect increased rates o f internal bo ne loss loss square6 square6 Expect no modeling on outer surface Expect no modeling on outer surface square6 square6 Sectio n modulus and density should Sectio n modulus and density should decrease decrease Geometry from mass profiles Geometry from mass profiles using DXA Scanners using DXA Scanners 01 2 3 4 Shaft Profile Shaft Profile Neck Pro f ile Neck Pro f ile Bone BoneMassMass (g/cm (g/cm 22 ) ) Dista n ce (cm) Dista n ce (cm) 01 2 3 4 Distance (cm) 5 Mass Projection of Shaft Cross Mass Projection of Shaft Cross - - Sectio n Sectio n W ∫ ? = dA x x I c x ) ( ∫ = dA A Subperiosteal widthCross-sectio nal area Cross-sectional m o m e nt of inertia Section Modulus Properties measured from bone Properties measured from bone mass profiles mass profiles At all cross At all cross - - sectional regions: sectional regions: square6 square6 BMD BMD square6 square6 Subperiosteal Width Subperiosteal Width square6 square6 Cross Cross - - Sectional Area (cortical bone Sectional Area (cortical bone eq uiv a l e n t ) eq uiv a l e n t ) square6 square6 Sectio n Modulus Sectio n Modulus Need for a model of the cross Need for a model of the cross - - section section square6 square6 Measur ed prop erti es d o n’t co mpletel y Measur ed prop erti es d o n’t co mpletel y describe the cross describe the cross - - section. section. square6 square6 In absenc e of complete da ta (pic ture of In absenc e of complete da ta (pic ture of cross cross - - sectio n) we need a model. sectio n) we need a model. square6 square6 Model assumes reasonable shape and has Model assumes reasonable shape and has geometry measured from DXA data. geometry measured from DXA data. square6 square6 V a lidity de pe nds on how well mode l V a lidity de pe nds on how well mode l corresp onds to act u al cross corresp onds to act u al cross - - section. section. Properties modeled Properties modeled square6 square6 Sh ap e o f cross Sh ap e o f cross - - section section square6 square6 Proportion of trabecular and cortical Proportion of trabecular and cortical bone. bone. square6 square6 En docor tical d i ameter En docor tical d i ameter square6 square6 Cortical thicknesses Cortical thicknesses 01 2 3 4 Measur ed Measur ed Bone Mass Bone Mass Profile Profile Distance (cm) Cortical Cortical 100% M a ss 100% M a ss 5 Modeled Shaft Cross Modeled Shaft Cross - - Section Section 01 2 3 4 Measur ed Measur ed Bone Mass Bone Mass Profile Profile Distance (cm) Distance (cm) Trab ecu l ar Trab ecu l ar Cortical Cortical 40% Mass 40% Mass 60% Mass 60% Mass 5 Modeled Neck Cross Modeled Neck Cross - - Section Section Some Examples: Some Examples: Study Populations: Study Populations: square6 square6 National H e alth and N u trition Examination National H e alth and N u trition Examination Surv e y (NHAN ES III) Surv e y (NHAN ES III) square6 square6 Study o f Study o f Osteoporotic Osteoporotic Fra c tures (SOF) Fra c tures (SOF) square6 square6 Russian Cosmo n auts o n Mir Space Statio n Russian Cosmo n auts o n Mir Space Statio n NHANES III: A structural view of NHANES III: A structural view of normal aging in the hip normal aging in the hip square6 square6 Cross Cross - - sectio nal sample o f US po pulatio n sectio nal sample o f US po pulatio n >14,000 hip DXA scans. >14,000 hip DXA scans. square6 square6 White sub White sub - - sample including 2719 males sample including 2719 males an d 2904 f e mal e s ag e 20 an d 2904 f e mal e s ag e 20 - - 90+. 