Evaluation of Bone Consolidation in External Fixation with an Electromechanical System

  Citation: Paulino, M.F.; Roseiro, L.M.; Balacó, I.; Neto, M.A.; Amaro, A.M. Evaluation of Bone Consolidation in External Fixation with an Electromechanical System. Appl. Sci. 2022,12, 2328. https://doi.org/ 10.3390/app12052328 Academic Editor: Antonio Scarano Received: 10 January 2022 Accepted: 16 February 2022 Published: 23 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). applied sciences Article Evaluation of Bone Consolidation in External Fixation with an Electromechanical System Maria F. Paulino 1,* , Luis M. Roseiro 1,2 , Inês Balacó3, Maria A. Neto 1and Ana M. Amaro 1 1Department of Mechanical Engineering, Center for Mechanical Engineering, Materials and Processes (CEMMPRE), University of Coimbra, 3030-788 Coimbra, Portugal; lroseir[email protected] (L.M.R.); [email protected] (M.A.N.); ana.amar[email protected] (A.M.A.) 2Polytechnic of Coimbra, ISEC, Rua Pedro Nunes–Quinta da Nora, 3030-199 Coimbra, Portugal 3 Pediatric Orthopedics Service of the Pediatric Hospital of Coimbra—CHUC, EPE, 3004-561 Coimbra, Portugal; [email protected] *Correspondence: [email protected]; Tel.: +351-239-790-700 Featured Application: The findings of this work can help doctors decide when it is appropriate to remove the external fixator. Abstract: The monitoring of fracture or osteotomy healing is vital for orthopedists to help advise, if necessary, secondary treatments for improving healing outcomes and minimizing patient suffering. It has been decades since osteotomy stiffness has been identified as one main parameter to quantify and qualify the outcome of a regenerated callus. Still, radiographic imaging remains the current standard diagnostic technique of orthopedists. Hence, with recent technological advancements, engineers need to use the new branches of knowledge and improve or innovate diagnostic technologies. An electromechanical system was developed to help diagnose changes in osteotomy stiffness treated with the external fixator LRS Orthofix ® . The concept was evaluated experimentally and numerically during fracture healing simulation using two different models: a simplified model of a human tibia, consisting of a nylon bar with a diameter of 30 mm, and a synthetic tibia with the anatomical model from fourth-generation Sawbones ® . Moreover, Sawbones ® blocks with different densities simulated the mechanical characteristics of the regenerated bone in many stages of bone callus growth. The experimental measurements using the developed diagnostic were compared to the numerically simulated results. For this external fixator, it was possible to show that the displacement in osteotomy was always lower than the displacement prescribed in the elongator. Nevertheless, a relationship was established between the energy consumption by the electromechanical system used to perform callus stimulus and the degree of osteotomy consolidation. Hence, this technology may lead to methodologies of mechanical stimulation for regenerating bone, which will play a relevant role for bedridden individuals with mobility limitations. Keywords: external fixation; micromovements; bone callus; electromechanical system; bone consolidation 1. Introduction External fixators are a surgical method of bone immobilization commonly applied to allow a fracture to heal appropriately, providing stability to long bones and soft tissue after a severe fracture. However, they can also be used to protect soft tissues after a burn or severe injury and as a procedure to correct bone misalignment and restore limb length, for example, in the case of dwarfism. The main advantage of external fixation is related to the quickness and facility of its application. Still, because it involves a surgical procedure, it needs to be performed by an orthopedic surgeon. When an external fixation system is applied, the risk of infection at the fracture site is minimal. However, there is some hypothesis that disease may occur at the connection between the rods and the Appl. Sci. 2022,12, 2328. https://doi.org/10.3390/app12052328 https://www.mdpi.com/journal/applsci Appl. Sci. 2022,12, 2328 2 of 17 skin [ 1 ]. External fixation systems establish a link in the fragmented bone, allowing load transfer between the parts and promoting interfragmentary movements for bone healing [ 2 ]. The interfragmentary movement is the relative movement between the bone fragments, which can appear during a patient’s weight-bearing activities. These micromovements in the fracture site are crucial to promoting bone callus growth and the control of bone regeneration [ 3 ]. Hence, the controlled physical activity of the patient might represent a mechanical stimulation that contributes to bone healing. Nevertheless, it is also worth stating that excessive mobility would disturb bone consolidation and perturb the healing process, leading to infections and bone misalignments [ 4 – 6 ]. Hence, these interfragmentary movements are crucial for the complex process of consolidating fracture [7]. Nevertheless, mechanical stimulation by patients’ weight-bearing activities is only possible in people who can walk. In the case of bedridden patients or of those with reduced mobility, the bone union is more complicated and may even be inhibited by other health problems in the patients that might cause improper or impaired bone healing, leading to a significant increase in treatment time. Hence, all biomechanical devices that can introduce controlled micromovements at the fracture site, contributing to the rehabilitation of patients and reducing the recovery time, are an alternative to help those patients. According to Barcik and Epari [ 8 ], the mechanical manipulation of the local fracture environment can significantly decrease fracture patients’ healing time, suggesting that additional experiments should be conducted to determine the best parameters. For instance, it is necessary to know when the interfragmentary motion needs to be stopped to allow for consolidation and establish the best stimulation/rest ratio. As radiographic evaluation shows some limitations, several authors are trying to develop methods of healing assessment that can give information about the progression of the mechanical properties of the fracture repair tissue. For example, using implants with sensing capabilities [ 9 , 10 ] or instrumented implants can improve the clinical outcome of total hip replacements [11,12]. These innovative implants can be implementable, provide therapeutic benefits, and have diagnostic capabilities. Surgical procedures involving bone regeneration and the identification of bone consolidation will help define the exact moment to remove the fixation system. Right now, this identification is assured by equipment having radiation emissions, such as densitometry or tomography. Hence, the development of tools allowing an early identification of the consolidation phase has applicability interest in the scope of patient recovery, particularly for bedridden situations. This study intends to contribute to the introduction of micromovements and the earlier identification of the healing phase of the regenerated bone through an electromechanical system. The presented electromechanical system may also play an essential role in bone stretching, as it can replace the manual introduction made by the patient, automating this process. The prototype was developed in the Orthofix ® monoplane external fixation system, but the concept can extend to another external fixation type where linear movement might occur. 2. Materials and Methods 2.1. Experimental Models This study considered a tibial osteotomy model in the central area of the diaphysis, stabilized using a unilateral external fixator LRS (Limb Reconstruction System), from Orthofix ® (Munich, Germany), supplied by Orthofix GmbH, Munich, Germany, used in a wide variety of situations. Two experimental models were implemented, one using a synthetic tibia, and another using a single rod representing a simplified tibia geometry [ 3 ]. The models did not include soft tissue. Figure 1illustrates the experimental model set with simplified and anatomical features. Appl. Sci. 2022,12, 2328 3 of 17 Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 17 Figure 1. Anatomical model/tibial simplified—external fixation. The anatomical model used a fourth-generation Sawbones® tibia, whose geometry has the CAD reference #3401. The model considered the mechanical characteristics of the cortical and trabecular bone as isotropic with the properties given in Table 1. The osteotomy fixation included the LRS unilateral external fixator application and the attached electromechanical system. Schanz pins of 6 mm in diameter and 150 mm in length allowed connecting the fixator to the bone. Schanz pins are produced in AISI 316L steel, and their mechanical properties are shown in Table 1. Table 1. Mechanical properties of cortical and trabecular bone. Mechanical properties of the external fixator. Designation Density [kg/m3] Young Modulus [GPa] Coefficient of Poisson Trabecular Bone, [13] 300 0.7 0.20 Cortical Bone, [13] 1800 17.0 0.30 External fixator Orthofix® LRS (AISI 7075 T6), [14] 2810 72.0 0.33 Schanz pin (AISI 316L), [14] 8027 200.0 0.27 As shown in Figure 1, the osteotomy was perpendicular to the mechanical axis of the bone, and the two opposite faces were at a distance of 10 mm. The axis of the fixator was 70 mm away from the mechanical axis of the tibia [15,16]. The closest distance from the Schanz pin to the osteotomy was 28 mm. All values were defined according to the indication of the medical team that supported the work. The electromechanical system presented in Figure 1 includes a motor and an electronic control unit, both placed in a box and coupled to the end of the mobile clamp of the fastener. The worm screw of the elongator is connected