Acta Mech Sin (2010) 26:13–19 DOI 10.1007/s10409-009-0309-8

RESEARCH PAPER

Microstructures and properties of cancellous bone of avascular necrosis of femoral heads Xuefeng Yao · Peng Wang · Ruchun Dai · Hsien Yang Yeh

Received: 16 June 2009 / Accepted: 3 August 2009 / Published online: 15 October 2009 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH 2009

Abstract The aim of this study is to investigate microscopic structure and characterize cancellous bone of avascular necrosis of the femoral head (ANFH). The rabbit model of the ANFH is established. The histopathologic features are studied successfully. The differences between the steroidinjection group (S.G.) and the controlled group (C.G.) are examined, including the weight of rabbits, the hematological examination and the three-dimensional structures. It is found that the plasma levels of cholesterol (CHO), high-density lipoprotein (HDL) and low-density lipoprotein (LDL) in S.G. are lower than those in C.G. when the triglyceride (TG) increased in the S.G.; but the bone mineral content (BMC) and the structural model index (SMI) of the organ and tissue decreased significantly in S.G. Three-dimensional structures of the femoral head are obtained using micro-computed tomography (CT) scanning and the mechanical model is established to analyze the influences of these structural changes on the mechanical properties of the cancellous bone.

The project was supported by the National Natural Science Foundation of China (30470430 and 30400514). X. Yao (B) · P. Wang · R. Dai Department of Engineering Mechanics, AML, Tsinghua University, 100084 Beijing, China e-mail: [email protected] R. Dai Institute of Metabolism and Endocrinology, The Second Xiang-Ya Hospital, Central South University, 410011 Changsha, China H. Y. Yeh Department of Mechanical and Aerospace Engineering, California State University, Long Beach, CA 90840-8305, USA

Keywords Avascular necrosis of the femoral head · Cancellous bone · Microstructure · Mechanical properties

1 Introduction The osteonecrosis (ON) disease is discovered frequently in clinic. According to the pathogeny, there are two kinds of osteonecrosis: one is traumatic, the other is non-traumatic. It is found that the non-traumatic avascular necrosis is predominantly caused by steroids or alcohol in clinical practice. In the treatment of some respiratory disease, the steroid is used and the ANFH always occurs due to the side effect of the steroid, especially, when lots of people were infected by the severe acute respiratory syndrome (SARS) in 2003. The pathology of non-traumatic osteonecrosis is unclear now. The effective therapy has not been discovered for the terminal ANFH except arthroplasty [1–3]. The mechanical properties of the femoral head are changed and it can not take the same load as the normal one for patients with ANFH. Animal models are widely used in studying the ANFH. Yamamoto [4] reported an experimental rabbit model in 1997. Miyanishi [5] used the rabbit model to determine the size of the bone marrow fat cell size, the intraosseous pressure and the blood flow rate difference between the steroid-treated group and the controlled group. Kabata [6] examined the onset time of osteonecrosis in the rabbit model. According to the results, osteonecrosis appeared 1 week later after the steroid was injected. The rate of osteonecrosis increased till the second week, and then reached to a plateau. Cancellous bone is a connective tissue with the extracellular matrix and cells [7,8]. The architecture of living bone continuously adapts the surrounding operational stresses resulting from precise and efficient structural patterning, and

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this is the famous Wolff’s Law [9]. The low-density trabecular bone is similar to the open-cell foam. The high-density one is a more plate-like structure. The density, stiffness and strength are varied at different location in the cancellous bone [10]. Gibson and Ashby studied the relationships between the relative density and the relative Young’s modulus as well as the relative density and the relative compressive strength [11]. To study the micro-structure of the ANFH and analyze the influence of the ANFH on mechanical properties of the Femoral Head, the rabbit model is established using the method mentioned by Kabata [6]. Three-dimensional structure of the femoral head is investigated using micro-CT scanning and the mechanical model is established to analyze the influences of these structural changes on its mechanical characterizations.

physiologic saline was injected into the rabbits. The rabbits were killed one day after the last injection.

