Ceramic heads are used in hip revision surgery to mitigate corrosion concerns. Manufacturers recommend using a pristine titanium sleeve in conjunction with a well-fixed metal stem to prevent early failure of the ceramic head. However, the influence of impact force, head size, and sleeve offset on pull-off strength and seating displacement of a revision head assembly is not fully understood. Therefore, the purpose of this study was to investigate the pull-off strength and displacement of commercially available revision ceramic heads and titanium taper sleeve offsets (BIOLOX OPTION, CeramTec GmbH, Plochingen, Germany) while covering a range of clinically relevant impaction forces. Two head sizes (28 mm, n = 12 and 36 mm, n = 12) and two taper adapter sleeve offsets (small, n = 12 and extra-large, n =12) were tested in this study. A dynamic impaction rig was constructed to seat the head, sleeve, and stem assembly. Consistent impaction forces were achieved by a dropping a hammer fixed to a lever arm from a pre-determined height onto a standard impactor instrumented with a piezoelectric force sensor (PCB Piezotronics Inc.). Axially applied forces of 2 kN and 6 kN were used to cover a range of typical impaction forces. Three non-contact differential variable reluctance transducers (LORD Sensing Systems) were used to track the displacement of the head relative to the stem. Subsequently, samples were transferred a servo hydraulic testing machine, and a pull-off test was carried out per ISO 7206- 10 to measure the disassembly force.INTRODUCTION
METHODS
As an alternative to total hip arthroplasty (THA), hip resurfacing arthroplasty (HRA) provides the advantage of retaining bone stock. However, femoral component loosening and femoral neck fracture continue to be leading causes of revision in HRA. Surgical technique including cementation method and bone preparation, and patient selection are known to be important for fixation. This study was designed to understand if and to what extent compromise in bone quality and the presence of cysts in the proximal femur contribute to resurfacing component loosening. A finite element (FE) model of a proximal femur was used to calculate the stress in the cement layer. Bone density to Young's modulus relationship was used to calibrate the bone stiffness in the model using computed tomography. A contemporary resurfacing implant (BHR, Smith & Nephew) was used in the FE model. The effect of reduced bone quality (35% reduction relative to normal baseline; osteoporosis threshold) and presence of cysts on stress in the bone cement layer was then assessed using the same FE model. The center of the cyst (a localized spherical cavity 1 cm in diameter) was located directly under the contact patch. Simulations were run with two locations of the center of the cyst, on the surface of the resected bone and 1 cm below it. The surface cyst was filled with bone cement, but the inner cyst was empty. The contact force and location for the model were obtained from instrumented implant studies. Simulations were run representing the peak loads during two activities, jogging and stand-up from seated position. While density reduction of the bone reduced the stress in the CoCr femoral head, the Von-Mises stress in the cement layer was amplified. The peak Von-Mises stress in the cement layer under the contact patch increased more than six times for the jogging activity, and more than ten times for the stand-up activity, relative to values for normal bone density. The impact of cysts on the cement layer stress or the strain distributions in the bone were minimal. The results show a greater risk of failure of the cement layer under conditions of reduced bone density. In contrast cement stresses and bone strains appeared to be relatively immune to a surface cyst filled with bone cement or an empty inner cyst. Contraindications of hip resurfacing include severe osteopenia and multiple cysts of the femoral head, however no strict or quantitative criteria exist to guide patient selection. Research similar to the one presented herein, maybe key to developing better patient selection criteria to reduce risk associated with compromised femoral head fixation.
