Indentation response of human patella with elastic modulus correlation to localized fractal dimension and bone mineral density

Candy box technique for the fixation of inferior pole patellar fractures: finite element analysis and biomechanical experiments

BACKGROUND

Maintaining effective reduction and firm fixation in inferior pole patellar fractures is a highly challenging task. There are various treatment methods available; although tension-band wiring combined with cerclage wiring (TBWC) is the mainstream approach, its effectiveness is limited. Herein, we propose and evaluate a new technique called candy box (CB), based on separate vertical wiring (SVW), for the treatment of inferior pole patellar fractures. Specifically, we provide biomechanical evidence for its clinical application.

METHODS

Five fixation models were built: SVW combined with cerclage wiring (SVWC); TBWC; modified SVW with the middle (MSVW-A) or upper (MSVW-B) 1/3 of the steel wire reserved, and CB. A finite element analysis was performed to compare the displacement and stress under 100-N, 200-N, 300-N, 400-N and 500-N force loads. Three-dimensional printing technology was utilized to create fracture models, and the average displacement of each model group was compared under a 500-N force.

RESULTS

The results of the finite element analysis indicate that CB technology exhibits significantly lower maximum displacement, bone stress, and wire stress compared to that with other technologies under different loads. Additionally, in biomechanical experiments, the average force displacement in the CB group was significantly smaller than that with other methods under a 500-N force (P < 0.05).

CONCLUSIONS

CB technology has the potential to overcome the limitations of current techniques due to its superior biomechanical characteristics. By incorporating early functional exercise and ensuring strong internal fixation, patient prognosis could be enhanced. However, further clinical trials are needed to fully evaluate the therapeutic effects of CB technology.

Relation between mechanical and densimetric properties to fractal dimension in human rib cortical bone

BACKGROUND

Numerous prior studies hypothesized a power-law relationship (E∝ρ^α) between cortical bone Young's modulus (E) and density (ρ) with an exponent 2.3≤α≤3.0, that has not been previously justified in the literature on a theoretical level. Moreover, despite the fact microstructure have been extensively studied, the material correlate of Fractal Dimension (FD) as a descriptor of bone microstructure was not clear in previous studies.

METHODS

This study examined the effect of mineral content and density on the mechanical properties of a large number of human rib cortical bone samples. The mechanical properties were calculated using Digital Image Correlation and uniaxial tensile tests. CT scans were used to calculate the Fractal Dimension (FD) of each specimen. For each specimen, the mineral (f_min), organic (f_org) and water (f_wat) weight fractions were determined. In addition, density was measured after a drying-and-ashing process. Then, Regression Analysis was employed to investigate the relationship between anthropometric variables, weight fractions, density and FD, as well as its impact on the mechanical properties.

FINDINGS

Young's modulus exhibited a power-law relationship with an exponent of α>2.3 when using the conventional density (wet density), but α=2 when using dry density (desecated specimens). In addition, FD increases with decreasing cortical bone density. A significant relationship has been found between FD and density, whereby FD is correlated with the embedding of low density regions in cortical bone.

INTERPRETATION

This study provides a new insight in the exponent value of the power-law relation between Young's Modulus and density, and relates bone behavior with the fragile fracture theory in ceramic materials. Moreover, the results suggest that Fractal Dimension is related to presence of low-density regions.

Separate vertical wiring plus bilateral anchor girdle suturing fixation for the fractures of the inferior pole of the patella

BACKGROUND

The fixation of inferior pole fractures of the patella (IPFPs) is still a great challenge for surgeons.

MATERIALS AND METHODS

We introduced a new fixation method for IPFP fixation, that is, separate vertical wiring plus bilateral anchor girdle suturing fixation (SVW-BSAG). Three finite element models including the anterior tension band wiring (ATBW) model, separate vertical wiring (SVW) model and SVW-BSAG model, were built to evaluate the fixation strength of different fixation methods. A total of 41 consecutive patients with IPFP injury were enrolled in this retrospective study, including 23 patients in the ATBW group and 18 patients in the SVW-BSAG group. The operation time, radiation exposure, full weight-bearing time, Bostman score, extension lag versus contralateral healthy leg, Insall-Salvati ratio, and radiograph outcomes were employed to assess and compare the ATBW group and SVW-BSAG group.

