Finite Element Analysis for Transverse Carpal Ligament Tensile Strain and Carpal Arch Area

Abstract

Mechanics of carpal tunnel soft tissue, such as fat, muscle and transverse carpal ligament (TCL), around the median nerve may render the median nerve vulnerable to compression neuropathy. The purpose of this study was to understand the roles of carpal tunnel soft tissue mechanical properties and intratunnel pressure on the TCL tensile strain and carpal arch area (CAA) using finite element analysis (FEA). Manual segmentation of the thenar muscles, skin, fat, TCL, hamate bone, and trapezium bone in the transverse plane at distal carpal tunnel were obtained from B-mode ultrasound images of one cadaveric hand. Sensitivity analyses were conducted to examine the dependence of TCL tensile strain and CAA on TCL elastic modulus (0.125–10 MPa volar-dorsally; 1.375–110 MPa transversely), skin-fat and thenar muscle initial shear modulus (1.6–160 kPa for skin-fat; 0.425–42.5 kPa for muscle), and intratunnel pressure (60–480 mmHg). Predictions of TCL tensile strain under different intratunnel pressures were validated with the experimental data obtained on the same cadaveric hand. Results showed that skin, fat and muscles had little effect on the TCL tensile strain and CAA changes. However, TCL tensile strain and CAA increased with decreased elastic modulus of TCL and increased intratunnel pressure. The TCL tensile strain and CAA increased linearly with increased pressure while increased exponentially with decreased elastic modulus of TCL. Softening the TCL by decreasing the elastic modulus may be an alternative clinical approach to carpal tunnel expansion to accommodate elevated intratunnel pressure and alleviate median nerve compression neuropathy.

Introduction

The carpal tunnel is formed by the carpal bones and transverse carpal ligament (TCL), providing passage of the median nerve and nine flexor tendons. The mechanical environment of the carpal tunnel is the main determinant for compression neuropathy of the median nerve. Increases in tissue thickness and stiffness of the TCL have been shown in patients with carpal tunnel syndrome (Miyamoto et al. 2013; Marquardt et al., 2016), suggesting the etiological mechanisms of the neuropathy. The mechanical role of the TCL in median nerve compression is also illustrated by carpal tunnel release surgery, in which the TCL is transected to reduce the mechanical constraint of the carpal tunnel as a means of nerve decompression.

Surgical transection of the TCL is a standard treatment for carpal tunnel syndrome. The procedure aims to increase tunnel volume and decrease carpal tunnel pressure by increasing compliance of the volar region, thereby decreasing compression on the median nerve (Okutsu et al., 1989; Kato et al. 1994). Notably, flattening of the median nerve at distal level of the carpal tunnel is increased in patients with carpal tunnel syndrome (Buchberger et al., 1991; Horch et al., 1997) and carpal tunnel release surgery helps reduce the nerve flattening and restore its normal shape (El-Karabaty et al., 2005; Momoso et al., 2014). However, persistent weakness of grip and pain over the thenar and hypothenar origins, known as “pillar pain”, are common surgical complications. Carpal tunnel release in conjunction with ligament lengthening reconstruction has been proposed to alleviate postoperative pillar pain, improved early grip strength and earlier return of function compared with traditional open carpal tunnel release (Pavlidis et al., 2010; Seitz and Lall, 2013; Saravi et al., 2016).

Carpal tunnel area is strongly dependent on the characteristics of the soft tissues volar to the carpal tunnel. It has been shown that carpal tunnel expansion after TCL release surgery is mainly (93%) contributed by the increase in CAA (Kato et al., 1994). In a geometrical model, Li et al. (2009) showed that carpal arch width shortening or TCL elongation is effective in forming a greater arch to gain increased CAA. Thus the increase in TCL tensile strain might be an alternative approach to enlarging the carpal tunnel area. Furthermore, the carpal tunnel is compliant to accommodate physiological variations of carpal tunnel pressure, and an increase in pressure led to greater CAA and carpal tunnel area (Li et al., 2011). Clinically, elevated pressure has been observed in patients with carpal tunnel syndrome (Gelberman et al., 1981). Under pathophysiological intratunnel pressure, carpal arch morphology may be particularly dependent on the mechanical properties of the TCL. Furthermore, tissues (i.e. thenar muscles, skin, and fat) volar to the TCL are a mechanically constraining factor that could also affect carpal arch formation.