2.1.2 Hematological examination Before killing the rabbits, blood samples were collected from the marginal ear vein and kept in the plastic curette for 1 h. Then the blood samples were centered at the rate of 3000 r/ min for 7 min in a centrifugal machine. The serum were obtained and stored in the Ep. Pipe. The high-density lipoprotein (HDL), cholesterol (CHO), triglycerides (TG) and low-density lipoprotein (LDL) were measured by means of enzymatic methods using the automatic biochemical analytical instrument (Hitachi 7170A, Japan).

2.1.3 Tissue preparation 2 Materials and methods 2.1 Animal model and examination 2.1.1 Animal model Follow the rabbit model of the ANFH established in Ref. [6], fourteen 6-month-old female Zelanian rabbits were housed in the Animal Center at Tsinghua University in China. These 14 rabbits were divided randomly into two groups: the steroid-treated group (S.G.) and the controlled group (C.G.). The weight of rabbits in each group is shown in Table 1. The average weight is 2.957 kg for steroid-treated group and 3.028 kg for the controlled group. The probability (P) value of weight variation is 0.067, which is higher than 0.05. They were maintained on a standard laboratory, and both their diet and water are given in standard way by the full-time technician. Fourteen rabbits were fed without injecting anything for the first 10 days to meet the feeding environment in the animal center. After that, the rabbits were injected with 0.2 ml/kg body weight of methylprednisolone once a week for 4 weeks in the steroid-treated group. The methylprednisolone was made by PHARMACIA (40 mg/bottle) and diluted into 20 mg/ml with physiologic saline. The solution of methylprednisolone was injected into the right and the left gluteus medius muscle alternatively: twice in the right gluteus and twice in the left one. For the controlled group, the 0.2 ml/kg

Table 1 The weights (kg) of rabbits in each group on the first housing day

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Rabbits were killed by injecting air into the marginal ear vein. The femoral heads were taken out from the body and cut onehalf along the coronal plane in the proximal at the time of death. Take the left half leg of femoral head of each rabbit and fix it for 1 week with 10% formalin (0.1 mol/l) phosphate buffer (pH 7.4). After that, the samples were decalcified with 25% formic acid for 3 days and were neutralized with 0.35 mol/l sodium sulfate for 3 days. The bone sample were embedded in paraffin, cut into 4 µm sections and stained with hematoxylin and eosin.

2.2 Micro CT scanning The right femoral heads were taken to dehydration in 70% ethanol for 3 days, 95% ethanol for 3 days, and 100% ethanol for 2 days. After that, the femoral heads were immersed into the deionized water and scanned using the Micro CT specimen scanner (GE eXpolre LocusSP Specimen Scanner; GE Healthcare Company, London, Canada) [12,13], which is a cone-beam scanning system. The voltage and current on the scanning protocol was 80 kV and 80 µA, respectively, with an isotopic resolution 6.5 µm × 6.5 µm × 6.5 µm voxel size and an exposure time of 3000 ms per frame. The angle of increment around the sample was set to 0.4◦ resulting in a set of 900 2D images acquisition. In order to increase the signal-to-noise ratio, each image was averaged by the four X-ray projections together. Both bright fields (an X-ray

Group

Weight (kg)

S.G.

2.95

3.05

2.975

3.025

2.8

2.975

2.925

C.G.

2.9

3.1

3.325

3.1

2.875

2.9

2.975

Microstructures and properties of cancellous bone of avascular necrosis of femoral heads

projection with no object in the view field) and dark fields (an image acquired without any X-rays) were collected for correcting the obtained images. A modified Feldkamp conebeam algorithm was used to reconstruct the 2D projections into the 3-dimensional (3D) volume [13]. To obtain the original 3D images of the femoral head, a fixed threshold value was used to binarize the spongiosa and cortex, separating the bone from other components. The original 3D image was displayed and analyzed with the software Microview TM ABA2.1.1 (GE Healthcare Company, London, Canada). The volume of interest (VOI) was defined as a cylindrical volume (110 µm × 110 µm × 450 µm voxel size). Trabecular bone volume fraction (BV/TV) was calculated from the bone volume (BV) and the total volume (TV). The BS/BV represents the ratio of bone surface and the bone volume. The organ BMC was defined as the bone mineral content. The trabecular organ BMD was defined as the bone mineral density divided by all voxels in the volume of interest including the trabecular bone as well as the bone marrow cavities. The tissue BMC was defined as the BMC only in the voxels of interest. The trabecular tissue BMD was defined as the BMD divided by the trabecular voxels in the volume of interest only. Both the mean trabecular thickness (Tb.Th) and the trabecular separation (Tb.Sp) were measured [14]. The trabecular number was taken as the inverse of the mean distance between the mid-axes of the observed structure [15]. Structure model index (SMI) is a parameter used to characterize “rod-like” or “plate-like” trabecular architectures. For ideal plates and rods, the SMI is 0 and 3, respectively [16]. The trabecular connectivity was quantified by calculating the connectivity density, which would artificially increase due to the perforation of plates without breaking the trabecular connection [17,18].

