Does the Proximal Humerus Nail with 2 Distal Screws Provide Sufficient Rotational Stability?
The Institutional Review Board waived the requirement for informed consent for this study because it did not involve any human or animal subjects, and thus did not require Institutional Review Board approval. Methods Computed tomography scanning with a 1-mm slice thickness was performed on the humerus of a healthy 20-year-old person. A solid model of the humerus was reconstructed using 3D-DOCTOR software (version 18.0, Able Software Corp.) to detect the boundary edge in each slice and Rapidform software (INUS Technology Inc.) to stack the slices and convert the images into an Initial Graphics Exchange Specification-type model. Then, the dimensions were keyed into a computer-aided design (CAD) program (CATIA 2016) to reconstruct 3-dimensional models. The geometrical dimensions of the Humerus Interlocking Nail System (TDM) were obtained from the implant manufacturer’s catalog. The geometric model of the humerus and internal fixation were imported into the FEA preprocessing software HyperMesh 18.0 (Altair) to draw the mesh. After the convergence measurement, the mesh size was determined to be 0.5 mm. FEA was performed using MSC-Marc 18.0 (MSC Software Inc.). A geometric model of the implants was assembled as a humerus model (length, 160–200 mm; diameter, 8 mm; and 6 proximal holes and 3 distal holes). The proximal screw holes were unpenetrated and the distal screw holes were penetrated. A 1-mm fracture gap was applied at the surgical neck to model the fracture line of the humeral bone. A fracture gap of up to 1 mm is tolerated, and a transverse osteotomy gap of more than 2 mm reduces healing. Therefore, an osteotomy gap of 1 mm was applied in this study . The stress distribution applied to the screws and bone holes was calculated in 3 groups divided according to the number and location: group 1 using all 3 distal locking holes; group 2 using the dynamic hole and the proximal static hole only to fix a total of 2 screws; and group 3 using the dynamic hole and the distal static screw only to fix a total of 2 screws . Materials Material properties Materials were assumed to be linearly homogenous, isotropic, and elastic. Although bones are viscoelastic, they are almost always considered elastic because of the relatively low physiologic loading involved. Therefore, most studies have assumed the elasticity of bone, and this study also assumed the same. The heterogeneous properties of the bone were also applied to specific cases, but in most cases, homogeneity and isotropy of the bone were assumed and applied in this study. The humerus intramedullary nail (Humerus Interlocking Nail System; TDM) was composed of a Ti6Al4V 64 alloy. The material properties of the bony models were obtained from a previous article. The cortical and cancellous bones were assumed to have elastic moduli of 16.7 GPa and 279 MPa, respectively, and Poisson’s ratios of 0.3 and 0.34, respectively, were used for normal bone. By applying a 20% reduced value for normal bone quality as an assumption of osteoporotic bone, the elastic moduli of cortical and cancellous bone were modeled at 13.3 GPa and 220 MPa, respectively . Boundary and loading conditions The attachment muscles of the humeral head shared 6 degrees of freedom in the same center of rotation with the supraspinatus, subscapularis, subscapularis, and teres minor (dx, dy, dz, Rx, Ry, and Rz). Translational and rotational movements were fixed . Since the bone holes of all screws used for the proximal and distal were fastened by penetration, the screw and bone tying conditions were applied (tied with 6 degree of freedom: dx, dy, dz, Rx, Ry, and Rz). The transepicondylar area, a distal part of the bone, linked 6 degrees of freedom as the center of rotation, and +3,000 N·mm torque was applied in the Rx direction . The friction coefficient was 0.3 for each bone-implant interaction and implant-implant interaction. Observation index To evaluate the failure of the model, the maximum stress values under von Mises stresses were calculated around the proximal and distal locking screws and bone holes in all 3 groups. Maximum stress values of the bone holes under component 11 and 22 stresses were calculated to evaluate the possibility of model failure in the tensile or compressive direction. Component 11 and 22 stresses were normalized based on the tensile strength of 135 MPa and compression of 200 MPa. 

