1- Introduction
Carpal tunnel syndrome (CTS) is one of the most important peripheral chronic nerve compression disorders that is characterized by a collection of symptoms that result from compression of the median nerve within the carpal tunnel. The disorder is associated with pain, paresthesia and numbness in the median nerve of the hand and its branches [1].
The reasons lying behind the genesis and development of CTS are not very clear. It develops in certain individuals while others do not, even while performing identical activities. Yet, it is well recognized that mechanical insult to the median nerve is the proximate cause of CTS where the nerve is in the interaction with the digital flexor tendons as it passes through the carpal tunnel [2, 3]. From biomechanical viewpoint, median nerve insult occurs, when the nerve stress from physiological environment exceeds the patient pain threshold. This stress is often measured as the von Mises stress acting on the median nerve.
Decades of studies on the CTS show that the reduction of carpal tunnel volume is one of the most important factors related to median nerve insult [4], but to date, there are few attempts to objectively quantify the associated median nerve stresses results from several mechanical conditions such as external loadings (EL) and tendons swelling (TS).
Some studies have numerically investigated the effect of environmental parameters on the carpal tunnel area based on finite element (FE) method. Guo et al. [5] investigated the elongation of the transverse carpal ligament and its effects. Similarly, Javanmardian and Haghpanahi [6] studied the effect of carpal ligament damage and carpal bones movement. However, few studies have been done on the modeling of CTS in order to correlate the median nerve stress and its biomechanical features, as well as finite element (FE) method development.
Ko and Brown [3] performed an FSI study on image-based Carpal tunnel geometrical models using multi-body contact between the nerve, the tendons and the carpal tunnel wall. They concluded that the direct structural contact between the tunnel elements greatly affect the median nerve stresses than the fluid pressure. An interesting investigation on biomechanics of CTS is the study proposed by Hanrong [7] with the help of a realistic approximate carpal tunnel geometry. It presented an early approach for tunnel volume reduction and tendons swelling. It is hoped that by developing the computer processing abilities, FSI simulations can better predict the median nerve stress values resulting from the interaction of carpal tunnel elements. In a more recent attempt to numerically investigate the CTS, Mouzakis et al. [2] present a non-FSI simulation to analyze the effects of computer work on the carpal area using finite element method. Their model had some simplifications, but well predicted the high stress area of carpal tunnel.
In this study, fully coupled FSI simulations of three patient-specific three dimensional (3D) geometrical models of carpal tunnel with considering a healthy wrist and two CTS diagnosed wrist are presented. To the authors’ knowledge, this study also represents the first fully coupled FSI simulation of carpal tunnel with realistic geometrical models which allows the study of median nerve stresses due to the all 9 digital tendons swelling. Furthermore, the developed numerical model is also capable to examine the effects of external loading to the tunnel wall on stress distribution of median nerve in a FSI approach.
2- Methods
Carpal models reconstruction and material properties
Three different 3D patient-specific carpal tunnel geometrical models were constructed for this study based on the MRI data including anatomical details of the median nerve, nine digital flexor tendons and the carpal tunnel boundary from a healthy wrist (HR) and two CTS diagnosed wrist for a male (CTSm) and a female (CTSf), respectively. This study was approved by the internal review boards of Aja University of Medical Sciences. The margins of the nerve, tendons and the tunnel wall are manually segmented. Afterwards, the models were exported to 3D CAD software, Solidworks. An extruding procedure was performed in Solidworks to create 3D volumes. The resulting volumes were divided into two domains: one is the fluid contained in the carpal tunnel and the other was the solid domain including the nerve, tendons and tunnel wall. Then, the resulting bodies were imported into ADINA v8.9 software package (Watertown, MA). Fig. 1 shows the geometrical models produced by the above methodology.
Fig. 1 Reconstruction of carpal tunnel geometrical model. The MRI images for (a) the healthy wrist, (b) the male CTS, and (c) the female CTS geometrical models are taken from [8], [9], and [10], respectively.