Posterior stabilized (PS) total knee arthroplasty (TKA), wherein mechanical engagement of the femoral cam and tibial post prevents abnormal anterior sliding of the knee, is a proven surgical technique. However, many patients complain about abnormal clicking sensation, and several reports of severe wear and catastrophic failure of the tibial post have been published. In addition to posterior cam-post engagement during flexion, anterior engagement with femoral intercondylar notch can also occur during extension. The goal of this study was to use dynamic simulations to explore sensitivity of tibial post loading to implant design and alignment, across different activities. LifeModeler KneeSIM software was used to calculate tibial post contact forces for four contemporary PS implants (Triathlon PS, Stryker; Journey BCS and Legion PS, Smith & Nephew; LPS Flex, Zimmer Biomet). An average model of the knee, including cartilage and soft tissue insertion locations, created from MRI data of 40 knees was used to mount and align the component. The Triathlon femoral component was mounted with posterior and distal condylar tangency at: a) both medial and lateral condylar cartilage (anatomic alignment), b) at the medial condylar cartilage and perpendicular to mechanical axis (mechanical alignment with medial tangency), and c) at lateral condylar cartilage and perpendicular to mechanical axis (mechanical alignment with lateral tangency). The influence of implant design was assessed via simulations for the other implant systems with the femoral components aligned perpendicular to mechanical axis with lateral tangency. Five different activities were simulated. The anterior contact force was significantly smaller than the posterior contact force, but it varied noticeably with tibial insert slope and implant design. For Triathlon PS, during most activities anatomic alignment of the femoral component resulted in greater anterior contact force compared to mechanical alignment, but absolute magnitude of forces remained small (<100N). Mechanical alignment with medial tangency resulted in greater posterior contact force for deep knee bend and greater anterior force for chair sit activity. For all implants, peak posterior contact forces were greater for activities with greater peak knee flexion. The magnitude of posterior contact forces for the various implants was comparable to other reports in literature. Overall activity type, implant design and slope had greater impact on post loading than alignment method. Tibial insert slope was shown to be important for anterior post loading, but not for posterior post loading. Anatomic alignment could increase post loading with contemporary TKA systems. In the case of the specific design for which effect of alignment was evaluated, the changes in force magnitude with alignment were modest (<200N). Nonetheless, results of this study highlight the importance of evaluating the effect of different alignment approaches on tibial post loading.
Postoperative functional limitations after Total Knee Arthroplasty (TKA) are caused, in part, by a mismatch between a patient's natural anatomy and conventional “off-the-shelf” implants. To address this, we propose a new concept combining off-the-shelf femur and tibia implants with custom polyethylene tibial inserts designed to account for a patient's unique anatomy. Our goal in this study was to use knee specific computational modeling to determine the neutral path of motion and laxity of an intact knee under axial compression and shear forces through full flexion and compare intact motion against the same knee implanted with a conventional off-the-shelf vs. a custom tibial insert. 3D models of a healthy knee joint were acquired from an open development repository funded by the National Institute of Biomedical Imagining and Bioengineering (Harris et al., 2016). The knee model was virtually implanted with conventional (off-the-shelf) posterior cruciate retaining (CR) components including the femoral component, tibial tray, and a conventional insert. A custom CR tibial insert was designed taking into account native articular geometry and compatibility with placement of the off-the-shelf femoral/tibial tray. Bone, cartilage and implant models were imported into ANSYS Workbench. Ligaments were calibrated using data from in-vitro experimental tests (Harris et al., 2016). The following load conditions were applied to the femur: 20 N axial compression (neutral path), 20 N axial compression with 80 N anterior shear force, and 20 N axial compression with 80 N posterior shear force. Simultaneously for each loading condition, the knee was flexed from 0 – 120 degrees. A circular axis system was used to describe the motion of the femur relative to the tibia.INTRODUCTION
METHODS
