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Miniature specimens for cortical bone tests.

Introduction

Bone is a basic structural part of human physiology and its quality is susceptible to aging, disease, and trauma due to accidents. Assessment of bone quality is necessary for understanding bone as a material and maintaining the quality of engineered bone tissue. Several researchers have identified this need and used various techniques to assess the bone quality [1-5].

Bone has a highly hierarchical structure. It contains mineral crystals and collagen fibrils at the ultrastructural levels. Lacunae, canaliculi, and haversian canals of size varying from nano to micro meters, act as natural cavities. Thus the quality and mechanical behavior of bone are affected at different length scales [6].

The load bearing bone shafts (like femur) are mainly composed of cortical bone. Cortical bone is relatively dense compared to trabecular bone and is subjected to mechanical failure. Therefore the mechanical characteristics of this part of bone are of concern.

Bone is responsible for the motion of the body and support of load. Hence it is desirable to assess the bone quality in terms of mechanical properties. Applications of the conventional mechanical tests initially developed for testing engineering materials are limited due to the bone stock, size, orientation dependency, and non-homogeneity of the tissue. In such cases, modified mechanical tests are required for bone.

Methods

Compact sandwich specimen

Compact sandwich (CS) specimen (fig. 1) utilizes small samples for fracture toughness testing of bone. CS specimen has the overall configuration of the Compact Tension (CT) specimen as specified in ASTM E399 [7]. However, the configuration of the CS specimen gives a better choice of bone sample size and therefore suits to certain fracture toughness testing needs and constraints; eg: size, bone stock limitation, and properties specific to sampling sites and crack orientations.

Sandwich specimen was initially developed for testing adhesives joining two substrates [8] and was later modified for testing bone, and accounted for a finite interlayer thickness [9]. The modified equation is,

[K.sub.Ic] = [[lambda].sup.[phi]][K.sup.[infinity].sub.IC]

where, [lambda] = [square root of ([E.sub.i](1 - [[upsilon].sup.2.sub.h]/[E.sub.h]z(1 - [[upsilon].sup.2.sub.i]))]

[phi] = -174.97[(h/W).sup.3] + 56.22[(h/W).sup.2] - 7.39(h/W) + 1.008

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[E.sub.i] and [E.sub.h] are the Elastic Moduli of the interlayer and holder materials respectively. [n.sub.i] and [n.sub.h]--are the Poisson's ratios of the interlayer and holder materials respectively. [K.sub.Ic.sup.[yen]] is the apparent stress intensity factor measured from the applied loads as if the CS specimen were homogeneous (made of one material, like CT specimen). a, h, B, W, and [P.sub.c] are the initial crack length, interlayer thickness, specimen thickness, specimen width and critical load respectively. Equation (1) is valid for h/W [less than or equal to] 0.1571.

[FIGURE 1 OMITTED]

A direct test method for measuring the Mode I critical strain energy release rate, [G.sub.Ic] (a fundamental measure of fracture toughness) using the CS specimen of finite interlayer thickness was established [10]. This method to estimate fracture toughness (equation 2) is free of the other material properties, unlike equation (1). The critical strain energy release rate of the interlayer, [G.sub.Ic], is estimated by,

[G.sub.Ic] = [G.sub.Ic.sup.[infinity]] = [P.sub.c.sup.2]/2B (dC/da)

where, [G.sub.Ic.sup.[yen]] is the apparent critical strain energy release rate, measured as if the CS specimen were homogeneous (made of one material, like CT specimen) and C = elastic compliance (ratio of the displacement along the line of load to the corresponding load).

Overall specimen size and normalized specimen thickness requirements of CS test for practically evaluating the fracture toughness of bone are addressed [11-13]. A specimen width (W), as low as 8 mm is experimentally tested and the compliance curve is found to be satisfactory in the range of 0.3 [less than or equal to] a/W [less than or equal to] 0.7. A normalized specimen thickness (B/W) of 0.14 was experimentally verified at the lower end.

CS specimen was used to investigate the suitability of small laboratory animals for testing the new orthopaedic prostheses [14]. A study was carried out to investigate the differences in the fracture properties between bovine, baboon, rabbit and canine bone and the correlation of the compositional and microstructural properties with these differences. In spite of the ethical issues involved in using baboons (primates) and canine (pet animals) for medical research, the study concluded that these two species offer subjects that are better suitable for orthopaedic research. CS specimen was utilized [15] to investigate the sampling site and orientation dependency of the fracture toughness of bone. Correlation between two important measures of fracture toughness namely, the stress intensity factor and the energy release rate (equation 3) defined for linear elastic, homogeneous, and isotropic materials under plane strain conditions, was experimentally verified for tangential cracks in bone using CS specimen [16]. In addition, this specimen is utilized for testing bone at macro and sub-millimeter scales.