RESULTS

The finite element analysis confirmed that the SVW-BSAG fixation method was as reliable as the ATBW fixation method in terms of fixed strength. Through retrospective analysis, we found that there was no significant difference between the SVW-BSAG and ATBW groups in age, sex, BMI, fracture side, fracture type, or follow-up time. There were no significant differences between the two groups in the Insall-Salvati ratio, 6-month Bostman score, and fixation failure. Compared with the ATBW group, the SVW-BSAG group showed advantages in intraoperative radiation exposure, full weight-bearing time, and extension lag versus the contralateral healthy leg.

CONCLUSION

The finite element analysis and clinical results showed that SVW-BSAG fixation methods are a reliable and valuable for IPFP treatment.

Comparative evaluation of trabecular bone structures of bruxist and non-bruxist individuals with bone apposition in the mandible angle region by fractal analysis

OBJECTIVE

This study aimed to compare the trabecular internal structure of different regions of the mandible according to the grades of appositional classification in the mandible angle region in probable bruxist individuals and non-bruxist G0(Convex course of the basal cortex, no directional change, no bone apposition) individuals by measuring fractal dimension (FD) on panoramic radiographs.

METHODS

200 sample jaws, bilaterally, of 80 probable bruxists and 20 non-bruxist G0 individuals were included in the study. According to the classification in the literature, each mandible angle apposition severity was classified as G0-G1-G2-G3. FD was calculated by selecting the region of interest (ROI) area of 7 regions from each sample. Gender differences in changes between ROIs in radiographs and independent samples t-test were evaluated. Relation between categorical variables was determined by chi-square test (p < .05).

RESULTS

In the comparison of the probable bruxist and non-bruxist G0 groups, FD was found to be statistically significantly higher in the mandible angle (p = 0.013) and cortical bone (p = 0.000) regions in the probable bruxist group than in the non-bruxist G0 group. There is a statistically significant difference between probable bruxist G0 and non-bruxist G0 grades in terms of FD averages in cortical bone (p < 0.001). A statistically significant difference was found in the relationship of ROIs with gender in canine apex (p = 0.021) and canine distal (p = 0.041) regions.

CONCLUSION

FD was found to be higher in the mandibular angle region and cortical bone in probable bruxist individuals than in non-bruxist G0 individuals. Morphological changes seen in the mandible angulus region may be a finding that may raise suspicion for bruxism for clinicians.

Biomechanical comparison of different screw-included angles in crossing screw fixation for transverse patellar fracture in level walking: a quasi-dynamic finite element study

BACKGROUND

A minimally invasive technique with various screw configurations without open surgery is currently used for the fixation of transverse patellar fractures. Percutaneous crossing screw configuration has been reported to have a good bone union rate in patellar fractures. However, the difference in mechanical stability of the fractured patella between different screw-included angles has not been fully investigated. Hence, this study aims to compare the mechanical stability of parallel and crossing screw fixations with different screw-included angles for the fixation of transverse patellar fractures during level walking.

METHODS

A finite element knee model containing a patella with a transverse fracture is created. Two headless compression screws with different angles (0°, 30°, 60°, and 90°) are used to fix the fracture. The loading conditions of the knee joint during level walking are used to compare the stability of the fractured patella with different fixation screw configurations.

RESULTS

The results indicate that the maximum fracture gap opening distance increased with an increase in the included angle. Two parallel screws yield the smallest gap distance among all screw configurations. The maximum gap opening distances at the anterior leading edge of the fractured patella with two parallel screws and two screws having an included angle of 90° are 0.73 mm and 1.31 mm, respectively, at 15% walking cycle.

CONCLUSIONS

Based on these results, the superior performance of two parallel screws over crossing screw fixations in the fixation of transverse patellar fractures is established. Furthermore, the smaller the angle between the crossing screws, the better is the stability of the fractured patella.