Finite element (FE) modeling is an effective tool to perform parametric analyses of different mechanical factors that might be challenging to extrapolate from experimental data. Subject-specific FE models based on medical imaging providing representation of patient-specific anatomy have been utilized in many fields. Specifically for the carpal tunnel, previous FE modeling has been used to examine the effects of TCL release on displacement of carpal bones and contact stress in the midcarpal joints (Guo et al., 2009), and carpal arch enlargement under optimal force direction (Walia et al., 2017). However, carpal tunnel FE modeling has paid little attention to the mechanical properties of the various soft tissues, i.e. skin, fat, and thenar muscles in the volar aspect of the tunnel. The TCL, skin, fat and thenar muscles might constrain the carpal arch through their structural and mechanical interactions. For the carpal tunnel pressure, previous FE modeling has been used to examine the effect of increased carpal tunnel pressure caused by awkward wrist postures on the deformation of median nerve (Mouzakis et al., 2014). The intratunnel pressure might also alter the carpal arch and TCL geometry.

The current study was developed using subject-specific FE model to investigate the biomechanical behavior of the carpal tunnel influenced by mechanical properties of soft tissues including TCL, skin, fat, thenar muscles in the volar carpal tunnel. A comprehensive understanding of the subject-specific carpal arch biomechanics and morphology depends both on subject-specific anatomy and tissue mechanical properties. We developed the model in this study to understand the roles of TCL, skin, fat, thenar muscles mechanical properties and intratunnel pressure on TCL tensile strain and CAA using parametric analysis. It was hypothesized that TCL tensile strain and CAA would increase by decreasing stiffness of TCL, skin, fat, and thenar muscles.

Methods

Cadaveric specimen for ultrasound imaging

One fresh frozen cadaveric hand (male; left; age 74 years; height 177 cm; weight 95 kg) was used in this study. The specimen had no hand injury, surgery, or musculoskeletal disorders to the hand or upper extremity. The specimen was thawed overnight at room temperature prior to experimentation. The specimen was positioned in a supinated, anatomically neutral position at the wrist with all fingers naturally curled (Fig 1a). High frequency (17 MHz) B-mode ultrasound images were captured at the distal carpal tunnel using an ultrasound system (ACUSON S2000, Siemens Medical Solutions USA, Inc., Mountain View, CA, USA). A linear array 18L6 HD transducer was aligned at the transverse plane of distal carpal tunnel along the line connecting hook of hamate and ridge of trapezium (Fig 1a). The depth of the image field was 2.5 cm with image resolution as 0.0624 mm/pixel and gain as 8 dB.

Fig 1.

FE model of the volar carpal tunnel based on ultrasound image. (a) Ultrasound image collection of the distal carpal tunnel; (b) The ultrasound image showing thenar muscles, skin-fat, TCL, hook of hamate and ridge of trapezium (c) FE model components including hamate bone, trapezium bone, thenar muscles, skin-fat and TCL. SF: skin-fat; HH: hook of hamate; T: TCL; RT: ridge of trapezium; TM: thenar muscles.