Ceramic heads are used in hip revision surgery to mitigate corrosion concerns. Manufacturers recommend using a pristine titanium sleeve in conjunction with a well-fixed metal stem to prevent early failure of the ceramic head. However, the influence of impact force, head size, and sleeve offset on pull-off strength and seating displacement of a revision head assembly is not fully understood. Therefore, the purpose of this study was to investigate the pull-off strength and displacement of commercially available revision ceramic heads and titanium taper sleeve offsets (BIOLOX OPTION, CeramTec GmbH, Plochingen, Germany) while covering a range of clinically relevant impaction forces. Two head sizes (28 mm, n = 12 and 36 mm, n = 12) and two taper adapter sleeve offsets (small, n = 12 and extra-large, n = 12) were tested in this study. A dynamic impaction rig was constructed to seat the head, sleeve, and stem assembly (Fig. 1). Consistent impaction forces were achieved by dropping a hammer fixed to a lever arm from a pre-determined height onto a standard impactor instrumented with a piezoelectric force sensor (PCB Piezotronics Inc.). Axially applied forces of 2 kN and 6 kN were used to cover a range of typical impaction forces. Three non-contact differential variable reluctance transducers (LORD Sensing Systems) were used to track the displacement of the head relative to the stem. Subsequently, samples were transferred to a servo hydraulic testing machine, and a pull-off test was carried out per ISO 7206–10 to measure the disassembly force.Introduction
Methods
One of the key factors responsible for altered kinematics and joint stability following contemporary total knee arthroplasty (TKA) is resection of the anterior cruciate ligament (ACL). Therefore, retaining the ACL is often considered to be the “holy grail” of TKA. However, ACL retention can present several technical challenges, and in some cases may not be viable due to an absent or non-functional ACL. Therefore, the goal of this research was to investigate whether substitution of ACL function through an anterior post mechanism could improve kinematic deficits of contemporary posterior cruciate ligament (PCL) retaining (CR) implants. This was done using KneeSIM, a previously established dynamic simulation tool based on an Oxford-rig setup. Deep knee bend, chair-sit, stair-ascent and walking were simulated for a contemporary ACL sacrificing (CR) implant, two ACL retaining implants, and an ACL substituting and PCL retaining implant. The motion of the femoral condyles relative to the tibia was recorded for kinematic comparisons. Our results revealed that, like ACL retaining implants, the ACL substituting implant could also provide kinematic improvements over contemporary ACL sacrificing implants by reducing early posterior femoral shift and preventing paradoxical anterior sliding. Such ACL substituting implants may be a valuable addition to the armament of joint surgeons, allowing them to provide improved knee function even when ACL retention is not feasible. Further research is required to investigate this mechanism in vitro and in vivo to verify the results of the simulations, and to determine whether kinematic improvements translate into improved clinical outcomes.
Dual-mobility (DM) liners provide increased range of motion and stability. However, large head diameters have been associated with anterior hip pain due to impingement with surrounding soft-tissues, particularly the iliopsoas. Further, during hip extension the liner can get trapped due to anterior soft-tissue impingement that resists rotation being imparted to the liner from posterior stem-liner contact. Over time this can cause liner rim damage, leading to intra-prosthetic dislocation of the small diameter inner head. To address this, an anatomically contoured dual mobility (ACDM) liner was designed to reduce the volume of the liner below the equator that can interact with soft-tissues The average uniaxial stiffness (350 N/mm), and average dimensions (width × thickness = 14mm × 4mm) of 10 cadaver psoas tendon samples were determined in a separate study. The iliopsoas tendon was modelled as a Yeoh hyper-elastic material, and the material constants were tuned to match the experimental uniaxial test data. Cadaver specific FEA models were created for 5 specimens (10 hips) using computed tomography (CT) scans. The implant components were modeled as being rigid relative to the iliopsoas tendon. The iliopsoas tendon was modelled as extending from its insertion point on the lesser trochanter to the psoas notch on the pelvis for hip flexion angles of −15°, 0°, 15° and 30°. Appropriately sized DM components were implanted virtually for each specimen. Once placed in its proper position, the liner was rotated about the flexion axis until it contacted the stem posteriorly to represent its orientation during hip extension (Introduction
Methods
Dual Mobility (DM) implants have gained popularity for the treatment and prevention of hip dislocation, with increased stability provided by a large diameter mobile insert. However, distal regions of the insert may impinge on soft tissues like the iliopsoas, leading to groin pain. Additionally, soft-tissue impingement may trap the mobile insert, leading to excessive loading of the insert rim from engagement with the femoral neck and subsequent intra-prosthetic dislocation. To address this, an Anatomically Contoured Dual Mobility (ACDM) insert with a soft-tissue friendly distal geometry was developed Fluoroscopic imaging was used to evaluate soft-tissue interaction with ACDM and conventional DM inserts in four cadaver hips (Introduction
Methods