Triangular configuration with headless compression screws in the fixation of transverse patellar fracture

A triangular configuration with three parallel cannulated screws is an established treatment for fixing transverse patellar fractures; however, the stability achieved with this approach is slightly lower than that attained with cannulated screws combined with anterior wiring. In the present study, triangular configurations were modified by partially or totally replacing the cannulated screws with headless compression screws (HCSs). Through finite element simulation involving a model of distal femoral, patellar, and proximal tibial fractures, the mechanical stability levels of the modified triangular configurations were compared with that of two cannulated screws combined with anterior wiring. Four triangular screw configurations were developed: three HCSs in a forward and backward triangular configuration, two deep cannulated screws along with one superficial HCS, and two superficial cannulated screws with one deep HCS. Also considered were two parallel cannulated screws (inserted superficially or deeply) combined with anterior wiring. The six approaches were all examined in full knee extension and 45° flexion under physiological loading. The highest stability was obtained with the three HCSs in a backward triangular configuration, as indicated by the least fragment displacement and the smallest fracture gap size. In extension and flexion, this size was smaller than that observed under the use of two deeply placed parallel cannulated screws with anterior wiring by 50.3% (1.53 vs. 0.76 mm) and 43.2% (1.48 vs. 0.84 mm), respectively. Thus, the use of three HCSs in a backward triangular configuration is recommended for the fixation of transverse patellar fractures, especially without the use of anterior wiring.

Biomechanical Analysis of the Kirschner-Wire Depth of the Modified Tension Band Wiring Technique in Transverse Patellar Fractures: An Experimental Study Using the Finite-Element Method

Backgroud

Modified tension band wiring is one of the most preferred surgical methods for transverse patellar fractures. However, the optimal depth or sagittal position of a Kirschner wire (K-wire) in modified tension band wiring has yet to be determined. The purpose of this study was to evaluate whether the depth of a K-wire affects the biomechanical characteristics of modified tension band wiring using the finite-element method.

Methods

A patella model was designed with a cuboid shape (length, 34.3 mm; width, 44.8 mm; and thickness, 22.4 mm) and divided into the cortical and cancellous bone parts. A transverse fracture line was formed on the midline of the cuboid shape model. The cuboidal model was applied to modified tension band wiring. The depth or sagittal position of the K-wire was divided into superficial, center, and deep. With the Abaqus v2017 program (Dassault System Inc.), the distal part of the model was fixed, and a tensile load of 850 N was applied to the proximal part of the model at an angle of 45°. The maximum pressures of the cortical and cancellous bones at the fracture plane were measured. The largest von Mises values of the K-wire and stainless steel wire were also measured. The fracture gap on the distracted or anterior side was measured.

Results

In deep K-wire placement, the highest peak von Mises values of the cortical and cancellous bones were observed. The K-wire and stainless steel wire showed the highest von Mises values in deep K-wire placement. The fracture gap was also largest in deep K-wire placement.

Conclusions

The depth of the K-wire affects the biomechanical characteristics of modified tension band wiring. Deep placement of the K-wire will be more favorable for bone union than the empirically known 5-mm anterior or center placement of the K-wire.

An experimental simulation model to assess wear of the porcine patellofemoral joint

A range of surgical techniques and osteochondral interventions have been developed for early stage chondral/osteochondral repair interventions in the knee however, methods for functional, pre-clinical assessment of these therapies are limited. In this study, a method for simulating physiological loading and motion in the porcine patellofemoral joint was developed using a 6-axis simulator. As an example of how the method can be used, the influence of surgical positioning of osteochondral allografts in the patella on cartilage wear, deformation and damage and graft stability was investigated in this porcine patellofemoral joint model. The functional performance of allografts implanted either optimally (flush with the cartilage surface) or 1 mm proud of the cartilage surface was compared to a positive control (stainless steel pin implanted 1 mm proud of the cartilage surface), a negative control (no intervention) and a defect model. Allografts implanted flush with the surrounding cartilage could restore the articulating surface of the patella resulting in low wear, damage and deformation of the opposing cartilage surface, similar to that of the negative control group. Implanting the graft proud of the patella surface resulted in cartilage lesions on the femoral trochlea (ICRS grade 2) and a cartilage volume difference of 2.0 ± 3.9 mm3; the positive controls resulted in more severe lesions, a higher volume difference (14.2 ± 7.4 mm3) which in some cases exposed subchondral bone (ICRS grade 4). Defects in the patella caused deformation of the opposing cartilage surface. All grafts implanted in the patella subsided over the duration of the study. This study demonstrated a method that can be used to evaluate osteochondral repair strategies in the patellofemoral joint applying physiological loading and motions.