Subject-specific finite element modeling

The contours of thenar muscles, skin, fat, TCL, volar boundary of hamate bone and trapezium bone (Fig 1b) were extracted with manual segmentation using the grey value threshold in ImageJ 1.46r (US National Institutes of Health, Bethesda, USA). With a thickness of 1 mm, a pseudo-three dimensional (3D) volar carpal arch structure was reconstructed using solid modeling (SolidWorks 2012, Dassault Systems, Waltham, MA, USA) and then exported to finite element (FE) software ABAQUS CAE (v6.10, Simulia, Providence, RI, USA) for FE analysis. The model components included hamate bone, trapezium bone, thenar muscle, skin, fat, and TCL (Fig 1c). Skin and fat were modeled as a single skin-fat tissue. Parts of the hamate and trapezium bones attached with skin-fat, muscle and TCL were modeled since the effects of bone strains are negligible relative to soft tissue deformation. Material properties of all components were listed in the Table 1. Material properties of hamate and trapezium bones were assumed as isotropic, homogeneous and linearly elastic. The elastic modulus of the hamate and trapezium bones was assumed as 10 GPa with Poisson’s ratio as 0.3 (Pistoia et al. 2002). The TCL showed anisotropic material property in volar-dorsal, proximal-distal direction and radial-ulnar direction (Holmes et al. 2012), which might due to the fiber orientation in the TCL (Prantil et al., 2012). The TCL was modeled as linearly elastic and anisotropic with volar-dorsal and proximal-distal elastic modulus of 0.5 MPa (Holmes et al. 2012). Transverse elastic modulus of TCL was assumed as 5.5 MPa (Holmes et al. 2012) by using user-defined non-linear spring elements (CONN3D2, two-noded 3D connector elements in ABAQUS) assumed to sustain only tension tied to the TCL elements at the four edge boundaries. Non-linear spring elements were generated using the criteria that there was no force with zero or negative strain and linear force with positive strain. The TCL’s Poisson’s ratio was assumed as 0.4. Hyperelasticity of muscle and skin-fat was determined by a Neo-Hookean strain energy potential in the following form:

$$U=\frac{1}{2}G({\underset{\_}{I}}_1-3)+\frac{1}{2}K{(J_{el}-1)}^2$$ (1)

where U is the strain energy per unit reference volume; J_el is the elastic volume ratio;I₁ is the first deviatoric strain invariant defined as :

$${\underset{\_}{I}}_1={{\underset{\_}{\lambda }}_1}^2+{{\underset{\_}{\lambda }}_2}^2+{{\underset{\_}{\lambda }}_3}^2$$ (2)

Table 1.

Mechanical properties for the model.

Hamate and trapezium bones (Pistoia et al., 2002)	Elasticity	Elastic modulus as 10 GPa	Poisson’s ratio as 0.3
Transverse TCL (Holmes et al., 2012)		Elastic modulus as 5.5 MPa (user-defined spring elements )	Poisson’s ratio as 0.4
Volar-dorsal TCL (Holmes et al., 2012)		Elastic modulus as 0.5 MPa
Muscle (Palevski et al., 2006)	Hyperelasticity (Neo-Hookean strain energy potential)	Initial shear modulus as 4.25 kPa	Poisson’s ratio as 0.49
Skin-fat (Broshn and Arcan, 2000)		Initial shear modulus as 16 kPa
Hamate-trapezium bone to bone stiffness (Gabra and Li, 2016)	11.8 N/mm in transverse direction and 2.9 N/mm in volar-dorsal direction

λ_i are the deviatoric principal stretches, ${\underset{\_}{\lambda }}_i=J^{-\frac{1}{3}}{\lambda }_i$ where λ_i are the principal stretches and J is the total volume ratio. G is the initial shear modulus. K is the bulk modulus calculated given the shear modulus, G, and Poisson’s ratio, ν, using the following equation:

$$v=\frac{3\frac{K}{G}-2}{6\frac{K}{G}+2}$$ (3)