2.3 Statistical analysis Statistical analysis was performed using SPSS 13.0 of windows statistical software (SPSS, Chicago, IL, USA). Independent-sample test was employed for the comparison of two groups after determining the normal distribution of the data. The result is represented in the form of X ± σ . Here, X means the average value and σ is the standard deviation. A probability (P) value of less than 0.05 is considered acceptable. Table 2 The weights of rabbits at different times

Values are expressed as means ± SD. Difference: S.G. versus C.G.

Time of injection

15

3 Results 3.1 Animal model and examination 3.1.1 Body weight The weight of rabbits was obtained at the first housing day and each time before injection as shown in Table 2 and Fig. 1. The weights of rabbits were obtained when they were brought from the animal center. After that, those data were recorded each time before injection. It is found that the average weight is the same in the first ten days. At the time of the second injection, in other words, 7 days after the first injection, it was found that the weight of S.G. decreased and the rabbits were heavier in C.G. and the P value has significant difference. At the time of the third and the fourth injection, the average weights increased in both groups. It is an interesting phenomenon that the weight increments were equal in both groups at the time of the third and fourth in injections. The P value has significant difference at the time of the third injection. The possible explanation of unchanged weight at the first ten days is that the rabbits adjusted themselves within the new environment in the first 10 days. After the adaptation the weight of rabbits starts to increase in controlled group. The methylprednisolone affects the weight after the first injection and the body has already adapted the steroid-injection after the second injection, therefore weight increased after that. 3.1.2 Hematologic examination From the results of hematologic examination in Table 3, the P value indicates significant difference in all the factors, including Plasma levels of CHO, HDL and LDL were smaller in S.G. than those in C.G. when the TG was increased in the S.G. 3.1.3 Histopathologic features It shows that the osteoblast and osteoclast are hardly seen and the fibrin-necrosis can be found in the steroid-injection group (Fig. 2a) compared with those in the controlled group (Fig. 2b), the bone marrow cavity can be seen in the controlled

1st

2nd

3rd

4th

Day of housed

0

10

17

24

31

S.G.

2.96 ± 0.08

2.96 ± 0.08

2.87 ± 0.11

2.93 ± 0.11

3.01 ± 0.13

C.G.

3.03 ± 0.16

3.03 ± 0.16

3.10 ± 0.19

3.16 ± 0.19

3.23 ± 0.27

P

0.067

0.323

0.029

0.023

0.093

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Fig. 1 The relationship between the housing-time and the weight in two groups Table 3 The results of hematological examination ( mmol/l) Group

S.G.

C.G.

P

HDL

0.49 ± 0.25

0.89 ± 0.19

0.006

CHO

1.19 ± 0.54

3.08 ± 1.53

0.016

TG

1.91 ± 0.63

0.70 ± 0.19

0.004

LDL

0.23 ± 0.26

2.08 ± 1.57

0.020

Values are expressed as means ± SD. Difference: S.G. versus C.G.