Role of an additional third screw in the fixation of transverse patellar fracture with two parallel cannulated screw and anterior wire

BACKGROUND

Two parallel cannulated screws along with an anterior wire to construct a tension band is a popular approach in transverse patellar fractures. However, the optimal screw proximity, either deep or superficial screw placements, remains controversial. Hence, a new concept of the addition of a third screw to form a triangular configuration along with the original two parallel screws was proposed in this study. Therefore, the biomechanical effect of the additional third screw on the stability of the fractured patella was investigated with finite element (FE) simulation.

METHODS

An FE knee model including the distal femur, proximal tibia, and fractured patella (type AT/OTA 34-C) was developed in this study. Four different screw configurations, including two parallel cannulated screws with superficial (5-mm proximity) and deep (10-mm proximity) placements and two parallel superficial screws plus a third deep screw, and two parallel deep screws plus a third superficial screw, with or without the anterior wire, were considered for the simulation.

RESULTS

Results indicated that the addition of a third screw increased stability by reducing the dorsal gap opening when two parallel screws were deeply placed, particularly on the fractured patella without an anterior wire. However, the third screw was of little value when two parallel screws were superficially placed. In the existence of two deep parallel screws and the anterior wire, the third screw reduced the gap opening by 23.5% (from 1.15 mm to 0.88 mm) and 53.6% (from 1.21 mm to 0.61 mm) in knee flexion 45° and full extension, respectively. Furthermore, in the absence of the anterior wire, the third screw reduced the gap opening by 73.5% (from 2 mm to 0.53 mm) and 72.2% (from 1.33 mm to 0.37 mm) in knee flexion 45° and full extension, respectively.

CONCLUSION

Based on the results, a third cannulated screw superficially placed (5-mm proximity) is recommended to increase stability and maintain contact of the fractured patella, fixed with two parallel cannulated screws deeply placed (10-mm proximity), particularly when an anterior wire was not used. Furthermore, the third screw deeply placed is not recommended in a fractured patella with two parallel superficial screws.

Prediction of mechanical properties of human rib cortical bone using fractal dimension

A large number of post mortem human subjects was used to investigate the relation between the micro-structure of rib cortical bone and the mechanical properties using Fractal Dimension. Uniaxial tensile tests were performed on coupons of rib cortical bone. Tensile strength, yield stress, Young's Modulus, maximum strain, and work to fracture were determined for each coupon. Fractal dimension was computed using CT images and Digital Image Correlation procedures. A highly significant effect of fractal dimension in the mechanical properties was found. In addition, the variation in mechanical properties was found to be adequately represented by Generalized Extreme Value type distributions.

Role of screw proximity in the fixation of transverse patellar fractures with screws and a wire

PURPOSE

Clinical and biomechanical studies have reported that using supportive screws and a wire instead of the common Kirschner wires for modified tension band wiring improves the stability of fractured patellae. However, the effect of screw proximity on the fixation of a fractured patella remains unclear. Therefore a numerical study was conducted to examine the effects of screw proximity on biomechanical responses in a simulated patellar fracture fixed using two parallel cannulated screws and anterior tension band wiring.

METHODS

A patellar model with a transverse fracture and loads simulating patellar tendon forces applied on the patella were used in the present simulation. The surgical fixation consisted of two 4.0-mm parallel partially threaded cannulated screws with a figure-of-eight tension band made using a 1.25-mm stainless steel wire. Biomechanical responses at two screw proximities, 5 and 10 mm from the leading edge of the patella, were investigated.

RESULTS

Superficial screw placement (5 mm) yielded higher stability, lower wire loads, and lower bone contact pressures than the deep placement (10 mm). The deep placement of screws exerted a higher load on the wire but a lower force on the screw than superficial placement did.

CONCLUSION

This is the first numerical study to examine the effects of screw location on the fixation of a fractured patella using cannulated screws and tension band wiring. Considering the favorable biomechanical responses, superficial placement (5 mm below the leading edge of the patella) is recommended for screw insertion when treating a transverse fractured patella.