to the motor shaft and assures the axial movement of the worm screw. The principal components of the electromechanical system are presented in Figure 2. The system consists of a micromotor with the reference Rail Shanz pin Fixed Clamp Osteotomy (10 mm) Elongator Mobile clamp Electromechanical System Fixation System Orthofix® Fixation System Orthofix® Tibial Mechanical Axis Figure 1. Anatomical model/tibial simplified—external fixation. The anatomical model used a fourth-generation Sawbones ® tibia, whose geometry has the CAD reference #3401. The model considered the mechanical characteristics of the cortical and trabecular bone as isotropic with the properties given in Table 1. The osteotomy fixation included the LRS unilateral external fixator application and the attached electromechanical system. Schanz pins of 6 mm in diameter and 150 mm in length allowed connecting the fixator to the bone. Schanz pins are produced in AISI 316L steel, and their mechanical properties are shown in Table 1. Table 1. Mechanical properties of cortical and trabecular bone. Mechanical properties of the external fixator. Designation Density [kg/m3]Young Modulus [GPa] Coefficient of Poisson Trabecular Bone, [13] 300 0.7 0.20 Cortical Bone, [13] 1800 17.0 0.30 External fixator Orthofix®LRS (AISI 7075 T6), [14]2810 72.0 0.33 Schanz pin (AISI 316L), [14] 8027 200.0 0.27 As shown in Figure 1, the osteotomy was perpendicular to the mechanical axis of the bone, and the two opposite faces were at a distance of 10 mm. The axis of the fixator was 70 mm away from the mechanical axis of the tibia [ 15 , 16 ]. The closest distance from the Schanz pin to the osteotomy was 28 mm. All values were defined according to the indication of the medical team that supported the work. The electromechanical system presented in Figure 1includes a motor and an electronic control unit, both placed in a box and coupled to the end of the mobile clamp of the fastener. The worm screw of the elongator is connected to the motor shaft and assures the axial movement of the worm screw. The principal components of the electromechanical system Appl. Sci. 2022,12, 2328 4 of 17 are presented in Figure 2. The system consists of a micromotor with the reference A-max 16, Maxon ® (Sachseln, Suíça), Precious Metal Brushes CLL, 2 Watt, with a 16 mm diameter, which guarantees the axial displacement induction if the mobile clamp is loose, but also the blocking of the movement if required. The micromotor is controlled through a control unit developed on the Arduíno®programming platform. Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 of 17 A-max 16, Maxon® (Sachseln, Suíça), Precious Metal Brushes CLL, 2 Watt, with a 16 mm diameter, which guarantees the axial displacement induction if the mobile clamp is loose, but also the blocking of the movement if required. The micromotor is controlled through a control unit developed on the Arduíno® programming platform. The electromechanical system was powered with a battery and electronically activated using an Encoder MR Type M, 32 CPT, 2/3 Channel for positional control. The hardware systems of the Arduino® board used a DRV8801 plate from Texas Instruments® (Dallas, TX, USA), allowing the bidirectional control of a bridged DC micromotor. The board could supply a direct current up to 1 A, tolerating peak currents that might, for a few seconds, reach values of 2.8 A. Two conductors were needed to power the micromotor to the DRV8801 board, which would receive a voltage of 12 V between the “VMM” e the “GND”. The passage of electric current between the board and the micromotor was assured through the “motor+” e “motor−“ pins. Additionally, an encoder coupled to the micromotor obtained results in the elongator’s instant closing or opening position. The developed software integrates an interface implemented through the Azande® program allowing the user to define some parameters, such as motor speed and position. This program enables the selection of movement type, choosing the linear velocity of the movement, the displacement distance, and the number of repetitions to be performed. Figure 2. Connection of the electromechanical system into the external fixator Orthofix®. Because the micromotor needed a power supply to ensure the mechanical stimulus, there was also a mechanical resistance, and the motor current consumption was related to the mechanical resistance. Although the resistance depends on several factors, such as the sliding friction among several surfaces, the resistance opposition in the osteotomy mainly contributes to the system’s mechanical resistance. Hence, it is crucial to find a relationship between the rigidity of the osteotomy and the energy to supply to the motor that guarantees the necessary mechanical stimulus. Moreover, after calibration, the electromechanical system creates displacement relationships between the fixator clamp and the osteotomy. A support platform built-in Aluminum