90+. square6 square6 Data co urtesy o f Dr. Anne Loo k er, US Data co urtesy o f Dr. Anne Loo k er, US National Center for Health Statistics, and National Center for Health Statistics, and Dr. Heinz Dr. Heinz Wa hne r Wa hne r , Mayo Clinic , Mayo Clinic BMD and Section Modulus BMD and Section Modulus -- -- Males Males -4 0 % -3 0 % -2 0 % -1 0 % 0% 10% 20% N e ck BM D Sh a f t BM D Ne c k se c t ion m o d u lu s S h a f t s e cti o n m o dul us 20-29 30-39 40-49 50-59 60-69 70-79 80+ BMD and Section Modulus BMD and Section Modulus -- -- Females Females - 40% - 30% - 20% - 10% 0% 10% 20% Ne c k B M D S h a ft BM D N e ck s ecti o n m o dul us S h a ft s ecti o n m o dul us 20-29 30-39 40-49 50-59 60-69 70-79 80+ Subperiosteal Subperiosteal Widths Widths 0% 2% 4% 6% 8% 10% 12% 14% 20-29 30-39 40-49 50-59 60-69 70-79 80+ Shaft ma le s Neck ma les Shaft F e ma les Neck Fema les Youn g Femur Youn g Femur Aging Caus es Internal Bone Loss Agin g Femur Agin g Femur Simultaneous Loading Stimulates Ne w Bo ne Formation (Modeling) Changes in Aging Long Bones Changes in Aging Long Bones View of Normal Aging Process View of Normal Aging Process Agin g Bone Agin g Bone Cross Cross - - Sec t ion Sec t ion Reduced BMD Reduced BMD But No t Streng th But No t Streng th Young Bone Young Bone Cross Cross - - Sec t ion Sec t ion Example: Example: can can compensate compensate for for 10% loss in 10% loss in BMD with < 1 BMD with < 1 mm increase in mm increase in outer diameter outer diameter Frost’s Frost’s Mechanostat Mechanostat Implies: Implies: square6 square6 If skeletal loading is static If skeletal loading is static : : Bone strength should be maintained Bone strength should be maintained square6 square6 If skeletal loading increases: If skeletal loading increases: Bone strength should improve Bone strength should improve square6 square6 If skeletal loading decreases: If skeletal loading decreases: Bone strength should decline Bone strength should decline The Classic Hip Fracture Case The Classic Hip Fracture Case square6square6 An elderly woman who is: An elderly woman who is: barb4rightbarb4right Physically inactive Physically inactive barb4rightbarb4right Lo w bo dy weig ht Lo w bo dy weig ht barb4rightbarb4right Reduced muscle m a ss Reduced muscle m a ss square6square6 Her skeletal loading is Her skeletal loading is considerably reduced from considerably reduced from levels when she was levels when she was younger and more active. younger and more active. square6square6 Longitudinal sample of white post Longitudinal sample of white post - - meno pausal meno pausal women ages > 65 at entry. women ages > 65 at entry. square6square6 Two hip scans averaging 3.6 years apart on 1876 Two hip scans averaging 3.6 years apart on 1876 subjects. subjects. square6square6 Subjects categorized by weight change: Subjects categorized by weight change: barb4rightbarb4right Static ( Static ( + + 1 kg of base 1 kg of base - - line) N = 479 line) N = 479 barb4rightbarb4right Gainers N = 654 Gainers N = 654 barb4rightbarb4right Losers N = 743 Losers N = 743 square6square6 Data Courtesy of Drs. Steve Cummings and Katie Ston e, Data Courtesy of Drs. Steve Cummings and Katie Ston e, University of California at San Francisco University of California at San Francisco SOF: The Loading Hypothesis SOF: The Loading Hypothesis Femoral Neck Changes Femoral Neck Changes -5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% We i g h t L o s e r s St a t ic W e ig ht W e ig ht G a iner s B M D S e c t i o n M o dulus ns ** * * p < .0002 * * Femoral Neck Changes Femoral Neck Changes -5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% We i g h t L o s e r s St a t ic W e ig h t W e ig ht G a ine r s Subpe r . W i dt h A v g . C o r t . T h ic k n e s s ** * ** ** ** *p < . 005 **p < . 