Digital Tomosynthesis and Fractal Analysis Predict Prevalent Vertebral Fractures in Patients With Multiple Myeloma: A Preliminary In Vivo Study

OBJECTIVE. The objective of this study was to investigate the association of fractal-derived bone microstructural parameters with vertebral fracture status using in vivo digital tomosynthesis images of the spine. MATERIALS AND METHODS. Digital tomosynthesis images of the thoracic and lumbar spine from T1 to L5 were acquired from 36 patients with newly diagnosed multiple myeloma or monoclonal gammopathy of uncertain significance (age range, 39-85 years old). Scans were performed with patients in the supine position with reconstructed planes formed in the coronal direction. Bone mineral density (BMD) was recorded for 10 patients who had recently undergone dual x-ray absorptiometry. Vertebral fracture and lytic lesion status was determined by a radiologist from digital radiographs. Radiologist interpretation was reviewed to identify levels with a minimum number of fractures or lesions. For fractal analysis, the largest possible cuboid volume of interest within the cancellous bone was cropped from T7 and T11 images. Mean and SD of fractal variables between slices of fractal dimension (FD, a measure of self-similarity in the texture), mean lacunarity (λ, a measure of heterogeneity) and the slope of lacunarity versus box size relationship (S_λ, a measure of sensitivity of heterogeneity to size scale) were calculated using a box-counting method. A generalized estimating equation (GEE) platform was used to examine fractal variables as predictors of fracture status. RESULTS. Fracture status was not significantly associated with sex, race, age, stage of myeloma, presence of lesion in the spine, or BMD. In light of these results, no correction was made for these variables in further analyses of fractal variables. No interaction was found between vertebral level and any of the fractal variables (p = 0.12-0.77). Therefore, vertebral level was not considered further as an independent variable. Logistic regression analysis within GEE indicated that probability of fracture decreased with increasing mean FD (p = 0.02). In contrast, probability of fracture increased with increasing mean λ (p = 0.03). Although not to a statistically significant degree, probability of fracture increased with increasing mean S_λ (p = 0.08), SD of FD (p = 0.07), SD of λ (p = 0.07), and SD of S_λ (p = 0.06). CONCLUSION. We found FD and lacunarity calculated within the cancellous centrum of T7 and T11 vertebrae to be significantly associated with the presence of a vertebral fracture in this cohort. The decreased probability of fracture with increasing fractal dimension and increased probability of fracture with increasing lacunarity are consistent with the idea that cancellous bone with a better organized trabecular architecture is mechanically more competent. To our knowledge, this is the first in vivo evidence that fractal analysis of vertebral bone from tomosynthesis images may be useful in assessing vertebral fracture risk in patients with multiple myeloma.

Roles of the screw types, proximity and anterior band wiring in the surgical fixation of transverse patellar fractures: a finite element investigation

BACKGROUND

Cannulated screws with an anterior wire are currently used for managing transverse patellar fracture. However, the addition of anterior wiring with various types of screws via open surgery to increase the mechanical stability is yet to be determined. Hence, this study aimed to compare the mechanical behaviors of a fractured patella fixed with various screws types and at various screw locations with and without the anterior wire. The present study hypothesized that using the anterior wire reduces the fracture gap formation.

METHODS

A finite element (FE) model containing a fractured patella fixed with various types of cannulated screws and anterior wiring was created in this study. Three types of screws, namely partial thread, full thread, and headless compression screws, and two screw depths, namely 5 and 10 mm away from the anterior surface of the patella, were included. The effect of the anterior wire was clarified by comparing the results of surgical fixation with and without the wire. Two magnitudes and two loading directions were used to simulate and examine the mechanical responses of the fractured patella with various fixation conditions during knee flexion/extension.

RESULTS

Compared with partial thread and headless compression screws, the full thread screw increased the stability of the fractured patella by reducing fragment displacement, fracture gap formation, and contact pressure while increasing the contact area at the fracture site. Under 400-N in the direction 45°, the full thread screw with 5-mm placement reduced the gap formation by 86.7% (from 2.71 to 0.36 mm) and 55.6% (from 0. 81 to 0. 36 mm) compared with the partial thread screw with 10-mm placement, respectively without and with the anterior wire.

CONCLUSION

The anterior wire along with the full thread screw is preferentially recommended for maintaining the surgical fixation of the fractured patella. Without the use of anterior wiring, the full thread screw with 5-mm placement may be considered as a less invasive alternative; however, simple screw fixation at a deeper placement (10 mm) is least recommended for the fixation of transverse patellar fracture.

