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Models: You and your new work colleague decide to estimate the bending stiffness of bones in 85+ year old women and men by calculating the area moment of inertia for the diaphyseal shaft of an idealized long bone. You each decide to model it as a long hollow cylinder consisting of a cortical shell (outer bone diameter dob) surrounding a hollow intramedullary canal (with diameter dic). You estimate the cortical thickness as 7 mm for the model of the male bone. Your colleague assumes bone loss occurs at the outer bone surface (outer diameter) and therefore reduces the outer diameter 2 mm for the woman model. You assume the bone loss occurs at the inner cortical bone surface (inner diameter) and therefore increase the inner diameter 2 mm for the woman model. Colleague's model Your model 85 yo woman dob=32 mm dic=27mm dob = 34 mm dic =29mm 85yo man dob = 34 mm dic=27mm dic dob Intramedullary Canal Cortical Bone Figure 1: Assume a simplified bone modeled as a hollow cylinder of cortical bone only.

Models: You and your new work colleague decide to estimate the bending stiffness of bones in 85+ year old women and men by calculating the area moment of inertia for the diaphyseal shaft of an idealized long bone. You each decide to model it as a long hollow cylinder consisting of a cortical shell (outer bone diameter dob) surrounding a hollow intramedullary canal (with diameter dic). You estimate the cortical thickness as 7 mm for the model of the male bone. Your colleague assumes bone loss occurs at the outer bone surface (outer diameter) and therefore reduces the outer diameter 2 mm for the woman model. You assume the bone loss occurs at the inner cortical bone surface (inner diameter) and therefore increase the inner diameter 2 mm for the woman model. Colleague's model Your model 85 yo woman dob=32 mm dic=27mm dob = 34 mm dic =29mm 85yo man dob = 34 mm dic=27mm dic dob Intramedullary Canal Cortical Bone Figure 1: Assume a simplified bone modeled as a hollow cylinder of cortical bone only.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Changes in cortical bone density and bone geometry occur with aging in both men and women (Table 1 from Russo 2003). These changes manifest as decreased bone strength, which has the clinical impact of increasing the risk of fracture with increasing age. However, elderly men are much less prone to fracture than elderly women. It has been suggested that age-related bone loss is the consequence of endosteal bone resorption resulting in changes in bone geometry (~2mm less cortical bone thickness in women as they age) and contributing to relative differences in fracture risk between men and women. Cortical bone area decreases in women between the ages of 20 and 85, whereas there is no significant change in cortical bone area for men over the same age range (Table 1). Table 1: Changes in bone density and cortical bone area - from Italian population of 612 men and 693 women Age group (years) ANOVA 20-39 Total bone density 4% (mg/cm³) Men Women Cortical bone area 38% (mm²) Men 318.9±47.9 Women 288.8 +41.2 342.344.9 307.134.8 40-49 Colleague's model Your model 315.2 38.2 286.9±27.9 329.1±54.9 289.2 34.3 50-64 85 yo woman dob = 32 mm dic=27mm dob = 34 mm dic = 29mm 302.131.8 274.6±40.3 319.756.8 287.9 +53.5 85yo man 65-74 dob = 34 mm dic=27mm 288.635.5 253.932.2 324.9±42.2 281.1+52.7 75-84 290.0+ 45.4 241.6±36.8 326.8+46.0 265.0+ 60.0 85+ Models: You and your new work colleague decide to estimate the bending stiffness of bones in 85+ year old women and men by calculating the area moment of inertia for the diaphyseal shaft of an idealized long bone. You each decide to model it as a long hollow cylinder consisting of a cortical shell (outer bone diameter dob) surrounding a hollow intramedullary canal (with diameter dic). You estimate the cortical thickness as 7 mm for the model of the male bone. Your colleague assumes bone loss occurs at the outer bone surface (outer diameter) and therefore reduces the outer diameter 2 mm for the woman model. You assume the bone loss occurs at the inner cortical bone surface (inner diameter) and therefore increase the inner diameter 2 mm for the woman model. 284.845.1 229.233.1 332.751.2 230.2 72.4 p<0.0001 p<0.0001 dic p=0.28 p<0.0001 dob Intramedullary Canal Cortical Bone Figure 1: Assume a simplified bone modeled as a hollow cylinder of cortical bone only. Q3 What is the percent difference of the moment of inertia between the 85 year old man and your colleague's 85 year old woman model? What is the percent difference of the moment of inertia between the 85 year old man and your 85 year old woman model?
Transcribed Image Text:Changes in cortical bone density and bone geometry occur with aging in both men and women (Table 1 from Russo 2003). These changes manifest as decreased bone strength, which has the clinical impact of increasing the risk of fracture with increasing age. However, elderly men are much less prone to fracture than elderly women. It has been suggested that age-related bone loss is the consequence of endosteal bone resorption resulting in changes in bone geometry (~2mm less cortical bone thickness in women as they age) and contributing to relative differences in fracture risk between men and women. Cortical bone area decreases in women between the ages of 20 and 85, whereas there is no significant change in cortical bone area for men over the same age range (Table 1). Table 1: Changes in bone density and cortical bone area - from Italian population of 612 men and 693 women Age group (years) ANOVA 20-39 Total bone density 4% (mg/cm³) Men Women Cortical bone area 38% (mm²) Men 318.9±47.9 Women 288.8 +41.2 342.344.9 307.134.8 40-49 Colleague's model Your model 315.2 38.2 286.9±27.9 329.1±54.9 289.2 34.3 50-64 85 yo woman dob = 32 mm dic=27mm dob = 34 mm dic = 29mm 302.131.8 274.6±40.3 319.756.8 287.9 +53.5 85yo man 65-74 dob = 34 mm dic=27mm 288.635.5 253.932.2 324.9±42.2 281.1+52.7 75-84 290.0+ 45.4 241.6±36.8 326.8+46.0 265.0+ 60.0 85+ Models: You and your new work colleague decide to estimate the bending stiffness of bones in 85+ year old women and men by calculating the area moment of inertia for the diaphyseal shaft of an idealized long bone. You each decide to model it as a long hollow cylinder consisting of a cortical shell (outer bone diameter dob) surrounding a hollow intramedullary canal (with diameter dic). You estimate the cortical thickness as 7 mm for the model of the male bone. Your colleague assumes bone loss occurs at the outer bone surface (outer diameter) and therefore reduces the outer diameter 2 mm for the woman model. You assume the bone loss occurs at the inner cortical bone surface (inner diameter) and therefore increase the inner diameter 2 mm for the woman model. 284.845.1 229.233.1 332.751.2 230.2 72.4 p<0.0001 p<0.0001 dic p=0.28 p<0.0001 dob Intramedullary Canal Cortical Bone Figure 1: Assume a simplified bone modeled as a hollow cylinder of cortical bone only. Q3 What is the percent difference of the moment of inertia between the 85 year old man and your colleague's 85 year old woman model? What is the percent difference of the moment of inertia between the 85 year old man and your 85 year old woman model?
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