0001 Increased Increased Load Load Constant Lo ad Constant Lo ad Stren gth Main tai n ed Stren gth Gained Reduced Load Reduced Load Stren gth Lost SOF Summary SOF Summary Same Subperiosteal Expansion In All Groups?? Same Subperiosteal Expansion In All Groups?? Bone Loss From Within Is Bone Loss From Within Is Load Dependent Load Dependent What If Loading Is Eliminated? What If Loading Is Eliminated? (i.e., Space (i.e., Space - - Flight) Flight) Since lo ading stimulates subperiosteal Since lo ading stimulates subperiosteal modeling and co ntrols rate internal modeling and co ntrols rate internal remodeling remodeling head2right head2right Ac ce le ra te d inte rna l bone loss Ac ce le ra te d inte rna l bone loss head2right head2right No s ubpe r ios t ea l ex pa ns ion No s ubpe r ios t ea l ex pa ns ion head2right head2right Both BMD and bone s t re ngth should be Both BMD and bone s t re ngth should be re duc e d re duc e d Effects of Space Effects of Space - - Flight Flight square6 square6 Pre and post flig ht hip data o n 19 Russian Pre and post flig ht hip data o n 19 Russian Cosmonauts. Cosmonauts. square6 square6 Average of 178 (126 Average of 178 (126 - - 312) days on Mir Space 312) days on Mir Space Station. Station. square6 square6 Follow Follow - - up d a t a on 8 Co smonau ts (~1.5 y post up d a t a on 8 Co smonau ts (~1.5 y post flight) flight) square6square6 Data co urtesy of Drs. A d ri an Le bla n c, Li nda Data co urtesy of Drs. A d ri an Le bla n c, Li nda Shackelford, Vict or Schnei d er and V. Shackelford, Vict or Schnei d er and V. Ogano v Ogano v . . -10% -8% -6% -4% -2% 0% 2% B M D S ect io n M o dul us Subpe r . Wi d t h Co r t . T h i c kne ss Po s t - F lig h t Fo llo w - U p ns ns ns ** ** ** * * p < 0.000 1 *p = 0.03 ns * Changes in Femoral Neck Changes in Femoral Neck Bone loss in space Bone loss in space - - flight flight Pre Pre - - Flight Flight Condition Condition Internal bone loss Internal bone loss without loading without loading stimul us stimul us No modeling No modeling ot ot outer surface outer surface Reduced BMD Reduced BMD and and reduced strength reduced strength Post-FlightCondition So What do we know about bone loss? So What do we know about bone loss? square6 square6 Bones adapt to loading conditio ns, getting Bones adapt to loading conditio ns, getting strong er or weaker as lo ad d e man d s ch ang e strong er or weaker as lo ad d e man d s ch ang e square6 square6 Loss of bone do esn’t necessarily mean loss of Loss of bone do esn’t necessarily mean loss of strengt h strengt h -- -- bo nes get mo re mechanically bo nes get mo re mechanically efficient as we age efficient as we age square6 square6 The home os ta tic e n dpoint that the body strive s The home os ta tic e n dpoint that the body strive s to maintain is the sectio n modulus to maintain is the sectio n modulus square6 square6 Absence of load (space flight) removes Absence of load (space flight) removes s timulus for ada p tive mode ling, bone s get s timulus for ada p tive mode ling, bone s get weak er as bon e is lost weak er as bon e is lost Differences Between Fracture Cases Differences Between Fracture Cases and Contr o ls and Contr o ls square6 square6 121 hi p fract ure cases co mpared to 4082 121 hi p fract ure cases co mpared to 4082 contro ls contro ls square6 square6 Results adjusted for age, knee Results adjusted for age, knee - - height and height and weight weight % Differ ences Between Fracture Cases and % Differ ences Between Fracture Cases and Control s Control s Ag e, W e igh t & Kn ee H e ight Ad jus t ed (p < . 0 001) Ag e, W e igh t & Kn ee H e ight Ad jus t ed (p < . 