G = [K.sup.2](1 - [[upsilon].sup.2])/E

By extension, the CS specimen configuration was applied to evaluate the interfacial fracture toughness of Bone-Biomaterial systems under normal and mixed mode loading (equations 4 and 5) as illustrated in fig. (2 and 3) respectively [17,18].

Interfacial fracture toughness under normal loading (fig. 2) is given by,

[K.sub.c] = [[lambda].sup.[psi]][K.sub.Ic.sup.[infinity]][h.sup.-i[epsilon]][e.sup.i[omega]]

where, [lambda] = [square root of (1-[alpha]/1-[[beta].sup.2])]

[epsilon] = 1/2[pi] ln[1-[beta]/1+[beta]]

[alpha] = [E.sub.1](1-[[upsilon].sup.2.sub.2]) - [E.sub.2](1-[[upsilon].sup.2.sub.1])/ [E.sub.1](1-[[upsilon].sup.2.sub.2]) - [E.sub.2](1-[[upsilon].sup.2.sub.1])

[beta] = [E.sub.1](1-[[upsilon].sub.2]-2[[upsilon].sup.2.sub.2]) - [E.sub.2](1-[[upsilon].sub.1] 2[[upsilon].sup.2.sub.1])/2[E.sub.1](1-[[upsilon].sup.2.sub.2]) + 2[E.sub.2](1-[[upsilon].sup.2.sub.1])

u is the phase shift [19], and [K.sub.Ic.sup."] as shown in equation (1).

Interfacial stress intensity factor under mixed mode loading is given by,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[K.sup.[infinity].sub.IC] and [K.sup.[infinity].sub.IIC] are critical Mode I and Mode II apparent stress intensity factors, respectively. a is the loading angle for the mixed mode test [18]. e, a, and u are taken as defined in equation (4), and p and k are functions of loading angle, and tabulated elsewhere [18].

Minimum destructive tests

Minimum destructive nanoindentation and nanoscratch tests [20-29] to measure the material properties of bone are at various stages of development. A micro/ nano scratch test (fig. 4 and 5) of bone distinguished the fracture toughness of human cadaver bone that was obtained from different age groups, and addressed the finite element simulation. A study was conducted on the suitability of the Damage Plastic Model for finite element simulation of bone tests. A comparative study which involved finite element simulation using perfect plastic model and damage plastic model has concluded that the later is more appropriate for simulation of nanoindentation tests. Damage Plastic Model was successfully used in predicting the In-Situ properties of bone, more accurately.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Discussion

Compact sandwich specimen enabled study of the fracture properties of bone in small laboratory animals that are easily grown and managed subject to preset conditions of research interest. Compact sandwich specimen provided an exclusive means to verify the direct relation between the stress intensity factor and the energy release rate of bone for tangential cracks. This specimen is successfully used in the study of the variation in fracture toughness of bone with crack orientation. In addition this specimen provided an exemplary means for study of the variation in fracture toughness of bone with sampling site and across radial layers.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Orthopaedic implants often loosen prematurely in patients after undergoing surgery and effectiveness of bonebiomaterial interface plays an important role in ensuring long service. Compact sandwich specimen is successfully utilized in evaluating the bone-biomaterial interface. Further this specimen is proved effective in evaluating the mixed mode fracture toughness of bone-biomaterial interface.

Methods stated in section 2 help in understanding bone as a material by means of scientific evidence, and advancement of research in the areas of science, technology, engineering, and medicine.

Conclusion

Compact sandwich specimen and other minimum destructive tests provide a size efficient means for carrying out pathological evaluation of bone, and quality assurance of engineered bone tissue. These tests also pave way for in vivo tests and anthropological tests. In addition, these size-efficient tests can be used for conducting risk assessment studies in bone as a result of habits, gait etc.

References

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Satya Prasad Paruchuru (1) *, C. Mauli Agrawal (2)

(1) Department of Mechanical Engineering, Vallurupalli Nageswara Rao (VNR) Vignana Jyothi Institute of Engineering and Technology, Bachupally, Nizam Pet (S.O.), Hyderabad 500 090, India

(2) Department of BioMedical Engineering, College of Engineering, University of Texas at San Antonio, 1 UTSA Circle, TX 78249, USA.

* Corresponding author, Dr. Satya Prasad Paruchuru (paruchuru1@yahoo.co.in)

Received 31 May 2012; Accepted 7 October 2012; Available online 15 October 2012
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Author:Paruchuru, Satya Prasad; Agrawal, C. Mauli
Publication:Trends in Biomaterials and Artificial Organs
Date:Oct 1, 2012
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