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Computational Analysis of Strength and Fracture Location of Different Types of Femurs under Falling Condition using CT-Image based Finite Element Method
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**
Zaw Linn Htun1,3, Mitsugu Todo1,2, Manabu Tsukamoto4, Takuaki Yamamoto5, Masaaki Mawatari6, Yasuharu Nakashima7
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1 Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan;

2 Research Institute for Applied Mechanics, Kyushu University Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan;

3 Department of Physics, University of Yangon, 11041 Kamayut, Yangon, Myanmar;

4 Department of Orthopaedic Surgery, University of Occupational and Environmental Health, 1-1 Iseigaoka, Yahatanishi-ku, Kitakyushu, Fukuoka 807-8555, Japan;

5 Department of Orthopedic Surgery, Fukuoka University, 7-45-1 Nanakuma, Jonan-ku, Fukuoka 814-0180 Japan;

6 Department of Orthopedic Surgery, Saga University, 5-1-1 Nabeshima, Saga 849-8501, Japan;

7 Department of Orthopaedic Surgery, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8580, Japan.

**Conflict-of-interest statement:** The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.

**Open-Access:** This article is an open-access article which was selected by an in-house editor and fully peer-reviewed by external reviewers. It is distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http: //creativecommons.org/licenses/by-nc/4.0/

**Correspondence to:** Mitsugu Todo, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan.

**Email:** todo@riam.kyushu-u.ac.jp

**Received:** May 24, 2022

**Revised:** June 9, 2022

**Accepted:** June 10 2022

**Published online:** June 28, 2022

Sideways falling has been considered as a leading cause of hip fracture in elderly people with a high risk of morbidity and mortality. Therefore, early investigation of optimum femoral strength and fracture location of people at greatest risk can be clinically very useful for the preventive measures. It is also considered that some typical femoral diseases such as osteoarthritis (OA) and avascular necrosis (AVN) could affect the strength and fracture behaviour of the femurs. In this study, 130 computational femoral models were constructed using CT images of 73 patients. Then, CT image based finite element method combined with the damage mechanics analysis was applied to predict the fracture load as the femoral strength and the fracture location of the femoral models. The computational results exhibited that the fracture load tended to increase with increase of the volumetric bone mineral density estimated in the femoral head and neck region in all the three types of models. The bone fracture behaviour was expressed as expressed as the distribution of failure elements in the head and neck region. Under fall loading, the bone fracture mainly took place in the greater trochanter region for all types of femoral model. In addition, a combination of the greater trochanter and multifarious neck fracture was also observed in all the models. A combination of greater trochanter and intertrochanteric fracture was also observed in the AVN group.

**Key words: **
Finite element analysis (FEA); Femoral strength; Fracture location; Osteoarthritis (OA); Avascular necrosis (AVN); Bone mineral density (BMD)

© 2022 The Author(s). Published by ACT Publishing Group Ltd. All rights reserved.

Htun ZL, Todo M, Tsukamoto M, Yamamoto T, Mawatari M, Nakashima Y. Computational Analysis of Strength and Fracture Location of Different Types of Femurs under Falling Condition using CT-Image based Finite Element Method.* International Journal of Orthopaedics* 2022;** 9(3)**: 1669-1675 Available from: URL: http://www.ghrnet.org/index.php/ijo/article/view/3298

Recent years, the risk of hip fractures in elderly people has dramatically increased due to the degradation of bone structure caused by osteoporosis. A hip fracture can contribute a financial burden on patients, morbidity, and even mortality. Japan has the world’s largest ageing population, and the number of hip fracture incidences in 2017 was estimated as about 193,400, consisting of 44,100 males and 149,300 females[1]. Cummings and other researchers also suggested that the number of patients with hip fractures might double or triple by the year 2040[2]. It is also reported by Asian Federation of Osteoporosis Societies (AFOS) that hip fracture incidences in Asian countries will increase up to 2.28-fold from 2018 to 2050[3].

With the hip fracture incidence increasing worldwide, for each of the osteoporotic patients, the estimation of fracture location and optimum strength of the femur have actively been performed. For example, the bone densitometry and the diagnostic imaging methods have generally been used to predict the risk of bone fracture. These methods usually provide regional bone density values for speciﬁc portions of the proximal femur and can visualize ﬁgures and shapes of the speciﬁc areas of the bone that may be related to the possibility of hip fracture[4,5]. However, these methods cannot provide a quantitative strength which is directly related to the fracture risk of the femur because the femoral strength depends on its 3D geometry, heterogeneity, distributed mechanical properties, and loading conditions.