Effective Poisson’s ratios of muscle and skin-fat were assumed to be 0.49 as nearly incompressible. Initial shear modulus of muscle was assumed as 0.00425 MPa (Palevski et al. 2006). Initial shear modulus of skin-fat was assumed as 0.016 MPa (Broshn and Arcan 2000). The bulk modulus K was calculated to be 0.2111 MPa for the muscle and 0.7947 MPa for the skin-fat. Intratunnel pressure applied on the dorsal boundary of TCL was set as 24 mmHg in a normal physiological condition (Seradge et al. 1995). Tissues around and between carpal bones (i.e. intercarpal ligament and cartilage) were not included in the model. Instead, stiffness of hamate-to-trapezium was set 11.8 N/mm transversely and 2.9 N/mm in volar-dorsal direction (Gabra and Li, 2016) using linear springs to simulate overall effects of soft tissues around and between carpal bones. By applying the “tie” constraint in ABAQUS, “no-slip” contact condition was assumed at the interface between TCL and skin-fat, TCL and thenar muscles, thenar muscles and skin-fat, TCL and hamate, TCL and trapezium, skin-fat and hamate, thenar muscle and trapezium. Hamate, trapezium, muscle and skin-fat were modeled as C3D10 quadratic tetrahedral elements. TCL was modeled as linear C3D6 wedge elements. Hamate had 3044 elements with 5187 nodes; trapezium had 5251 elements with 8777 nodes; thenar muscles had 7200 elements with 12004 nodes; skin-fat had 4000 elements with 7617 nodes; TCL had 77 wedge elements with 130 nodes and 66 CON3D2 elements. A mesh convergence analysis was performed using h-refinement method, where around double and triple elements numbers in all components in the model with the same boundary conditions and material properties showed 1.6% and 1.9% error respectively on the result of TCL tensile strain. The mesh density used in this study was therefore deemed to be adequate for simulations. Displacement boundary condition being free in-plane and fixed out-of-plane was applied at both the distal and proximal surfaces of all the parts. Other surfaces were assumed to be free in displacement boundary condition. Hamate bone was rigidly fixed without any degree of freedom.

Parametric analysis

Mechanical properties of different tissues (TCL, thenar muscles, skin, and fat) and mechanical boundary condition (intratunnel pressure) could determine the geometric output of the carpal arch. Simulations with reference parameters, parametric analyses were conducted to study relative contributions of the various parameters to TCL tensile strain and CAA. The material property parameters included the transverse elastic modulus of TCL (0.25, 0.5, 0.75, 2.5, 5, 7.5 and 10 times the reference value) with the volar-dorsal elastic modulus adjusted to keep the ratio of transverse elastic modulus to volar-dorsal elastic modulus as 11, initial shear modulus of skin-fat and thenar muscles (0.1, 0.5, 5 and 10 times the reference value), and intratunnel pressure (2.5, 5, 7.5, 10, 12.5, 15, 17.5 and 20 times the reference value). A crossover effect by transverse elastic modulus of TCL and intratunnel pressure was also conducted. Linear and nonlinear regression analyses were performed among the independent and dependent variables.

The tensile strain of TCL was defined as the ratio of TCL dorsal length change to the original dorsal length. CAA was defined as the area bounded by the dorsal TCL boundary and the line connecting the two points on hamate and trapezium intercepted by dorsal TCL boundary respectively.

Model validation with pressure regulation

The hand was minimally dissected with the tunnel and volar soft tissue remaining intact. An incision was made 4 cm distal to the distal wrist crease, directly proximal to the second web space to provide access to the carpal tunnel. The palmar skin, fat and aponeurosis were dissected through until the flexor tendons were visible for further insertion of a medical air balloon (Advanced Polymers Inc., Salem, NH, USA) to apply artificial pressure in the tunnel. The balloon was aligned along the longitudinal axis of the tunnel with the assistance of ultrasound. This custom pressure regulating device consisting of air balloon and tube was designed to apply different intratunnel pressure (Li et al., 2011). The balloon extended beyond the proximal and the distal edges of the TCL. The specimen was positioned in a supinated and neutral position. The balloon was pressurized by inflation syringe (Cook Medical, Bloomington, IN, USA) and the pressure was monitored using a digital pressure gauge (CeComp Electronics, Libertyville, IL, USA). The balloon pressure was set at pressure levels from 0 mmHg to 300 mmHg with an increment of 50 mmHg. Under each pressure, a B-mode ultrasound image was taken at the transverse plane of the distal carpal tunnel along the line connecting ridge of trapezium and hook of hamate. The tensile strain of TCL was analyzed with manually tracing using the multi-point selection tool in ImageJ. Predictions of TCL tensile strain simulation under different intratunnel pressures were compared with the measurements obtained on the cadaveric specimen to validate the finite element analysis approach.