Computed tomography scanning with a 1-mm slice thickness was performed on the humerus of a healthy 20-year-old person. A solid model of the humerus was reconstructed using 3D-DOCTOR software (version 18.0, Able Software Corp.) to detect the boundary edge in each slice and Rapidform software (INUS Technology Inc.) to stack the slices and convert the images into an Initial Graphics Exchange Specification-type model. Then, the dimensions were keyed into a computer-aided design (CAD) program (CATIA 2016) to reconstruct 3-dimensional models. The geometrical dimensions of the Humerus Interlocking Nail System (TDM) were obtained from the implant manufacturer’s catalog. The geometric model of the humerus and internal fixation were imported into the FEA preprocessing software HyperMesh 18.0 (Altair) to draw the mesh. After the convergence measurement, the mesh size was determined to be 0.5 mm. FEA was performed using MSC-Marc 18.0 (MSC Software Inc.). A geometric model of the implants was assembled as a humerus model (length, 160–200 mm; diameter, 8 mm; and 6 proximal holes and 3 distal holes). The proximal screw holes were unpenetrated and the distal screw holes were penetrated. A 1-mm fracture gap was applied at the surgical neck to model the fracture line of the humeral bone. A fracture gap of up to 1 mm is tolerated, and a transverse osteotomy gap of more than 2 mm reduces healing. Therefore, an osteotomy gap of 1 mm was applied in this study . The stress distribution applied to the screws and bone holes was calculated in 3 groups divided according to the number and location: group 1 using all 3 distal locking holes; group 2 using the dynamic hole and the proximal static hole only to fix a total of 2 screws; and group 3 using the dynamic hole and the distal static screw only to fix a total of 2 screws . 

Material properties Materials were assumed to be linearly homogenous, isotropic, and elastic. Although bones are viscoelastic, they are almost always considered elastic because of the relatively low physiologic loading involved. Therefore, most studies have assumed the elasticity of bone, and this study also assumed the same. The heterogeneous properties of the bone were also applied to specific cases, but in most cases, homogeneity and isotropy of the bone were assumed and applied in this study. The humerus intramedullary nail (Humerus Interlocking Nail System; TDM) was composed of a Ti6Al4V 64 alloy. The material properties of the bony models were obtained from a previous article. The cortical and cancellous bones were assumed to have elastic moduli of 16.7 GPa and 279 MPa, respectively, and Poisson’s ratios of 0.3 and 0.34, respectively, were used for normal bone. By applying a 20% reduced value for normal bone quality as an assumption of osteoporotic bone, the elastic moduli of cortical and cancellous bone were modeled at 13.3 GPa and 220 MPa, respectively . Boundary and loading conditions The attachment muscles of the humeral head shared 6 degrees of freedom in the same center of rotation with the supraspinatus, subscapularis, subscapularis, and teres minor (dx, dy, dz, Rx, Ry, and Rz). Translational and rotational movements were fixed . Since the bone holes of all screws used for the proximal and distal were fastened by penetration, the screw and bone tying conditions were applied (tied with 6 degree of freedom: dx, dy, dz, Rx, Ry, and Rz). The transepicondylar area, a distal part of the bone, linked 6 degrees of freedom as the center of rotation, and +3,000 N·mm torque was applied in the Rx direction . The friction coefficient was 0.3 for each bone-implant interaction and implant-implant interaction. Observation index To evaluate the failure of the model, the maximum stress values under von Mises stresses were calculated around the proximal and distal locking screws and bone holes in all 3 groups. Maximum stress values of the bone holes under component 11 and 22 stresses were calculated to evaluate the possibility of model failure in the tensile or compressive direction. Component 11 and 22 stresses were normalized based on the tensile strength of 135 MPa and compression of 200 MPa. 

Materials were assumed to be linearly homogenous, isotropic, and elastic. Although bones are viscoelastic, they are almost always considered elastic because of the relatively low physiologic loading involved. Therefore, most studies have assumed the elasticity of bone, and this study also assumed the same. The heterogeneous properties of the bone were also applied to specific cases, but in most cases, homogeneity and isotropy of the bone were assumed and applied in this study. The humerus intramedullary nail (Humerus Interlocking Nail System; TDM) was composed of a Ti6Al4V 64 alloy. The material properties of the bony models were obtained from a previous article. The cortical and cancellous bones were assumed to have elastic moduli of 16.7 GPa and 279 MPa, respectively, and Poisson’s ratios of 0.3 and 0.34, respectively, were used for normal bone. By applying a 20% reduced value for normal bone quality as an assumption of osteoporotic bone, the elastic moduli of cortical and cancellous bone were modeled at 13.3 GPa and 220 MPa, respectively . 