In the meantime, a computer simulation method such as the CT-image based finite element method (CT-FEM) has been utilized to estimate the mechanical strength of femurs in order to assess the hip fracture risk of the elderly patient with osteoporosis[6-12]. Moreover, CT-FEM can analyse and predict not only the distributions of stress and strain within the bone model but also the fracture locations under the different boundary conditions[12-15].

Along with osteoporosis, some typical femoral diseases such as osteoarthritis (OA) and avascular necrosis (AVN) might significantly affect the femoral fracture behaviour and therefore the femoral strength; however, the effects of such diseases on the mechanical performance of femurs have not been investigated yet. In the present study, 3D computational finite element (FE) models of 130 femurs with healthy, OA and AVN conditions were constructed using CT images of lower limbs of 73 patients. Then, for each of the FE models, the mechanical testing was performed under a compressive loading condition in order to estimate its femoral strength and the fracture behaviour. Such fracture behaviour was recreated as the accumulation of failure elements under both the tensile and compressive stress conditions.

**Finite Element Modelling**

Femoral CT data of 73 patients (10 men aged 37-75 years old, the average age of 51.49 years old, and 63 women aged 19-87 years old, the average age of 65.06 years old) were provided from four different university hospitals. A total of 130 computational femoral models were constructed using these CT images. Based on the patient’s clinical data confirmed by orthopaedic surgeons, the 130 femurs were classified into three groups; 42 normal femurs (N1 group), 58 OA femurs (N2 group) and 30 AVN femurs (N3 group). The three different types of the femur are illustrated in Figure 1 and denoted by Normal, OA and AVN models, respectively, hereafter.

**Figure 1**Three different types of femoral models.

Three-dimensional numerical and finite element models of the femurs were constructed using Mechanical Finder v.11 (Research Center of Computational Mechanics Inc., Tokyo, Japan). Firstly, two-dimensional bone contours were extracted from the CT images, and then they were smoothly connected each other to construct three-dimensional femoral models. Then, the inside of each femoral model was filled with tetrahedral elements to create a finite element (FE) model[16]. The size of the tetrahedral elements was set to 2 to 4 mm. The whole surface of the FE model was also created using shell elements to imitate the stiff outer surface of the cortical bone with the greatest bone mineral density[17]. The average total number of the tetrahedral and the shell elements were roughly 178,000, and 28,000, respectively.

**Mechanical Modelling and Material Properties**

The tensile deformation behaviour of all the femoral bone models was assumed to be linear elastic characterized by two material parameters such as Young’s modulus and Poisson’s ratio, while their compressive deformation behaviour was assumed to be characterized by an elastic-plastic response with four material parameters such as Young’s modulus, Poisson’s ratio, yield strength and the work hardening coefficient.

For each of the tetrahedral elements, its mean bone mineral density (BMD) was firstly calculated from the corresponding CT value (CTv) by using the following linear equation[18-20]:

BMD = 0.001(CTv + 1.4246)/1.0580 (1)

Where the units of BMD and CTv are given by g/cm3 and Hounsfield Unit, respectively. Then Young’s modulus of the element was estimated from the corresponding BMD by using the empirical formulae proposed by Keyak, et al[21]. For all the tetrahedral elements, Poisson’s ratio was set to 0.4[6]. On the contrary, for all the shell elements, Young’s modulus and Poisson’s ratio were fixed to 20.6 GPa and 0.167, respectively. The distribution patterns of Young’s modulus in the three femoral models presented in Figure 1 are shown in Figure 2. Distribution of the higher moduli corresponded to the location of cortical bone, while the lower moduli expressed cancellous bone and marrow.

**Figure 2**Distribution of Young’s modulus in the cross-sectional area.

Under the compressive deformation of all the elements, it was assumed that the onset of yielding took place when the Drucker-Prager equivalent stress reached the compressive yield strength (this is called ‘Drucker-Prager yield criterion’). The yield strength of each element was also obtained from the element’s BMD by using the empirical formulae proposed by Keyak, et al[21], while the yield strength of all the shell elements was set to 20.6 MPa. The work hardening coefficient was set to 0.07 for all the elements.

In this FE analysis, bone fracture was reproduced as an aggregation of failure elements. Different failure criterions were used in the tensile and compressive stress conditions. Under the tensile stress condition, the maximum principal stress criterion was utilized to express the onset of localized tensile fracture of bone. It was assumed that the tensile failure of an element took place when the maximum principal stress reached its critical value, which was equal to 0.8 × (compressive yield strength)[12]. On the contrary, under the compressive stress condition, the minimum principal strain criterion was used to express the localized compressive bone fracture. It was assumed that the compressive failure of an element took place when the minimum principal strain reached its critical value which was equal to -10,000 µ strain, following the yielding of the element[22]. The failure of the element under both the tensile and compressive conditions was expressed by reducing the modulus down to the minimum value in the whole femoral model. The strength of the femoral model was then defined as a critical value of the applied load when 15 shell elements were failed[23].