profile of Minitec® (30 × 30) was developed for the two models, allowing the positional adjustment of the components. This structure intended to replicate, in a simplified way, the positioning of the lower limb in the horizontal position, like in a bedridden patient. It included a fixed support, representing the position of knee connection, and a free axial support, which mimicked the relationship with the foot and guided the axial movement introduced in the assembly, as shown in Figure 3. The osteotomy’s displacement was characterized using a Mitutoyo® analogue comparator, with a measurement accuracy of 1 µm and located on one of the faces of Sawbones® block. Mobile Clamp Electromechanical System Figure 2. Connection of the electromechanical system into the external fixator Orthofix®. The electromechanical system was powered with a battery and electronically activated using an Encoder MR Type M, 32 CPT, 2/3 Channel for positional control. The hardware systems of the Arduino ® board used a DRV8801 plate from Texas Instruments ® (Dallas, TX, USA), allowing the bidirectional control of a bridged DC micromotor. The board could supply a direct current up to 1 A, tolerating peak currents that might, for a few seconds, reach values of 2.8 A. Two conductors were needed to power the micromotor to the DRV8801 board, which would receive a voltage of 12 V between the “VMM” e the “GND”. The passage of electric current between the board and the micromotor was assured through the “motor+” e “motor−“ pins. Additionally, an encoder coupled to the micromotor obtained results in the elongator’s instant closing or opening position. The developed software integrates an interface implemented through the Azande ® program allowing the user to define some parameters, such as motor speed and position. This program enables the selection of movement type, choosing the linear velocity of the movement, the displacement distance, and the number of repetitions to be performed. Because the micromotor needed a power supply to ensure the mechanical stimulus, there was also a mechanical resistance, and the motor current consumption was related to the mechanical resistance. Although the resistance depends on several factors, such as the sliding friction among several surfaces, the resistance opposition in the osteotomy mainly contributes to the system’s mechanical resistance. Hence, it is crucial to find a relationship between the rigidity of the osteotomy and the energy to supply to the motor that guarantees the necessary mechanical stimulus. Moreover, after calibration, the electromechanical system creates displacement relationships between the fixator clamp and the osteotomy. A support platform built-in Aluminum profile of Minitec ® (30 × 30) was developed for the two models, allowing the positional adjustment of the components. This structure intended to replicate, in a simplified way, the positioning of the lower limb in the horizontal position, like in a bedridden patient. It included a fixed support, representing the position of knee connection, and a free axial support, which mimicked the relationship with the foot and guided the axial movement introduced in the assembly, as shown in Figure 3. The osteotomy’s displacement was characterized using a Mitutoyo ® analogue comparator, with a measurement accuracy of 1 µm and located on one of the faces of Sawbones®block. Appl. Sci. 2022,12, 2328 5 of 17 Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 of 17 Figure 3. Horizontal supporting platform: (a) support conditions of the simplified model; (b) support conditions of the anatomic tibia. This study used the Sawbones® blocks (Sawbones®, Malmö, Sweden, 2019) with different densities to simulate different osteotomy rigidities. According to the trademark, these materials allow for a good simulation of the mechanical characteristics of the regenerated bone in the many stages of bone callus growth [17], reproducing the variation in bone callus stiffness. The mechanical properties and the designation of the several materials are in Table 2. This material is applied in osteotomy to carry out advancement tests. These tests are intended to evaluate the resistance capacity of the material when subjected to compression. Table 2. Mechanical properties of the materials used in the osteotomy [18]. Solid Foam 10 PCF 15 PCF 20 PCF 30 PCF 40 PCF 50 PCF Density [g/cm3] 0.16 0.24 0.32 0.48 0.64 0.80 Tensile Strength [MPa] 2.1 3.7 5.6 12.0 19.0 27.0 Young Modulus (traction) [GPa] 0.086 0.173 0.284 0.592 1.0 1.469 Compressive Strength [MPa] 2.2 4.9 8.4 18.0 31.0 48.0 Young Modulus (Comp.) [GPa] 0.058 0.123 0.210 0.445 0.759 1.148 Coefficient of Poisson 0.3 0.3 0.3 0.3 0.3 0.3 The Sawbones® materials have rigidities (stiffness expressed in Young’s compression Modulus) between those of fibrous tissue, immature bone, and mature bone. Table 3 compares the Sawbones stiffness values at different densities with bone characteristics