Results

Parametric analyses showed that changes in the initial shear modulus of thenar muscle can lead to 1 % change in CAA and 6.1 % change in TCL tensile strain at most (Fig 2a) and changes in the initial shear modulus of skin-fat can lead to 5% change in CAA and 23.5% change in TCL tensile strain at most (Fig 2b). TCL strain and CAA were strongly dependent on TCL elastic modulus and intratunnel pressure (Fig 3).

Fig 2.

Changes of TCL tensile strain (blue) and CAA (green) with initial shear modulus of thenar muscles (a) and skin-fat (b). The vertical dash lines indicate the reference value of initial shear modulus of thenar muscles (a) and skin-fat (b) respectively.

Fig 3.

Changes of TCL tensile strain (blue) and CAA (green) with different transverse elastic modulus of TCL (a) and intratunnel pressure (b). The vertical dash lines indicate the reference value of transverse elastic modulus of TCL (a) and intratunnel pressure (b) respectively.

Specifically, TCL tensile strain and CAA decreased with increased elastic modulus of TCL (Fig 4a) and decreased intratunnel pressure (Fig 4b). The TCL tensile strain increased linearly with increased intratunnel pressure (R-square values > 0.99). However, TCL strain increased exponentially with decreased TCL elastic modulus (R-square values > 0.97). We used the following equation to describe the dependence of TCL tensile strain (ε) on intratunnel pressure (P) and TCL elastic modulus (E):

$$\epsilon ={\mathit{kPe}}^{bE}$$ (4)

Fig 4.

TCL tensile strain (a) and CAA (b) with different intratunnel pressures and TCL elastic moduli.

Least square curve fitting the curves in Fig 4(a) with Eq. (4) showed that k and b approximately equaled to 0.00053 mmHg⁻¹ and -0.304 MPa⁻¹, respectively (R-square values > 0.97). Fig 4(b) showed the CAA increased with increased intratunnel pressure and with decreased TCL elastic modulus. The relationship of CAA and the tensile strain of TCL was found to be second-order polynomial in the following form:

$$\mathit{CAA}=k_1{({Pe}^{bE})}^2+k_2{Pe}^{bE}+k_3$$ (5)

Least square curve fitting the curves in Fig 4(b) with Eq. (5) resulted in k₁, k₂, and k₃ values 2.29 × 10⁻⁸mm²mmHg⁻², 0.0021 mm²mmHg⁻¹, and 11.8 mm² respectively (R-square values > 0.98).

Under a simulated physiological condition where intratunnel pressure was set at 24 mmHg, TCL tensile strain increased 3.45-folds from 0.31% to 1.07% and CAA increased 1.3-folds from 12.5 mm² to 16.5 mm² when TCL elastic modulus was 0.25 times of reference value. Under high intratunnel pressure, such as 300 mmHg, TCL tensile strain increased over 3.2-folds from 3.48% to 11.12% and CAA increased 1.7-folds from 26.3 mm² to 45.0 mm² when TCL elastic modulus was 0.25 times of reference value.

We predicted the TCL tensile strain under different intratunnel pressure in the reference FE model. The TCL tensile strains of FE computational simulation and experimental cadaveric hand were shown in Fig 5 with an average difference of less than 14%. The tensile strain of TCL changed from 0% to 4.1% under the intratunnel pressure changing from 0 mmHg to 300 mmHg. Similar to FE results, TCL tensile strain showed linear relationship with intratunnel pressure (R-square value > 0.97) in the cadaveric experiment.

Fig 5.

TCL tensile strains under various intratunnel pressures based on FE analyses and experimental measurement.