0 001) -1 5% -1 0% -5% 0% 5% 10 % 15 % 20 % BMD C S A Wid t h S ec tio n M o dul us Mea n Co rt e x Bu c k lin g ra t i o Vi si t 2 Vi si t 4 Bending in a Thick Bending in a Thick - - Walled Tube Walled Tube Crack p r opag at es from out e r su rface Crack p r opag at es from out e r su rface Sectio n modulus predicts strength Sectio n modulus predicts strength Bending in a Thin Bending in a Thin - - Walled Tube Walled Tube Folds inward on inner surface(crumpling or lo cal buckling) Sectio n Modulus Overestimates Streng th Defining Thin Defining Thin - - Walled tubes Walled tubes Buckling Ratio = r r t t Buckling considered for ratios > 10 in hollow tubesFor trabecular fil l ed volumes (femoral neck) cri t ical value unknown but probably higher Local Buckling In the Femoral Neck Local Buckling In the Femoral Neck square6 square6 How thin does the cortex need to be? How thin does the cortex need to be? barb2ne barb2ne At visit 4 aft e r adju stment for ag e an d At visit 4 aft e r adju stment for ag e an d body si ze, cases av erag ed 24.3 body si ze, cases av erag ed 24.3 vs vs 20.6 in 20.6 in contro ls (18% higher). contro ls (18% higher). Overall Conclusions: Overall Conclusions: square6 square6 Depending on skeletal loading, geometric Depending on skeletal loading, geometric changes may compensate for net bone loss. changes may compensate for net bone loss. square6 square6 Structural adaptation appears to be the case Structural adaptation appears to be the case for most post for most post - - meno pausal women meno pausal women – – inde ed inde ed most do not fracture. most do not fracture. square6 square6 Progression toward fragility may actually be Progression toward fragility may actually be a a consequence consequence of the adaptation to reduced of the adaptation to reduced loading as fo llo ws: loading as fo llo ws: But what about elderly hip fractures? But what about elderly hip fractures? square6 square6 Why do th ey fractur e if bon e is ad ap ti n g Why do th ey fractur e if bon e is ad ap ti n g to their loading ? to their loading ? square6 square6 One would expect that bone have some One would expect that bone have some margin for overload. margin for overload. square6 square6 Could bones fail in o t her than pure Could bones fail in o t her than pure bending ? bending ? Evidence from Hip Fracture Cases Evidence from Hip Fracture Cases square6 square6 57 h i p fr act u re cases co mpared to 125 57 h i p fr act u re cases co mpared to 125 random contro ls random contro ls square6 square6 Results adjusted for age Results adjusted for age square6 square6 With and witho u t adjustment for With and witho u t adjustment for weig ht ( C ases w e re li ght e r on av erag e) weig ht ( C ases w e re li ght e r on av erag e) square6 square6 SOF data co urtesy of Dr. Stev en SOF data co urtesy of Dr. Stev en Cummings, analysis by Dr. Katie Cummings, analysis by Dr. Katie Sto n e Sto n e SOF Hip Fracture Cases SOF Hip Fracture Cases Relative to Random Controls Relative to Random Controls -2 0% -1 5% -1 0% -5% 0% 5% BMDBMD Section Section ModulusModulus Subper i os teal Subper i os teal Wid t h Wid t h Cor t i c a l Cor t i c a l ThicknessThickness Progress Toward Fragility Progress Toward Fragility square6 square6 Sk el et al lo ad ing is r e d u ced Sk el et al lo ad ing is r e d u ced square6 square6 Mechanostat accelerates Mechanostat accelerates barb2nebarb2ne Endocortical resorption Endocortical resorption barb2nebarb2ne Subperiosteal expansion? Subperiosteal expansion? square6 square6 Sectio n modulus adapts to reduced lo ad but Sectio n modulus adapts to reduced lo ad but square6 square6 Cortex thins to point w h ere failure o ccurs not Cortex thins to point w h ere failure o ccurs not in pure bending (perhaps in in pure bending (perhaps in lo cal buckling??) lo cal buckling??) Bending in a Thick Bending in a Thick - - Walled Tube Walled Tube Crack p r opag at es from out e r su rface Crack p r opag at es from out e r su rface Sectio n modulus predicts strength Sectio n modulus predicts strength Bending in a Thin Bending in a Thin - - Walled Tube Walled Tube Folds inward on inner surface(crumpling or lo cal buckling) Sectio n Modulus Overestimates Streng th Questions About Local Buckling Questions About Local Bucklingsquare6square6 When does this transition