The attachment muscles of the humeral head shared 6 degrees of freedom in the same center of rotation with the supraspinatus, subscapularis, subscapularis, and teres minor (dx, dy, dz, Rx, Ry, and Rz). Translational and rotational movements were fixed . Since the bone holes of all screws used for the proximal and distal were fastened by penetration, the screw and bone tying conditions were applied (tied with 6 degree of freedom: dx, dy, dz, Rx, Ry, and Rz). The transepicondylar area, a distal part of the bone, linked 6 degrees of freedom as the center of rotation, and +3,000 N·mm torque was applied in the Rx direction . The friction coefficient was 0.3 for each bone-implant interaction and implant-implant interaction. 

To evaluate the failure of the model, the maximum stress values under von Mises stresses were calculated around the proximal and distal locking screws and bone holes in all 3 groups. Maximum stress values of the bone holes under component 11 and 22 stresses were calculated to evaluate the possibility of model failure in the tensile or compressive direction. Component 11 and 22 stresses were normalized based on the tensile strength of 135 MPa and compression of 200 MPa. 

Stress Distribution for the Normal Bone Model FEA of the stress changes in the cortical bone holes and screws The stress distribution according to the screw arrangement was calculated. The maximum von Mises stress in group 1 was 30.5 MPa, group 2 was 31.3 MPa, and group 3 was 32.4 MPa. There were no significant differences between these 3 groups . In the stress of component 11 (longitudinal direction), the tensile strength of each group was 25.4, 26.2, and 26.8 MPa, respectively, and the compressive strength was 33.9, 34.9, and 36.0 MPa, respectively, so there was no difference . Component 22 (transversal direction) stress showed no difference in transversal direction stress as tensile strength was 21.2, 22.7, and 22.9 MPa in each group, and compressive strength was 30.9, 27.2, and 31.7 MPa, respectively . The distal screw number and location will not affect the stability of the bone. It was indirectly proved that it is possible to fix the distal screw with only 2 screws. FEA of the stress changes in the nail, screws, and nail screw connection As a result of the stress distribution applied to the nail and screw, the maximum von Mises stress was 292.9, 280.9, and 340.9 MPa in groups 1, 2, and 3, respectively. The equivalent stress distribution was similar, and a 10% increase was shown in group 3, but the effect was not significant to the extent that failure load was not reached. In the region of the proximal screw, all groups showed 86.8, 88.2, and 86.8 MPa, respectively. In the locking screw area, 53.9, 70.4, and 69.8 MPa were shown, respectively. In the case of the screws in the proximal part, the stress was uniformly generated, and there were no significant differences between these 3 groups. In the distal screws part, the stress was the lowest in group 1, but compared to the other 2 groups, the stress was not enough to lead to failure. All 3 groups were stable . Stress Distribution for the Osteoporotic Bone Model FEA of the stress changes in the cortical bone holes and screws As a result of the stress distribution according to the screw arrangement in the osteoporotic bone with the elastic modulus reduced by 20%, the maximum von Mises stress might be smaller than 30.4 MPa in group 1, 29.5 MPa in group 2, and 30.0 MPa in group 3 . In the osteoporotic bone, the effect of screw placement and the number of screws did not have significant difference. FEA of the stress changes in the nail and screws, and nail screw connection As a result of the stress distribution applied to the nail and screw, the maximum von Mises stress was 288.2, 283.3, and 327.5 MPa, respectively, in group 1, group 2, and group 3, like the stress distribution results in the normal bone. The maximum von Mises stress was 84.6, 84.0, and 87.5 MPa, respectively, in the region of the proximal screw and 53.7, 74.1, and 63.5 MPa, respectively, in the region of the distal screw. The stress distribution was the lowest in group 1 of the distal screw region, but there was no significant difference compared to that in the other 2 groups ( and ). 