Measuring bone stiffness using spherical indentation

Objectives

Bone material properties are a major determinant of bone health in older age, both in terms of fracture risk and implant fixation, in orthopaedics and dentistry. Bone is an anisotropic and hierarchical material so its measured material properties depend upon the scale of metric used. The scale used should reflect the clinical problem, whether it is fracture risk, a whole bone problem, or implant stability, at the millimetre-scale. Indentation, an engineering technique involving pressing a hard-tipped material into another material with a known force, may be able to assess bone stiffness at the millimetre-scale (the apparent elastic modulus). We aimed to investigate whether spherical-tip indentation could reliably measure the apparent elastic modulus of human cortical bone.

Materials and methods

Cortical bone samples were retrieved from the femoral necks of nineteen patients undergoing total hip replacement surgery (10 females, 9 males, mean age: 69 years). The samples underwent indentation using a 1.5 mm diameter, ruby, spherical indenter tip, with sixty indentations per patient sample, across six locations on the bone surfaces, with ten repeated indentations at each of the six locations. The samples then underwent mechanical compression testing. The repeatability of indentation measurements of elastic modulus was assessed using the co-efficient of repeatability and the correlation between the bone elastic modulus measured by indentation and compression testing was analysed by least-squares regression.

Results

In total, 1140 indentations in total were performed. Indentation was found to be repeatable for indentations performed at the same locations on the bone samples with a mean co-efficient of repeatability of 0.4 GigaPascals (GPa), confidence interval (C.I): 0.33–0.42 GPa. There was variation in the indentation modulus results between different locations on the bone samples (mean co-efficient of repeatability: 3.1 GPa, C.I: 2.2–3.90 GPa). No clear correlation was observed between indentation and compression values of bone elastic modulus (r = 0.33, p = 0.17). The mean apparent elastic modulus obtained by spherical indentation was 9.9 GPa, the standard deviation for each indent cycle was 0.11 GPa, and the standard deviation between locations on the same sample was 1.01 GPa. The mean compression apparent elastic modulus was 4.42 GPa, standard deviation 1.02 GPa.

Discussion

Spherical-tip indentation was found to be a repeatable test for measuring the elastic modulus of human cortical bone, demonstrated by a low co-efficient of repeatability in this study. It could not, however, reliably predict cortical bone elastic modulus determined by platens compression testing in this study. This may be due to indentation only probing mechanical properties at the micro-scale while platens compression testing assesses millimetre length-scale properties. Improvements to the testing technique, including the use of a larger diameter spherical indenter tip, may improve the measurement of bone stiffness at the millimetre scale and should be investigated further.

Microindentation - a tool for measuring cortical bone stiffness? A systematic review

Objectives

Microindentation has the potential to measure the stiffness of an individual patient’s bone. Bone stiffness plays a crucial role in the press-fit stability of orthopaedic implants. Arming surgeons with accurate bone stiffness information may reduce surgical complications including periprosthetic fractures. The question addressed with this systematic review is whether microindentation can accurately measure cortical bone stiffness.

Methods

A systematic review of all English language articles using a keyword search was undertaken using Medline, Embase, PubMed, Scopus and Cochrane databases. Studies that only used nanoindentation, cancellous bone or animal tissue were excluded.

Results

A total of 1094 abstracts were retrieved and 32 papers were included in the analysis, 20 of which used reference point indentation, and 12 of which used traditional depth-sensing indentation. There are several factors that must be considered when using microindentation, such as tip size, depth and method of analysis. Only two studies validated microindentation against traditional mechanical testing techniques. Both studies used reference point indentation (RPI), with one showing that RPI parameters correlate well with mechanical testing, but the other suggested that they do not.

Conclusion

Microindentation has been used in various studies to assess bone stiffness, but only two studies with conflicting results compared microindentation with traditional mechanical testing techniques. Further research, including more studies comparing microindentation with other mechanical testing methods, is needed before microindentation can be used reliably to calculate cortical bone stiffness.

Cite this article: M. Arnold, S. Zhao, S. Ma, F. Giuliani, U. Hansen, J. P. Cobb, R. L. Abel, O. Boughton. Microindentation – a tool for measuring cortical bone stiffness? A systematic review. Bone Joint Res 2017;6:542–549. DOI: 10.1302/2046-3758.69.BJR-2016-0317.R2.