In Cruciate Retaining (CR) Total Knee Arthroplasty (TKA), the Posterior Cruciate Ligament (PCL) is preserved but the Anterior Cruciate Ligament (ACL) is sacrificed. In contemporary CR implants, failure to substitute for ACL function causes abnormal knee motion, with the femur being located excessively posterior on the tibia in full extension ( The kinematics of an ACL-preserving implant, the ASCR implant, and a contemporary CR implant during deep knee bend was simulated using LifeMOD KneeSIM software (Introduction
Methods
Contemporary PCL sacrificing Total Knee Arthroplasty (TKA) implants (CS) consist of symmetric medial and lateral tibial articular surfaces with high anterior lips designed to substitute for the stability of the native PCL. However, designs vary significantly across implant systems in the level of anteroposterior constraint provided. Therefore, the goal of this study was to investigate kinematics of two CS designs with substantially different constraint levels. The hypothesis was that dynamic knee simulations could show the effect of implant constraint on kinematics of CS implants. LifeModeler KneeSIM software was used to analyze contemporary CS TKA (X) with a symmetric and highly dished tibia and contemporary CS TKA (Y) with a symmetric tibia having flat sections bounded by high anterior and posterior lips, during simulated deep knee bend and chair sit. The flat sections of CS-Y implant are designed to allow freedom prior to motion restriction by the implant lips. Components were mounted on an average knee model created from Magnetic Resonance Imaging (MRI) data of 40 normal knees. Relevant ligament/tendon insertions were obtained from the MRI based 3D models and tissue properties were based on literature values. The condyle center motions relative to the tibia were used to compare the different implant designs. In vivo knee kinematics of healthy subjects from published literature was used for reference.INTRODUCTION
METHODS
Femoral head diameter has a major influence on stability and dislocation resistance of the hip joint after Total Hip Arthroplasty (THA). Dual Mobility (DM) implants can also reduce the risk of dislocation due the large diameter mobile liner which forms the femoroacetbular articulation. However, recent studies have shown that large head prostheses can directly impinge against native soft tissues, particularly the iliopsoas, leading to anterior hip pain. Dual mobility systems have emerged as a revision option in the treatment of failed metal on metal devices because of the high incidence of post revision instability secondary to abductor loss and need for capsulectomy. We hypothesized that an Anatomically Contoured Dual Mobility (ACDM) liner could provide joint stability while better accommodating the soft tissues surrounding the hip joint. The dislocation resistance of a 44 mm ACDM implant was compared to that of a 44 mm conventional DM liner. Both implants consisted of a 28 mm inner small diameter head and the liner was abducted to be in the worst case position for dislocation (Fig. 1). The ACDM liner was based on a 44 mm sphere with smaller radii used to contour the peripheral region below the equator of the liner. MSC Adams was used for dynamic simulations based on two previously described dislocation modes: (A) Posterior dislocation (at 90° hip flexion) with internal rotation of the hip and a posterosuperior directed joint force; (B) Posterior dislocation (starting at 90° flexion) with combined hip flexion and adduction and a posteromedial force direction (Fig. 2). Impingement-free motion (motion without neck impingement against the acetabular cup) and jump distance (head separation from acetabulum at dislocation) were measured for each implant. The acetabular cup was placed at 42.5° abduction and 19.7° anteversion, while the femoral component was anteverted by 9.75° based on published data.INTRODUCTION
METHODS
While kinematic abnormalities of contemporary TKA implants have been well established, a solution has not yet been achieved. We hypothesized that contemporary TKA implants are not compatible with normal soft-tissue function and normal knee motion. We propose a novel technique for reverse engineering advanced implant articular surfaces (biomimetic surface), by using accurate 3D kinematics of normal knees. This technique accounts for surgical placement of the implants, and allows design of tibial and femoral articular surfaces in conjunction. Magnetic resonance imaging was used to create 3D knee models of 40 normal subjects (24 male, 16 female, age 29.9 ± 9.7 years), and bi-planar fluoroscopy was used to capture 3D knee motion during a deep knee bend. These data were combined to create a 3D virtual representation of an average normal knee and its motion pathway. A TKA femoral component was mounted on the average knee, and moved through its normal kinematic pathway to carve out an articular surface from a tibial template (Fig. 1 and 2). The geometry of the resulting biomimetic tibia was compared to that of the native tibia, and a contemporary TKA tibial insert that uses the same femoral component.Introduction:
Methods:
Large diameter femoral heads have been used successfully to prevent dislocation after Total Hip Arthroplasty (THA). However, recent studies show that the peripheral region of contemporary femoral heads can directly impinge against the native soft-tissues, particularly the iliopsoas, leading to activity limiting anterior hip pain. This is because the spherical articular surface of contemporary prosthesis overhangs beyond that of the native anatomy (Fig. 1). The goal of this research was to develop an anatomically shaped, soft-tissue friendly large diameter femoral head that retains the benefits of contemporary implants. Various Anatomically Contoured femoral Head (ACH) designs were constructed, wherein the articular surface extending from the pole to a theta (θ) angle, matched that of contemporary implants (Fig. 2). However, the articular surface in the peripheral region was moved inward towards the femoral head center, thereby reducing material that could impinge on the soft-tissues (Fig. 1 and Fig. 2). Finite element analysis was used to determine the femoroacetabular contact area under peak in vivo loads during different activities. Dynamic simulations were used to determine jump distance prior to posterior dislocation under different dislocation modes. Published data was used to compare the implant articular geometry to native anatomy (Fig. 3). These analyses were used to optimize the soft-tissue relief, while retaining the load bearing contact area, and the dislocation resistance of conventional implants.Introduction:
Methods:
Dual Mobility (DM) hip implants have gained popularity for the treatment and preventions of instability. In DM implants a large diameter mobile insert matches the native femoral head size. However, studies have shown that the peripheral regions of such large diameter implants overhang beyond the native anatomy and can directly impinge against nearby soft tissues, especially the iliopsoas, leading to groin pain (Fig. 1). Soft-tissue impingement can also trap the mobile DM insert, leading to damage of its peripheral rim, which secures the small diameter inner head (Fig. 2). The goal of this research was to develop an anatomically contoured soft-tissue friendly DM insert. Various Anatomically Contoured Dual Mobility (ACDM) insert designs were constructed, wherein the outer articular surface extending from the pole to a theta (θ) angle, matched that of contemporary implants (Fig. 3). However, the articular surface in the peripheral region was moved inward towards the center, thereby reducing implant volume that could impinge on the soft tissue (Fig. 1 and Fig. 3). Finite element analyses were used to determine the insert-acetabular contact area under peak in vivo loads during different activities. Finite element analysis was also used to determine resistance to extraction of the inner head. Published data was used to compare the implant articular geometry to native anatomy. These analyses were used optimize the soft-tissue relief, while matching the load bearing contact area and the resistance to extraction of the inner head in contemporary implants.Introduction:
Methods:
Large diameter femoral heads provide increased range-of-motion and reduced dislocation rates compared to smaller diameter femoral heads. However, several recent studies have reported that contemporary large head prostheses can directly impinge against the local soft tissues leading to anterior hip pain. To address this we developed a novel Anatomically Contoured large diameter femoral Head (ACH) that maintains the profile of a large diameter femoral head over a hemispherical portion and then contours inward the distal profile of the head for soft-tissue relief. We hypothesized that the distal contouring of the ACH articular surface would not affect contact area. The impact of component placement, femoral head to acetabular liner radial clearance, and joint loading during different activities was investigated. A finite element model was used to assess the femoroacetabular contact area of a 36 mm diameter conventional head and a 36 mm ACH (Fig. 1). It included a rigid acetabular shell, plastically deformable UHMWPE acetabular liner, rigid femoral head and rigid femoral stem. The femoral stem was placed at 0°, 10° and 20° of anteversion. The acetabular shell and liner were placed in 20°, 40° and 60° of abduction and 0°, 20° and 40° of anteversion. The femoral head to acetabular liner radial clearances modeled were 0.06 mm, 0.13 mm and 0.5 mm. Three loading cases corresponding to peak in vivo loads during walking, chair sit and deep-knee bend were analyzed (Fig. 2). This allowed a range of component positions and maximum joint loads to be studied.Introduction
Methods
Dual mobility (DM) implants provide increased stability and range-of-motion through the use of a large diameter mobile liner articulating against an acetabular shell. However, recent studies have reported that such contemporary large head prostheses can directly impinge against the local soft tissues leading to anterior hip pain. To address this drawback, a novel Anatomically Contoured Dual Mobility (ACDM) liner was developed that maintains the outer spherical geometry over an approximately hemispherical portion and then contours inward the distal profile of the DM liner for soft-tissue relief. The extent of the inner profile encapsulating the small diameter head is increased to provide more coverage of the head and maintain the inner head pullout force. We hypothesized that the ACDM liner for soft-tissue relief would not affect retention of the small diameter inner head or liner-acetabular load-bearing contact area. A finite element model to evaluate head