FEA of the stress changes in the cortical bone holes and screws The stress distribution according to the screw arrangement was calculated. The maximum von Mises stress in group 1 was 30.5 MPa, group 2 was 31.3 MPa, and group 3 was 32.4 MPa. There were no significant differences between these 3 groups . In the stress of component 11 (longitudinal direction), the tensile strength of each group was 25.4, 26.2, and 26.8 MPa, respectively, and the compressive strength was 33.9, 34.9, and 36.0 MPa, respectively, so there was no difference . Component 22 (transversal direction) stress showed no difference in transversal direction stress as tensile strength was 21.2, 22.7, and 22.9 MPa in each group, and compressive strength was 30.9, 27.2, and 31.7 MPa, respectively . The distal screw number and location will not affect the stability of the bone. It was indirectly proved that it is possible to fix the distal screw with only 2 screws. FEA of the stress changes in the nail, screws, and nail screw connection As a result of the stress distribution applied to the nail and screw, the maximum von Mises stress was 292.9, 280.9, and 340.9 MPa in groups 1, 2, and 3, respectively. The equivalent stress distribution was similar, and a 10% increase was shown in group 3, but the effect was not significant to the extent that failure load was not reached. In the region of the proximal screw, all groups showed 86.8, 88.2, and 86.8 MPa, respectively. In the locking screw area, 53.9, 70.4, and 69.8 MPa were shown, respectively. In the case of the screws in the proximal part, the stress was uniformly generated, and there were no significant differences between these 3 groups. In the distal screws part, the stress was the lowest in group 1, but compared to the other 2 groups, the stress was not enough to lead to failure. All 3 groups were stable . 

The stress distribution according to the screw arrangement was calculated. The maximum von Mises stress in group 1 was 30.5 MPa, group 2 was 31.3 MPa, and group 3 was 32.4 MPa. There were no significant differences between these 3 groups . In the stress of component 11 (longitudinal direction), the tensile strength of each group was 25.4, 26.2, and 26.8 MPa, respectively, and the compressive strength was 33.9, 34.9, and 36.0 MPa, respectively, so there was no difference . Component 22 (transversal direction) stress showed no difference in transversal direction stress as tensile strength was 21.2, 22.7, and 22.9 MPa in each group, and compressive strength was 30.9, 27.2, and 31.7 MPa, respectively . The distal screw number and location will not affect the stability of the bone. It was indirectly proved that it is possible to fix the distal screw with only 2 screws. 

As a result of the stress distribution applied to the nail and screw, the maximum von Mises stress was 292.9, 280.9, and 340.9 MPa in groups 1, 2, and 3, respectively. The equivalent stress distribution was similar, and a 10% increase was shown in group 3, but the effect was not significant to the extent that failure load was not reached. In the region of the proximal screw, all groups showed 86.8, 88.2, and 86.8 MPa, respectively. In the locking screw area, 53.9, 70.4, and 69.8 MPa were shown, respectively. In the case of the screws in the proximal part, the stress was uniformly generated, and there were no significant differences between these 3 groups. In the distal screws part, the stress was the lowest in group 1, but compared to the other 2 groups, the stress was not enough to lead to failure. All 3 groups were stable . 

FEA of the stress changes in the cortical bone holes and screws As a result of the stress distribution according to the screw arrangement in the osteoporotic bone with the elastic modulus reduced by 20%, the maximum von Mises stress might be smaller than 30.4 MPa in group 1, 29.5 MPa in group 2, and 30.0 MPa in group 3 . In the osteoporotic bone, the effect of screw placement and the number of screws did not have significant difference. FEA of the stress changes in the nail and screws, and nail screw connection As a result of the stress distribution applied to the nail and screw, the maximum von Mises stress was 288.2, 283.3, and 327.5 MPa, respectively, in group 1, group 2, and group 3, like the stress distribution results in the normal bone. The maximum von Mises stress was 84.6, 84.0, and 87.5 MPa, respectively, in the region of the proximal screw and 53.7, 74.1, and 63.5 MPa, respectively, in the region of the distal screw. The stress distribution was the lowest in group 1 of the distal screw region, but there was no significant difference compared to that in the other 2 groups ( and ). 