The Sussman-Bathe hyperelastic material model was employed for the nerve and tendons which is presented as a stress-strain values in Fig. 2 [11]. The carpal tunnel wall is modeled as a linear isotropic elastic material with Young modulus of E=65MPa [12] and a density of [13]. Also, a Newtonian behavior with a viscosity of [14] and a density of was adopted for the carpal tunnel fluid [15].
Fig. 2 Stress-strain curve fitting of Sussman-Bathe material model taken from [11].
Boundary conditions and numerical method
Displacements and forces are equal in fluid-structure interface, and also, contact offset conditions were invoked between the nerve, tendons and the tunnel wall, where the solid bodies closely meet each other to ensure fluid mesh existence between contacting solids. The tendons were expanded/swelled by an average of 19% [16] to investigate their effects on median nerve stress values. This swelling reduce the tunnel volume by 10% which is considered as a characteristic of the disorder [17]. In another approach, external loadings to outer surface of the tunnel wall are applied to examine how a physical condition can change the stress levels in median nerve. Again, these loadings aim to achieve a 10% reduction in tunnel volume and are categorized into two groups: external loading to the top wall and to the bottom wall.
The employed direct coupling method combines the solid and fluid matrices during the solution process. A sparse matrix solver based on the Gaussian elimination method is used in the solution process. The relative tolerance for all degrees of freedom is set to 0.001. Simulations were performed on the Intel®Core™i7-3770kCPU@3.50-3.90GHz and 32G (RAM). The simulation time for each simulation approximately 47 CPU-hours.
Four node tetrahedral elements were implemented for both solid and fluid domains. Table 1 summarized the number of elements for each models used in computational simulations. To establish the validity of the computational simulations, a mesh sensitivity analysis was performed by selecting five grid sizes for both fluid and solid domains of geometrical models. These grids are varying in the range of 59863-150781 and 72903-210725 elements for the solid and fluid domains, respectively. Von Mises stress and fluid pressure at several selected points were calculated using these different grid numbers. Results showed that for grid numbers listed in Table1, the average differences of fluid pressure and stress values was 0.21% and 0.37%, respectively.
Table 1 Number of elements for geometrical models
Healthy Wrist CTSm CTSf
Solid domain 74935 102432 72083
Fluid domain 135521 183125 106078
3- Results
Previous studies attempted to improve the understanding the mechanical insult of the median nerve. In a pure mechanical viewpoint, median nerve insult occurs when the mechanical stress due to the nerve environmental conditions exceeds its pain threshold. In this study, tendons swelling and external forces to the carpal tunnel are considered to better understanding the factors that could govern dominantly in the median nerve mechanical insult. Three patient-specific models at resting condition are considered: one is a healthy wrist and the others belongs to a male and a female diagnosed with CTS. The mechanical stresses in the carpal domain are then compared based on the disease symptoms such as tendons inflammation and tunnel volume reduction. Moreover, nerve stress distribution on the mid-surface of carpal tunnel is depicted to better understanding the situation correlated with this disorder.
In a step beyond previous studies, all 9 digital flexor tendons are swelled. This status represents a more realistic condition as compared to the conditions considered earlier in which one tendon is swelled [7]. Since the biological conditions associated with the CTS are identical for all tendons, when tendons inflammation occurs, all tendons are affected and swelled. To our knowledge, this approach was not considered in previous studies due to memory insufficiencies and processing inabilities of utilized computers. Fig. 3 shows the stress distribution of median nerve by swelling all digital tendons, and indicate that median nerve stresses are more influenced in CTSm and CTSf models as compared to the healthy wrist model by 49% and 95% increase in the peak nerve stress values, respectively.
Fig. 3 Comparison of mid-surface stress distributions of the median nerve under the tendons swelling condition for (a) the healthy wrist, (b) the male CTS, and (c) the female CTS geometrical models.