occur? When does this transition occur? square6 square6 How thin does the cortex need to How thin does the cortex need to be? be? square6 square6 What is the role of trabecular bone What is the role of trabecular bone in prevention of local buckling? in prevention of local buckling? square6 square6 Can this effect be measured with Can this effect be measured with DXA data? DXA data? Caveats Caveats square6 square6 Structural geometry can be measured with Structural geometry can be measured with current DXA scanners but not very well current DXA scanners but not very well square6 square6 Small changes in dimensions are Small changes in dimensions are structurally important, but can’t be structurally important, but can’t be reliably measured with current DXA reliably measured with current DXA scanners scanners DXA Clinical Prototype DXA Clinical Prototype Under Construction Under Construction Current DXA Scanner mass profiles Current DXA Scanner mass profiles 01 2 3 4 Shaft Profile Shaft Profile Neck Pro f ile Neck Pro f ile Bone BoneMassMass (g/cm (g/cm 22 ) ) Dista n ce (cm) Dista n ce (cm) Homework Homework square6 square6 Much we don’t know but yo u can speculate Much we don’t know but yo u can speculate on, based on results of simple simulations on, based on results of simple simulations square6 square6 Simulations can employ kno wn effects o n Simulations can employ kno wn effects o n bone from measured data bone from measured data Using Simulations of Bone Adaptation Using Simulations of Bone Adaptation square6 square6 Simulate fe mora l s h a f t a s a right c y lindric a l Simulate fe mora l s h a f t a s a right c y lindric a l hollow tube subje c te d to be nding: hollow tube subje c te d to be nding: barb2nebarb2ne Changing rates of remodeling Changing rates of remodeling barb2nebarb2ne Changing load Changing load barb2nebarb2ne Changing both load and rates of remodeling Changing both load and rates of remodeling square6 square6 Examin e effects on BM D, sect i o n mod u lu s an d Examin e effects on BM D, sect i o n mod u lu s an d bon e di amet er bon e di amet er Assumptions: Assumptions: square6 square6 Moment arms are constant in Moment arms are constant in ad ul tho o d, ch an ges in cr oss ad ul tho o d, ch an ges in cr oss - - sectional sectional dimensions and load magnitudes only dimensions and load magnitudes only square6 square6 Sectio n modulus chang e s linearly with Sectio n modulus chang e s linearly with load magnitude load magnitude square6 square6 Remodeling changes inner radius of Remodeling changes inner radius of tub u l a r bon e (can i n cr ease or d e crease tub u l a r bon e (can i n cr ease or d e crease we will assume only increase). we will assume only increase). Example 1: Example 1: square6 square6 Remodeling with consistent skeletal Remodeling with consistent skeletal loading loading square6 square6 Remodeling removes bone from inner Remodeling removes bone from inner surface (increases inner radius) at a surface (increases inner radius) at a c e rta i n ra te c e rta i n ra te square6 square6 Wha t inc r e a s e in oute r ra dius will Wha t inc r e a s e in oute r ra dius will result in a constant section modulus? result in a constant section modulus? Geometry of hollow tube Geometry of hollow tube I = π 4 (r o 4 -r i 4 ) A = π (r o 4 -r i 4 ) BMD = A ρρρρ m 2r o ρρρρ m = effectiv e m ineral density of solid bone ( use~1.05 g/cm 3 ) Starting dimensions Starting dimensions For young 25 y/o adult male r o = 1.67 cm r i = 1.16 cm For young 25 y/o adult female r o = 1.47 cm r i = 0.97 cm Remodeling Remodeling square6 square6 Assume Assume r r i i Increases at constant Increases at constant rate rate square6 square6 Measured data suggest Measured data suggest increase of .004 cm/y increase of .004 cm/y in males in males