As a result of the stress distribution according to the screw arrangement in the osteoporotic bone with the elastic modulus reduced by 20%, the maximum von Mises stress might be smaller than 30.4 MPa in group 1, 29.5 MPa in group 2, and 30.0 MPa in group 3 . In the osteoporotic bone, the effect of screw placement and the number of screws did not have significant difference. 

As a result of the stress distribution applied to the nail and screw, the maximum von Mises stress was 288.2, 283.3, and 327.5 MPa, respectively, in group 1, group 2, and group 3, like the stress distribution results in the normal bone. The maximum von Mises stress was 84.6, 84.0, and 87.5 MPa, respectively, in the region of the proximal screw and 53.7, 74.1, and 63.5 MPa, respectively, in the region of the distal screw. The stress distribution was the lowest in group 1 of the distal screw region, but there was no significant difference compared to that in the other 2 groups ( and ). 

In our study, using 2 distal screws demonstrated comparable rotational stability to using 3 screws in proximal humerus shaft fractures. Only a few studies addressed the optimal number of distal screws in long nails used for long bone fractures, such as those in the tibia and femur. Regarding tibia shaft fractures, a comparison between using 2 versus 3 distal screws revealed no statistically significant difference. It was suggested that fixation with only 2 screws was sufficient. In femur fractures, studies have shown no significant clinical or radiological discrepancy when comparing the dynamic locking and unlocking of distal screws. In our study, group 1 exhibited the most favorable outcome, displaying the lowest stress levels and superior stability across all bone holes, nails, proximal screws, and distal screws. In the normal bone model, group 2 revealed elevated stress levels on distal screws; in the osteoporotic bone model, group 3 exhibited increased stress on distal screws. Throughout all groups, stress levels remained below the threshold of failure strength . Hence, it can be inferred that stability was maintained across all groups. Regarding the use of 2 distal screws, our results suggest a preference for using distal static screws in the normal bone model (group 3). In the assumed osteoporotic bone model, using proximal static screws (group 2) may be more favorable. Rotational stress, a significant factor affecting the humerus, was a predominant focus in our study, and the results were in line with previous findings. Our study systematically varied the number and location of screws, enabling the calculation of resultant stress on individual screws and bone holes . Recent reviews have highlighted iatrogenic nerve injury rates ranging from 4% to 32% in cases involving plate fixation or intramedullary nailing. Altering the number or location of screws could potentially decrease the risk of nerve damage further. In proximal femoral nailing procedures involving a distal locking screw, there are reports of increased radiation exposure by approximately 12 minutes. Such findings emphasize the importance of optimizing screw configuration to minimize the associated risks and complications during surgical interventions. Surgeries for humeral shaft fractures using nailing were found to have a longer operating time (74–87 minutes) and increased fluoroscopy exposure (59–100 seconds) when distal locking screws were used, compared to cases without distal locking. Although many cases of exposure to such excessive radiation are often overlooked, the relative risk of cancer among orthopedic surgeons exposed to higher radiation than the general population is 5.37. Our study has some limitations. FEA is completely virtual and introduces simplification in all aspects. Boundary conditions become difficult to handle owing to the anatomical realistic structure and motion of the shoulder joint. It is impossible to simulate the real boundary conditions with all the muscles, tendons, ligaments, and bones acting together. These material properties are not standardized, so it is difficult to accurately reproduce or verify experiments. In this study, a simple 2-part fracture was assumed. Future studies assuming more complex fractures will be needed. Most of the FEA research was fundamental rather than clinical research. Therefore, individual interpretation is required for clinical application. In proximal humerus nails, stress distribution displayed stability across von Mises stress, longitudinal, and transversal directions within bone holes, nails, and both proximal and distal locking screws. In the case of distal screws within the proximal humerus nail of a normal bone, the application of solely 2 screws did not compromise stability. In osteoporotic bones, the fixation of 2 distal screws is not anticipated to impact stability. 