In a different approach, external loads are applied to the outer surfaces of carpal tunnel wall to achieve a 10% reduction in the tunnel volume. Two types of loads are applied: one from carpal bones to the outer surface of bottom wall and the other from environmental forces to the outer surface of top wall. Stress distribution of tunnel elements for all geometrical models are depicted in Figs. 4 and 5 for top and bottom wall loadings, respectively. As these figures show, the trend of increasing the nerve stresses is also observed for CTSm and CTSf geometrical models as compared to the healthy wrist model.
Fig. 4 Comparison of mid-surface stress distributions of the median nerve under the bottom wall loading condition for (a) the healthy wrist, (b) the male CTS, and (c) the female CTS geometrical models.
Fig. 5 Comparison of mid-surface stress distributions of the median nerve with the top wall loading condition for (a) the healthy wrist, (b) the male CTS, and (c) the female CTS geometrical models.
Regarding to Fig. 4 that is corresponding to the bottom wall loading condition, the peak stress values of CTSm and CTSf models are 31% and 45% higher than the healthy wrist model, respectively. Similarly, for top wall loading condition at Fig. 5, the peak stress values of CTSm and CTSf models are 18% and 39% higher than the healthy wrist model, respectively. Comparing Figs. 4 and 5 also indicate that the external loading to the top wall more influences the median nerve stresses than the top wall loading condition. The differences between these loading conditions are observed at higher values of peak stress for top wall loading condition by 15%, 4% and 10% for HR, CTSm and CTSf models, respectively. Fig. 6 shows the peak nerve stress values as a function of the geometrical models.
Fig. 6 Comparison of peak values of the median nerve stresses for all geometrical models under the corresponding conditions.
4-Discussion
Three patient-specific models is reconstructed from MRI data images and underwent to 3D FSI analysis to assess the median nerve stresses based on physical and physiological conditions. One of the main purposes of this study is to analyze the median nerve stresses by employment the tendons swelling. Toward this end, a complex FSI approach are performed in the basis of more realistic conditions by swelling all 9 digital flexor tendons for all three patient-specific geometrical models. The other purpose of this study was to investigate the effects of external loading to the tunnel wall. Two sets of loadings are separately applied to the top and bottom wall of the tunnel for all three patient-specific geometrical models.
According to Fig. 3, the location of peak nerve stress for all geometrical models are near the top wall. It indicates that swelling of tendons higher influence the median nerve stresses in the neighborhood of the carpal ligament. This confirm the surgical treatment which elongate the carpal tunnel by cutting the carpal ligament. Moreover, moving from healthy wrist model to CTS models, an increasing trend in peak stress values are observed. This increasing are more pronounced by CTSf model which is consistent by the clinical evidence that demonstrate the disorder are harsher in the females.
The trend of increasing of nerve stresses from healthy wrist model to CTS models are also observed in the Figs. 4 and 5 for tunnel volume reduction due to external loading to the tunnel wall. Comparison between figs. 4 and 5 indicates that external loading from top wall greatly influence nerve stresses as compared to the external loading from bottom wall. This fact is due to geometrical characteristics of tunnel such as the curvature of tunnel wall where the curvature of bottom wall for external loading is more favorable in comparison with the top wall curvature which is more resistant to the external loading. Therefore, for identical tunnel volume reduction, it is expected that the external loading is higher for top wall and consequently it effects the median nerve stresses by higher values. From another perspective, it can be concluded that by identical lodgings along the top and bottom walls, it is expected that the top wall loading causes lower tunnel volume reduction and nerve stress values as compared to the bottom wall loading condition.