retention and contact mechanics was created with a rigid acetabular shell, a plastically deformable UHMWPE DM liner, a rigid femoral head and a rigid femoral stem. For the head retention analysis, the extent of head coverage (Fig. 1) was optimized to match the inner head pullout force of a conventional DM liner. Contact mechanics of a conventional DM and ACDM liner were analyzed at the maximum joint load of three activities: gait, deep-knee bend and chair sit. One set of simulations was completed with the mobile liner and head axes aligned and another with the axes mal-aligned so that the mobile liner rim was adjacent to the femoral stem neck and the potential area of contact was away from the mobile liner apex. This allowed a broader range of potential contact to be assessed including what was determined to be a worst-case alignment.Introduction
Methods
Contemporary Posterior Cruciate Ligament (PCL) retaining TKA implants (CR) are associated with well-known kinematic deficits, such as absence of medial pivot motion, paradoxical anterior femoral sliding, and posterior femoral subluxation at full extension. The hypothesis of this study was that a biomimetic implant, reverse engineered by using healthy knee kinematics to carve the tibial articular surface, could restore normal kinematic patterns of the knee. Kinematics of the biomimetic CR and two contemporary CR implants (A, B) were evaluated during simulated deep knee bend and chair-sit in LifeModeler KneeSIM™ software. Anteroposterior motion of the medial and lateral femoral condyle centers was measured relative to a tibial origin. The implants were mounted on an average knee model created from magnetic resonance imaging (MRI) of 40 healthy knees. The medial and lateral collateral ligaments, posterior cruciate ligament, quadriceps mechanism, and the overall capsular tension were modeled. The soft-tissue insertions were obtained from the average knee model, and the mechanical properties were obtained from literature. In vivo knee kinematics of healthy subjects from published literature was used for reference.Introduction:
Methods:
ACL retaining (BCR) Total Knee Arthroplasty (TKA) provides more normal kinematics than ACL sacrificing (CR) TKA. However, in the native knee the ACL and the asymmetric shape of the tibial articular surface with a convex lateral plateau are responsible for the differential medial/lateral femoral rollback (medial pivot). Therefore, the hypothesis of this study was that an asymmetric biomimetic articular surface together with ACL preservation would better restore native knee kinematics than retention of the ACL alone. Normal knee kinematics from bi-planar fluoroscopy was used to reverse engineer the tibial articular surface of the biomimetic implant. This was achieved by moving the femoral component through the healthy knee kinematics and removing material from a tibial template. LifeModeler KneeSIM software was used to analyze a biomimetic BCR implant (asymmetric tibia with convex lateral surface), a contemporary BCR (symmetric shallow dished tibia) and a contemporary CR (symmetric dished tibia) implant during simulated deep knee bend and chair sit. Components were mounted on an average bone model created from Magnetic Resonance Imaging (MRI) data of 40 normal knees. The soft-tissue insertions were obtained from the average knee model and the mechanical properties were obtained from literature. Femoral condyle center motions relative to the tibia were used to compare different implant designs. In vivo knee kinematics of healthy subjects from published literature was used for reference.INTRODUCTION
METHODS
Femoral head diameter has a major influence on stability and dislocation resistance after Total Hip Arthroplasty (THA). Although routine use of large heads is common, several recent studies have shown that contemporary large head prostheses can directly impinge against native soft tissues, particularly the iliopsoas which wraps around the femoral head, leading to refractory anterior hip pain. To address this, we developed a novel Anatomically Contoured large diameter femoral Head (ACH). We hypothesized that anatomical contouring of the ACH implant for soft tissue relief would not compromise dislocation resistance, and the ACH implant would provide increased stability compared to small heads. In this study the dislocation resistance of a 36 mm ACH was compared to that of 28 mm and 36 mm contemporary heads. The ACH implant was based on a 36 mm sphere with smaller radii used to contour the peripheral region below the equator of the head. MSC Adams was used for dynamic simulations based on two previously described dislocation modes: (A) Posterior dislocation (at 90° hip flexion) with internal rotation of the hip and a posterosuperior directed joint force; (B) posterior dislocation (starting at 90° flexion) with combined hip flexion and adduction and a posteromedial force direction (Fig. 1). Impingement-free motion (motion without neck impingement against the acetabular liner) and jump distance (head separation from acetabulum prior to dislocation) were measured to evaluate the dislocation risk of each implant. The acetabular cup was placed at 42.5° abduction and 19.7° anteversion, while the femoral component was anteverted by 9.75° based on published data.INTRODUCTION
METHODS