in the various phases. Several authors [19,20] used these regenerated bone properties to represent bone regeneration in mathematical models, whereas other researchers created numerical models based on the same information [21–23]. The primary purpose of this experimental setup was to study the relationship between rigidity and micromovements on the osteotomy for the loading conditions defined at the micromotor. Moreover, it was also essential to evaluate the micromotor energy consumption (CEMotor) in forward and backward movements to determine its relationship with the material’s stiffness at the osteotomy. Hence, three different displacements were imposed in the osteotomy, corresponding to 1, 1.5, and 2 mm, and, to guarantee repeatability and reproducibility, five tests for each displacement were performed. Several authors argue that the recovery time can be reduced if osteotomy stimulation is promoted with displacements of 1 mm/day [13,24–29]. (a) (b) (a) (b) Figure 3. Horizontal supporting platform: ( a ) support conditions of the simplified model; ( b ) support conditions of the anatomic tibia. This study used the Sawbones ® blocks (Sawbones ® , Malmö, Sweden, 2019) with different densities to simulate different osteotomy rigidities. According to the trademark, these materials allow for a good simulation of the mechanical characteristics of the regenerated bone in the many stages of bone callus growth [ 17 ], reproducing the variation in bone callus stiffness. The mechanical properties and the designation of the several materials are in Table 2 . This material is applied in osteotomy to carry out advancement tests. These tests are intended to evaluate the resistance capacity of the material when subjected to compression. Table 2. Mechanical properties of the materials used in the osteotomy [18]. Solid Foam 10 PCF 15 PCF 20 PCF 30 PCF 40 PCF 50 PCF Density [g/cm3]0.16 0.24 0.32 0.48 0.64 0.80 Tensile Strength [MPa] 2.1 3.7 5.6 12.0 19.0 27.0 Young Modulus (traction) [GPa] 0.086 0.173 0.284 0.592 1.0 1.469 Compressive Strength [MPa] 2.2 4.9 8.4 18.0 31.0 48.0 Young Modulus (Comp.) [GPa] 0.058 0.123 0.210 0.445 0.759 1.148 Coefficient of Poisson 0.3 0.3 0.3 0.3 0.3 0.3 The Sawbones ® materials have rigidities (stiffness expressed in Young’s compression Modulus) between those of fibrous tissue, immature bone, and mature bone. Table 3 compares the Sawbones stiffness values at different densities with bone characteristics in the various phases. Several authors [ 19 , 20 ] used these regenerated bone properties to represent bone regeneration in mathematical models, whereas other researchers created numerical models based on the same information [21–23]. The primary purpose of this experimental setup was to study the relationship between rigidity and micromovements on the osteotomy for the loading conditions defined at the micromotor. Moreover, it was also essential to evaluate the micromotor energy consumption (CEMotor) in forward and backward movements to determine its relationship with the material’s stiffness at the osteotomy. Hence, three different displacements were imposed in the osteotomy, corresponding to 1, 1.5, and 2 mm, and, to guarantee repeatability and reproducibility, five tests for each displacement were performed. Several authors argue that the recovery time can be reduced if osteotomy stimulation is promoted with displacements of 1 mm/day [13,24–29]. Appl. Sci. 2022,12, 2328 6 of 17 Table 3. Stiffness of the material used to represent osteotomy/regenerative bone [18,20]. Stiffness [MPa] Fibrous Tissue 0.2 Sawbones®10 58 →Stimulation Sawbones®15 123 Sawbones®20 210 Sawbones®30 445 Sawbones®40 759 Immature Bone 1000 Sawbones®50 1148 Mature Bone 6000 Cortical Bone 20,000 The experimental results are presented using the following notation: {PA6 ; AN}Sivjdk(1) where PA6 represents the simplified model’s results, and AN those of the anatomical model. The index irepresents the type of Sawbones ® material, i.e., 10, 20, 30, 40, and 50, the index j identifies the speed imposed on the micromotor (2 mm/min), and the index kis related to the level of displacement set, i.e., 1 mm, 1.5 mm, and 2 mm. 2.2. Numerical Models The geometrical models were created based on the experimental simplified and anatomical models. Each one of the two model files was imported into the ADINA System for linear and nonlinear finite element analysis (ADINA AUI version 9.3.1, ADINA R&D Inc., Water-town, NY, USA). Figure 4illustrates the external fixation models that replicate the experimental conditions. Since these models were based on the stimulation concept performed on patients with reduced mobility, the boundary conditions mimicked these physical limitations. Hence, the main movement restrictions were in the knee area, while the support in the foot was less restrictive, and the displacement loading condition was assured at the mobile clamp. Figure 4also shows the numerical boundary