**Boundary Conditions**

Firstly, the bone axes were set on the basis of the femoral method and then, the boundary conditions were determined accordingly. The boundary conditions, i.e., the fixed and loading conditions, are shown in Figure 3, respectively. As the fixed condition, the femoral surface from the bottom condylar surface to the circumferential line on the diaphysis located approximately 15 mm below the lesser trochanter was totally fixed as shown in Figure 3(a). The distributed load was applied to the femoral head vertically to the ﬂoor with the femoral shaft inclined by α = 60° and internally rotated by β = 15° in reference to the ﬂoor as shown in Figure 3(b)[24,25]. The total value of the applied load was set to 10,000 N. The total load was divided into 10 main steps and each of the main steps was also divided into 4 sub-steps.

**Figure 3**Boundary conditions imitating a falling condition.

**Correlation Between Fracture Load and vBMD**

The correlations between the fracture load and the average volumetric BMD (vBMD) of Normal, OA and AVN models are shown in Figure 4. For each of the models, a linear regression was fitted on the data and then Pearson’s correlation coefficient was evaluated. Confidience interval (CI) statistics was also performed to precisely estimate the samples’ mean and 95% predicted and 95% confidence bands of the fitted curve are also shown in Figure 4. The mean fracture loads of lower and upper 95% confidence interval and their descriptive statistical value for each femur type are listed in Table 1.

Table 1 Mean fracture loads of individual femoral group (unit: N). | ||||||

Types of femur | Data | Mean | Standard Deviation | Minimum | Median | Maximum |

Normal | Lower 95% Confidence Interval | 896 | 186 | 513 | 945 | 1127 |

Upper 95% Confidence Interval | 1157 | 151 | 973 | 1108 | 1493 | |

OA | Lower 95% Confidence Interval | 1054 | 154 | 710 | 1109 | 1229 |

Upper 95% Confidence Interval | 1359 | 170 | 1163 | 1304 | 1724 | |

AVN | Lower 95% Confidence Interval | 962 | 222 | 504 | 1018 | 1237 |

Upper 95% Confidence Interval | 1369 | 166 | 1175 | 1314 | 1747 |

For Normal models shown in Figure 4(a), Pearson’s correlation coefficient was found to be r = 0.53. Although the graphic data was widely scatterd, it could be said that the higher vBMD tended to reuslt in the higher fracture load. Confidience interval (CI) statistics was also performed to precisely estimate the samples’ mean and 95% predicted and 95% confidence bands of the fitted curve are shown in Figure 4(a). The statistical results showed that the mean of 95% confidence interval was in a range from 896 ± 186 to 1,157 ± 151 N (mean ± standard deviation). This implyed that the mean fracture load of all 42 Normal models existed within this range with 95% confident.

For OA and AVN models shown in Figures 4(b) and (c), the Pearson’s r values were found to be 0.42 and 0.43, respectively. 95% CI means were also observed in a range from 1,054 ± 154 to 1359 ± 170 N for OA models and from 962 ± 222 to 1,369 ± 166 N for AVN models. It is worth noting that the load ranges of OA and AVN models were apparently wider than that of the normal models. This fact could closely be related to the peculiar structural and mechanical properties of the OA and AVN femurs, depending on the extra bone growths induced by femoroacetabular impingement (FAI) in the OA femurs and various stages of collapsed femoral head surface in the AVN femurs[26]. The AVN femurs used in this study were classified into the 4 stages and therefore, the different stages could result in the broad range of fracture load.

**Figure 4**Correlation between fracture load and vBMD, including 95% interval of prediction band (pink color) and confidence band (light red color).

**Fracture Characteristics**

For each femoral model, the fracture behaviour was expressed as the distribution of failure elements. For each of the three models, three different types of distribution partern of the failure elements are shown in Figure 5. Those microdamages consisted of three different failure modes, that is, tensile fracture (denoted by ‘cracked element’), compressive yielding (denoted by ‘plastic element’), and compressive fracture (denoted by ‘crushed element’). The fracture regions were classified into 5 different types as shown in Table 2. It was noted that the bone fracture mainly took place in the greater trochanter region, secondly followed by a combination of greater trochanter and basicervical neck region for all the femoral models. In addition, a combination of the greater trochanter and either subcapital neck or transcervical neck fracture was also observed in all the models. Especially, this mixed fracture mode was mainly observed in OA models, showing 15 out of 58 models. On the other hand, a combination of the greater trochanter and intertrochanteric fracture was significantly occurred in AVN models. This type of unique fracture mode was only observed in AVN models (4 out of 30). More importantly, it was suggested from the simulation resutls that AVN femurs might fracture in all possible locations. It could be due to the variety of AVN stages. It is also to be noteworthy that the AVN femurs with potentially intertrochanteric fracture mixed with greater trochanter were of stage-3 and stage-4.