group. From the histopathologic results, the animal model of the osteonecrosis may be considered successful. From the result of histopathologic features examination, it is found that the ANFH rabbit model was successful. After that, threedimensional structures are measured and analyzed. 3.2 Three-dimensional structure studied by micro CT scanning The Micro CT is an important tool for analyzing the mechanical property of the cancellous bone, e.g. the femoral head. By analyzing the parameters given by Micro CT, the mechanical property of the cancellous bone can be forecasted. The structure of femoral head is shown in Fig. 3. The trabeculae can be seen clearly in these pictures. The difference between the two groups is hardly seen from Fig. 3. Fig. 2 The histopathologic difference between the controlled and the steroid-injection rabbits. a In the steroid-injection group, the osteoblast and osteoclast are hardly seen and the fibrin-necrosis could be found (original magnification ×100); b In the controlled group, the bone marrow cavity can be seen (original magnification ×100)

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Therefore, it is necessary to refer to the hematological examination results of the ± SD difference between S.G. and C.G. in Table 3. The trabecular bone in the femoral head was analyzed using Micro CT as shown in Table 4. There is no significant difference between the two groups except in the parameters of organ BMC, the tissue BMC and SMI. The difference in P values of these parameters is less than 0.05. The organ BMC and the tissue BMC in S.G. are about 45% less than that in C.G., but the trabecular organ BMD (0.4%) and the tissue BMD (2.4%) have no significant difference between the two groups. SMI is significantly greater in S.G. than that in C.G., which represents the trabecular architecture changed from plates-like to rods-like. It means that the structure is looser in S.G. On the other hand, Tb.Th in trabecular bone decreased with the increase of Tb.Sp. It means that the trabeculars are thinner and the space between trabeculars become wider in S.G. than that in C.G. S.G. induced the deterioration of the micro architecture of the trabecular in the femoral head. Connectivity density is also significantly increased. Because the difference in P values of those parameters is no less than 0.05, there are no significant variation of those parameters in two comparing group and those changes are not considered in the following discussion. 4 Discussions According to the results of Micro CT, some changes occurred clearly in the structure of cancellous bone in S.G. For the cellular structure of the cancellous bone, there are two factors determining the mechanical properties.

4.1 Materials Because the materials of cancellous bone could be considered as composites that the collagen is embedded in mineral, the model of composite mechanics is used. The elastic moduli of the composite are

Microstructures and properties of cancellous bone of avascular necrosis of femoral heads

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Fig. 3 The three-dimensional structure of femoral head established by micro CT. a is from the S.G.; b is from the C.G.

Table 4 Trabecular volumetric BMD at organ and tissue levels and 3D microstructure evaluated by micro CT

Parameters

Steroid-injection group (n = 6)

Organ BMD (mg· mm−3 )

559.05 ± 68.74

561.44 ± 74.86

0.4

0.954

Tissue BMD (mg· mm−3 )

830.12 ± 40.78

810.75 ± 68.84

2.4

0.559

43.3 ± 4.8

46.3 ± 5.3

6.5

0.312

16.613 ± 1.684

15.313 ± 1.658

8.49

0.189

Tb.Th (µm)

121 ± 12

132 ± 14

8.3

0.193

Tb.Sp (µm)

159 ± 17

154 ± 22

3.2

0.625

3.563 ± 0.106

3.515 ± 0.260

1.4

0.682

Organ BMC (mg)

11.606 ± 4.514

20.936 ± 7.034

44.56

0.018

Tissue BMC (mg)

7.49 ± 2.98

14.046 ± 5.169

46.68

0.020

Structure model index (SMI)

0.657 ± 0.507

0.286 ± 0.560

–

0.009

Connectivity density ( mm−1 )

3.63 ± 6.45

3.51 ± 14.63

–

0.294

BV/TV (%) BS/BV

Tb.N ( mm−1 )

Values are expressed as means ± SD. Difference: S.G. versus C.G.

E 1 = E c Vc + E m Vm ,

(1)

where E c and E m are the elastic module of collagen and mineral, respectively. Vc and Vm are the volume fraction of those two components, respectively. According to the experiment in Ref. [19], both Vm = 36% and Vc = 64% are used in this calculation for the normal cancellous bone. The organ BMC and the tissue BMC in S.G. are about 45% less than that in C.G. And the Tb. Th and the Tb. Sp are not changed evidently. According to above results, the Vm decreases 45% and Vc is not changed. So the elastic module of the material will be:  Vm = E c Vc + 55%E m Vm . E 2 = E c Vc + E m

(2)