Discussion

This study presented a subject-specific, pseudo 3D FE model of the distal volar carpal tunnel with surrounding soft tissues including skin-fat, thenar muscles, TCL, hamate and trapezium. Parametric analysis showed the elastic modulus of TCL and intratunnel pressure strongly influence the carpal arch area and TCL tensile strain while the initial shear moduli of thenar muscle and skin-fat had little effect on the carpal arch structure and TCL tensile strain comparatively. The transverse elastic modulus of TCL was over 100-fold higher than equivalent elastic moduli of skin-fat and muscle surrounding TCL. The comparatively less stiff surrounding tissues, like fat and muscle, are an insignificant determinant for TCL morphology. Softening TCL by decreasing the elastic modulus of TCL could effectively increase tensile strain of TCL and modify carpal arch structure leading to the increase of CAA. We found that the increase of CAA was nonlinearly related to the increase of TCL tensile strain and elongation although the carpal arch width remains unchanged. Intratunnel pressure keeps the TCL in tension to form a carpal arch. With an increase of tunnel pressure, TCL tensile strain increases for tissue elongation and carpal arch area increase to enlarge the carpal tunnel. Adaptive tissue deformation under high intratunnel pressure may be a protective mechanism in reducing the compression of the median nerve.

It is well known that intratunnel pressure is elevated in patients with CTS (Gelberman et al., 1981). Relieving the chronic exposure of the increased pressure could alleviate compression neuropathy. The tunnel pressure at the distal tunnel level is higher than at the proximal tunnel (Luchetti et al., 1998) which indicates more constraints on the median nerve at the distal carpal tunnel. Electrophysiological studies also showed that the median nerve lesion tended to be at the distal edge of the carpal tunnel in CTS patients (Nathan et al., 1990; Kimura 1979). In this study, we modeled the distal level of carpal tunnel at the volar aspect to guide potential approach to reduce the constraints at the distal tunnel. The larger intratunnel pressure in patients with CTS might enlarge the carpal tunnel area compared with healthy controls (Uchiyama et al., 2005). Other cadaveric studies also showed the increased carpal tunnel pressure could resulted in increased carpal tunnel cross-sectional area (Li et al., 2011; Kim et al., 2013). Our model also showed similar results with previous studies. The increase in intratunnel pressure could increase the carpal arch area and result in more highly tensioned TCL. Our modeling results showed nonlinear relationship between intratunnel pressure and carpal arch area (second order polynomial), similar to that reported in Li et al. (2011). Intratunnel pressure has been shown to reach over 300 mmHg in pathological conditions (Luchetti et al., 1998) and when the upper extremity assumed certain postures (Uchiyama et al., 2010). Our FE model has the advantage of simulating a range of elevated intratunnel pressures under pathological condition. Validation of TCL tensile strain with the carpal tunnel of cadaveric hand under various pressure demonstrated the predictive utility of the FE model.

TCL anisotropic elastic modulus and failure tensile strain were reported in different studies. TCL elastic modulus is different in volar-dorsal direction and in radial-ulnar direction. The volar-dorsal elastic modulus of TCL was reported to be around 0.5 MPa with different values in different site of TCL (Main et al., 2012). While transverse radial-ulnar elastic modulus is much larger due to fiber alignment in the transverse direction (Prantil et al., 2012). Variable values of transverse elastic moduli have been reported in different studies as 0.76–3.38 MPa (Mathers et al., 2016), 2.8 MPa (Holmes et al., 2012), 52/38 MPa in males/females (Brett et al., 2014). TCL hypotrophy has been observed in patients with CTS (Yamagami et al., 1994) suggesting tissue maladaptation in thickness and stiffness. The transverse and volar-dorsal elastic moduli of the TCL were assumed to be in the range of values reported in pathophysiological conditions. Mechanical testing showed TCL failure strain as 9.2% in male and 15.5% in female (Brett et al., 2014). The tensile strain results in our FE analyses were less than 10% under different intratunnel pressures and TCL elastic moduli.