**Figure 5**Three different types of bone fracture behaviour. Fracture patterns were expressed as the distribution of failure elements.

Table 2 Classification of fracture region. | |||||

Type of Femur (Sample Size) | Estimated Fracture Location | ||||

Greater Trochanter | Greater Trochanter + Neck (Subcapital) | Greater Trochanter + Neck (Transcervical) | Greater Trochanter + Neck (Basicervical) | Greater Trochanter + IntertrochantericRegion | |

Normal (N=42) | N=26 (61.9%) | N=3 (7.1%) | N=1 (2.4%) | N=12 (28.6%) | N=0 |

OA (N=58) | N=27 (46.5%) | N=12 (20.7%) | N=3 (5.2%) | N=16 (27.6%) | N=0 |

AVN (N=30) | N=14 (46.7%) | N=1 (3.3%) | N=1 (3.3%) | N=10 (33.3%) | N=4 (13.3%) |

* Neck (Subcapital) = the femoral head and neck junction;* Neck (Transcervical) = the mid portion of femoral neck;* Neck (Basicervical) = the base of femoral neck. |

**Comparison of Fracture Mechanism of Three models with same vBMD**

Among all the 130 femoral models, it was found that some of them had the same vBMD with very different fracture load. In order to understand the difference in fracture mechanism, three models with the same vBMD of 0.32 mg/mm3 were picked up and they are denoted by A-Normal, B-OA and C-AVN hereafter. The fractue load values of the three models were 1,650, 1,375, and 1,150 N, respectively. Their corresponding volumes of the head and neck region are compared in Figure 6, and it was clearly seen that A-Normal had the smallest volume with the highest femoral strength. On the contrary, B-OA and C-AVN had larger volumes with apparently lower fracture loads. It was therefore considered that the strength of femoral bone greatly depended on not only its geometry but also its microstructural parameters such as the distribution pattern of the mineral content.

**Figure 6**Comparison of the volume of the femoral head and neck region.

For each of the three models, the accumulation of failure elements is shown as a function of load step in Figure 7. One step of load corresponded to 250 N. The strongest model, A-normal, reached up to 7 step, while the moderate model, B-OA, and the weakest model, C-AVN, reached only 6 and 5 steps, respectively. Distribution patterns of strain energy density (SED) on the cross-sections of the three models at the fracture load are also shown in Figure 8. In A-normal and B-OA models, it was clearly seen that high SED smoothly distributed from the femoral head to the base of greater trochanter, suggesting an ideal propagation of mechanical stress and resulting in the high fracture load. On the contrary, in C-AVN model, SED was largely concentrated on the greater trochanter region with low BMD, suggesting a higher risk of fracture.

**Figure 7**Accumulation of failure elements with increase of load steps in the three femoral models with the same vBMD.

**Figure 8**SED distribution patterns of three femoral models with the same vBMD.

## Conclusions

In this study, three different groups of computational femoral model were constructed using CT data of normal, OA and AVN femurs. Then, the fracture load as the patient-specific femoral strength and the fracture location were analysed under the fall loading condition using the finite element method combined with the damage mechanics. The conclusions were obtained as follows:

(1) The fracture load tended to increase with increase of the average vBMD of the head and neck region with wide scatters. The Pearson’s r values of Normal, OA and AVN models were evaluated as 0.53, 0.42 and 0.43, respectively, corresponding to the wider scatters observed in OA and AVN models than in Normal models.

(2) The bone fracture behaviour was expressed as the distribution of failure elements in the neck and trochanteric regions. It was noted that the bone fracture mainly took place in the greater trochanter region for all three models. In addition, a combination of the greater trochanter and neck fracture was also observed in all the models.

(3) A combination of greater trochanter and intertrochanteric fracture was also observed in AVN models, associated with disease levels of stage-3 and stage-4.

(4) Three models, A-normal, B-OA and C-AVN, with the same vBMD were compared. C-AVN exhibited the lowest fracture load with unnatural SED distribution which concentrated on the greater trochanter side, indicating a higher risk of fracture than the other regions.

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