# FEM-Based Compression Fracture Risk Assessment in Osteoporotic Lumbar Vertebra L1
###### Abstract  
This paper presents a finite element method (FEM)-based fracture risk assessment in patient-specific osteoporoporotic lumbar vertebra L1. The influence of osteoporosis is defined by variation of parameters such as thickness of the cortical shell, the bone volume-total volume ratio (BV/TV), and the trabecular bone score (TBS). The mechanical behaviour of bone is defined using the Ramberg-Osgood material model. This study involves the static and nonlinear dynamic calculations of von Mises stresses and follows statistical processing of the obtained results in order to develop the patient-specific vertebra reliability. In addition, different scenarios of parameters show that the reliability of the proposed model of human vertebra highly decreases with low levels of BV/TV and is critical due to the thinner cortical bone, suggesting high trauma risk by reason of osteoporosis.  
Keywords:bone tissue; elastoplasticity; finite element method; fracture risk; osteoporosis; trabeculae; trabecular bone score; vertebra +
Footnote †: journal: Medical  
To determine the level of stress and bone strength, classical criteria for fluidity at the continuum level are often applied. Thus, the von Mises yield criterion is the most frequently used [11] criterion used for the trabecular bone of a vertebra, but a tissue-dependent orthotropic yield criterion Tsai-Wu [16] was proposed also.  
In most cases, studies were perfomed by using static loads, while the number of investigations with dynamic loads are rather limited [13; 17]. Also, the computational biomechanics can provide the ability to assess fracture risk and can serve as a useful diagnostic tool for analysing the state of osteoporotic bones. One of the most effective modern indicators used to verify vertebral fragility is the the trabecular bone score (TBS). This method involves the measurment of gray level texture, which shows the average state of trabecular bone microarchitecture [18], closely related to the ratio volume-total bone volume (BV/TV) [19]. Although TBS is a rough estimate of the strength properties of bone tissue, it can also be provided to study bone fragility and predict bone fractures.  
There are several developed methods which employ bone mineral density (BMD) to predict the long-term fracture risk. BMD is usually assessed by dual-energy X-ray absorptiometry (DXA), and some studies have shown that a decrease of BMD is bonded with a higher risk for future fracture [20; 21; 22]. In addition, modern techniques of medical diagnostics also dispose computer-based algorithms, such as FRAX [23], which calculate fracture probability from clinical risk factors, such as age and body mass index(BMI), and dichotomized risk factors comprising prior fragility fracture, parental history of hip fracture, currently smoking tobacco, long-term oral glucocorticoid use, rheumatoid arthritis, other causes of secondary osteoporosis, and alcohol consumption [24]. In contrast, these methods do not verify the complicated relationship between the important parameters such as BV/TV, the thickness of the cortical shell, and the external load. The finite element method (FEM)-based continuum models can supply the additional patient-specific data to define the risk of fracture by additionally applying the reliability theory.  
One of the aims of present work is numerical investigation of the osteoporotic affect on strength properties of the proposed vertebrae model including the time-dependent load. The evaluation results might be useful for the medical diagnostics of the osteoporosis and for verifying the strength properties of the bone tissue of the patient. The main aim of this study is proposing the structural mechanics-based method of calculating fracture risk based on statistically processed results obtained by the numerical investigation of strength properties of the lumbar vertebral L1 body with various grades of osteoporotic degradation.