Compared with Eq. (1), the elastic module of material in ANFH is smaller than the one in the normal cancellous bone. 4.2 Network-structure To study the mechanical change when SMI increases, both the rod-like model and plate-like model are established according to the Wolff’s law as shown in Fig. 4. These models are assumed to be perfect square; tensile or compressive force

Controlled group (n = 7)

Difference (%)

P

is loaded axially in the main direction of the beam or loaded within the plane of plate [20]. For the rod-like model, the cubic structure includes 12 beams, the length of the beam is a and the cross section is t × t square (Fig. 4a). For the plate-like model, the cubic structure has 6 plates, which are a × a square plates and the plate thickness is t. 4.2.1 Rod-like model According to the geometrical model, the relative density of the cancellous bone versus the density of the solid material is a 3 − [(a − 2t)3 + 6 × (a − 2t)2 t] ρ0 = ρs a3 2 3 12at − 16t = , a3

(3)

where ρ0 represents the density of the cancellous bone and ρs is the density of the material. ρ0 /ρs is called the relative density. The elastic module of the rod-like model is E0 =

σ0 4 × t 2 × σsb 4t 2 = = Es, ε0 a 2 εsb a2

(4)

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Fig. 4 The network-structure’s model. a Rod-like model; b plate-like model

where E 0 represents the elastic module of the cancellous bone and E s is the elastic module of the material. Let σ0 and ε0 represent the stress and the strain applied to the cancellous bone; σsb and εsb represent the stress and the strain applied to the beams; E 0 /E s is called the relative elastic module. Combined Eqs. (3) with (4), the relationship between the relative density and the relative elastic module is
2
3
3/2 ρ0 t t E0 E0 = 12 − 16 =3 −2 . (5) ρs a a Es Es

Figure 5 shows that the relative elastic module will decrease when the plate-like model changes to the rod-like model at the same relative density. This means that the increase of SMI will lead to the reduction of the relative elastic module. According to the definition, the relative density is BV/TV which is obtained by the Micro CT. In this experiment, there are no significant differences between the two groups and the relative density could be considered the same.

4.2.2 Plate-like model

5 Conclusions

According to the geometrical model, the relative density of the cancellous bone versus the density of the solid material is

To study the three-dimensional structural change in ANFH, the rabbit model of ANFH is established, the histopathologic features are studied. At the same time, some characterizations of osteonecrosis such as the weight of rabbits and the hematologic examination are described between S.G. and C.G. After establishing the ANFH model, three dimensional structures of the two groups are examined and analyzed. Based on the theoretical composite mechanics model, the influence of

a 3 − (a − 2t)3 6a 2 t + 8t 3 − 12at 2 ρc = = , ρs a3 a3

(6)

where ρc represents the density of the cancellous bone. ρc /ρs is called the relative density. The elastic module of the platelike model is  2  a − (a − 2t)2 × σsp σc 4t (a − t) Ec = = = E s , (7) εc a 2 εsp a2 where E c represents the elastic module of the cancellous bone. Let σc and εc represent the stress and the strain applied to the cancellous bone; σsp and εsp represent the stress and the strain applied to the plates; E c /E s is called the relative elastic module. Combined Eqs. (6) and (7), the relationship between the relative density and the relative elastic module is obtained. 4.2.3 The influence of SMI increase To study the mechanical change when SMI increases, the relationships between the relative density and the relative elastic module of two models are shown in Fig. 5.

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Fig. 5 The relationships between relative density and relative elastic module of two models

Microstructures and properties of cancellous bone of avascular necrosis of femoral heads

structural change in biomechanics is investigated. The following conclusions are presented: (1) The weight of rabbits in S.G. decreased only in one week after the first injection and then increased to the same level as the controlled group after the other injections. (2) There are significant differences in the hematologic examination factors: Plasma levels of cholesterol (CHO), HDL and LDL in the S.G. are smaller than those in the C.G. when the triglyceride (TG) increased in the S.G. (3) From the results of the Micro CT, it is found that the organ BMC and the tissue BMC decreased significantly in the S.G. and the SMI increased significantly. (4) From the analysis of the composite model and the network model, those structural changes would reduce the elastic module of the cancellous bone.

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