Comparison between Fig. 3 and Figs. 4 and 5 shows that the external loading have lower influence on nerve stress values for tendons swelling condition. This comparison is on the basis of identical tunnel volume reduction by 10% for both tendons swelling and external loadings conditions. This 10% tunnel volume reduction by tendons swelling condition is achieved by an average of 19% expansion of the tendons. The 10% reduction of tunnel volume is caused by the genesis amd development of the disorder. Higher values of nerve stress for external loading condition is indicating that the disorder could be caused mostly by physical loads than the factors that lead to the inflammation of tendons. Moreover, higher values of nerve stress for top wall external loading in comparison with the bottom wall external loading, demonstrate that the repetitive loading by job activities such as what happen for typists is a stronger causative agent as compared to other activities that cause the wrist bones loadings to the bottom carpal tunnel wall. Hence, it could confirm the high-risk conditions of job activities like the typists that are repetitively encountering this situation. Similar to swelling condition, the nerve stress values in the vicinity of carpal ligament (top wall) is in the range 9kPa to 28kPa. This high-stress values confirm that the elongation of carpal ligament could be effective to increase the tunnel volume and lowering the stress values.
Furthermore, the external loading to the carpal tunnel wall cause plastic deformation of the wall tissue and the tunnel volume become smaller and smaller over the time. This squeezing also results to median nerve deformation. As seen in the CTS geometrical models, the median nerve tends to deform to a figure with sharp edges. This sharp edges have a high potential for occurrence the stress concentrations and higher values of stresses. As Figs. 3, 4 and 5 show, these locations are more pronounced by CTSf geometrical model which had been deformed to a triangular shape.
Due to the different geometry of carpal tunnel for each patient, a comprehensive study which includes both simulation and statistical approaches seems to be needed. It should be aimed to characterize the geometry features to have a better comparison based on the numerical simulations. Nevertheless, the present study goes a step beyond the current studies of CTS by considering the FSI simulations for various geometrical models that are under more common loading conditions. Despite the progresses that have been made in this study of CTS, there is still a lot to do to not only implement more accurate conditions for numerical simulation of CTS, but also to correlate these findings to clinical evidence.
One of the limitations of this study is to use an isotropic material model for solid elements of carpal tunnel. Yet, Sussman-bathe material model is one of the most accurate material models reported for the tendons. Future experimental studies that propose anisotropic orthotropic material models seem to be required. Applying some fixities to the tunnel wall is another simplification of this study which may affect the numerical simulations.
Despite the limitations for numerical simulation of this study the stress levels of 6.5kPa to 27.6 kPa for the models considered in this study show a reasonable agreement with pressure levels of carpal tunnel fluid measured in CTS diagnosed patient which is in the range of 1kPa to 10kPa. These findings could represent a better insight of the stress distribution of median nerve to the clinicians for surgical treatment such as transverse ligament release. Future studies should be conducted to correlate the stress field to biological factors that result pain feeling. In this regard, several CTS models should be monitored based on neurological methods and be verified experimentally.
5-Conclusion
In the present investigation, we have applied FSI simulations to three patient-specific carpal tunnel models reconstructed from MRI data in order to improve the stress based methodology of mechanical insult to the median nerve. In a comparative analysis, the effects of tendons swellings and external loading to the tunnel wall on median nerve stresses are investigated. Results indicate that the peak wall stress are greater for CTS models as compared to the healthy wrist model for these two types of physiological conditions. Moving from healthy wrist model to female CTS model, these differences become more pronounced at larger nerve stress values.
Results confirm that the female and male CTS models predict higher peak stresses in comparison with the healthy wrist model for both swelling and external loading conditions. Moreover, appliance the external loadings highly increases the peak nerve stresses in all three geometrical models as compared to the tendons swelling condition, indicating the importance of the environmental conditions such as job activities on increasing the median nerve stresses. The role of these conditions in the neighborhood of carpal ligament is well observed with higher stress values of median nerve.
Given the importance of patient-specific FSI simulations on presenting a more accurate predictor of median nerve stress levels, this approach could provide further insight to diagnose and warrant a surgical repair of the disease. In this regard, the methodology presented here goes a step beyond the previous studies by considering more realistic parameters of CTS physiological environment.