Studies of TCL stiffness adaptation (Marquardt et al., 2016) and released carpal tunnel by TCL dissection (Kim et al., 2013) suggest that the change in TCL mechanical property might affect the compliance of carpal tunnel potentially contributing or alleviating median nerve compression. The TCL mechanical property manipulation could also be achieved by injecting collagenase reducing ligament stiffness by over 50% after 3-hour treatment (Prantil et al., 2011). Our FE model also suggested the decrease in elastic modulus of TCL by 50% can increase CAA from 13% to 30% under intratunnel pressure from 24 mmHg to 300 mmHg. The increase of CAA was about 1.9 mm² when TCL transverse elastic modulus reduced from 5.5 MPa to 2.25 MPa under normal physiological condition. However, a reduction of TCL stiffness by 50% led to an increase of CAA of 10 mm² when a pathologically elevated intratunnel pressure of 300 mmHg was simulated. An in-vivo study indicated that an increase of 5–10 mm² in the arch area decreased median nerve flattening when the wrist was compressed in the radioulnar direction (Marquardt et al., 2015). The decrease in TCL stiffness by 50% might also relieve the median nerve from compression and flattening. It was shown that TCL releasing surgery led to an increase of carpal tunnel area of 27 mm² (from preoperative 150 mm² to postoperative 177 mm², Lee et al., 2005). Another study demonstrated that postoperative increase in total carpal tunnel area was mainly attributed to the increase in CAA accounting for 93% of the total change (Kato et al., 1994). Specifically, our FE model predicted an increase in carpal arch area of 19 mm² when TCL elastic modulus decreased by 75% while the intratunnel pressure maintained at 300 mmHg. Further decreasing the TCL elastic modulus under less intratunnel pressure (mimicking the scenario of mild CTS) could also increase the CAA to the extent comparable to that obtained from releasing surgery.

TCL elongation reported in the literature is somewhat inconsistent. Li et al. (2009) showed that the TCL was hardly stretchable when the force was applied palmerly from within the carpal tunnel, while Mathers et al. (2016) demonstrated >10% strain under tensile testing. The discrepancy may be explained by different force magnitude and testing methods. In our FE analysis, we found the TCL could be elongated to about 10% under elevated, pathophysiological intratunnel pressure when the modulus was reduced by 75%. Holmes et al. (2011) indicated that TCL lengthening contributes more greatly to changes in carpal tunnel shape. In a geometric model, Li et al. (2009) simulated the carpal arch formation and found a 1 mm increase in TCL length could also cause greater than 20% increase in total carpal tunnel area. The elongation of the TCL was from 0–2.4 mm in our FE analysis with various conditions of TCL material properties and intratunnel pressures. Our FE model allowed for simulation of various model parameters and estimation of resulting TCL strain which can be difficult to measure experimentally.

This study also presented predictive equations to describe the dependence of CAA and TCL tensile strain on intratunnel pressure and TCL elastic modulus. These relationships can be used to conveniently explore tissue manipulation to achieve desired outcome of CAA and TCL elongation. Clostridial collagenase has been successfully used to treat Dupuytren’s disease, which results from the formation of pathogenic nodules and cords within the hands palmar fascia (Hurst et al., 2009). Similar collagenolytic approaches to softening the TCL may be used to increase carpal tunnel volume and decrease carpal tunnel pressure, thereby alleviating pressure on the median nerve of CTS sufferers.

One limitation of this study is that the intratunnel pressure was modeled independently without considering its interactive effects with TCL elongation. The intratunnel pressure might change with the change of CAA or TCL elastic modulus. Increase in CAA might lead to decrease in intratunnel pressure, and this coupling effect warrants more investigation. Another limitation of this study is that the contents in the carpal tunnel were not included in the FE model, which did not take into consideration of potential contact forces among the structural components (Ko and Brown, 2007). Third, this study is a pseudo 3D FE model focusing on the distal level of carpal tunnel; future work can expand the modeling framework developed in this study to be 3-D carpal tunnel to determine the relationship among tissue properties, geometric configuration, and loading conditions. Fourth, the geometrical segmentation of all components was conducted manually which might introduce errors (e.g. insertion exactness of TCL). Assumption that muscle and skin fat were isotropic and homogeneous might also potentially introduce errors. In the future, improvements in the geometries and material properties of soft tissues could enhance FEA accuracy. Finally, the results in this study is geometrically specimen-specific, and future work on population-based modeling can provide more insights into the generalizability of the current results.