conditions. The three translational degrees of freedom in the tibia condyles regions and the displacements in the XX and ZZ axis in the foot area were restricted, allowing only axial movement. The contact among surfaces ensured the material continuity between the faces of the bone and the faces of the osteotomy material, between the pin surfaces and the inner surfaces of the hole bone. Even knowing that the fixation of the clamp to the rail was assured through a screw, the bonded contact allowed simplifying the numerical model. Material continuity guaranteed the connection between the pins and the clamps. The relative movement among the faces involved on the remaining contacts was included. Figure 5shows the several contact surfaces of the numerical models. A mesh sensitivity study was assured, assuming that grid displacement independence was achieved for variations in the order of 5%. Assignment of the mesh density to the several bodies of each model was supported by equally spaced subdivisions of the bodies, using the desired edge length dimensions between 1 mm e 3 mm. In some cases, the subdivision of specific faces was recalculated with smaller sizes to assure a more refined mesh in areas requiring higher precision of the results. The Delaunay free-form meshing algorithm guaranteed discretization of the domains, generating an eight-node hexahedral element. Additional displacement degrees of freedom were allowed by selecting the incompatible modes option. The total number of nodes and elements of each model are detailed in Table 4. Appl. Sci. 2022,12, 2328 7 of 17 Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 17 Figure 4. Finite elements models: Anatomical model (AN); Simplified model (PA6). The contact among surfaces ensured the material continuity between the faces of the bone and the faces of the osteotomy material, between the pin surfaces and the inner surfaces of the hole bone. Even knowing that the fixation of the clamp to the rail was assured through a screw, the bonded contact allowed simplifying the numerical model. Material continuity guaranteed the connection between the pins and the clamps. The relative movement among the faces involved on the remaining contacts was included. Figure 5 shows the several contact surfaces of the numerical models. Figure 5. Contact surfaces included in the numerical models: Anatomical model (AN); Simplified model (PA6). A mesh sensitivity study was assured, assuming that grid displacement independence was achieved for variations in the order of 5%. Assignment of the mesh density to the several bodies of each model was supported by equally spaced subdivisions of the bodies, using the desired edge length dimensions between 1 mm e 3 mm. In some cases, PA6 AN PA6 AN Figure 4. Finite elements models: Anatomical model (AN); Simplified model (PA6). Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 17 Figure 4. Finite elements models: Anatomical model (AN); Simplified model (PA6). The contact among surfaces ensured the material continuity between the faces of the bone and the faces of the osteotomy material, between the pin surfaces and the inner surfaces of the hole bone. Even knowing that the fixation of the clamp to the rail was assured through a screw, the bonded contact allowed simplifying the numerical model. Material continuity guaranteed the connection between the pins and the clamps. The relative movement among the faces involved on the remaining contacts was included. Figure 5 shows the several contact surfaces of the numerical models. Figure 5. Contact surfaces included in the numerical models: Anatomical model (AN); Simplified model (PA6). A mesh sensitivity study was assured, assuming that grid displacement independence was achieved for variations in the order of 5%. Assignment of the mesh density to the several bodies of each model was supported by equally spaced subdivisions of the bodies, using the desired edge length dimensions between 1 mm e 3 mm. In some cases, PA6 AN PA6 AN Figure 5. Contact surfaces included in the numerical models: Anatomical model (AN); Simplified model (PA6). Table 4. Description of the total number of elements and nodes per model. Simplified Anatomic Elements 272075 373624 Nodes This study assumed isotropic linear elastic properties for all components, and their mechanical properties were those previously presented in Table 1. The loading, representing the electromechanical stimulus, was included by prescribing a 2 mm displacement at the holes of the free clamp, where the elongator was connected, as indicated in Figure 4. Appl. Sci. 2022,12, 2328 8 of 17 3. Results 3.1. Experimental Results Figure 6compares the results for the several types of Sawbones ® (10, 15, 20, 30, 40, 50) blocks using the notation presented in Equation (1). The sawbones stiffness for the different blocks is shown in the graphic with the orange line; Figure 6a presents the results related to the simplified models, whereas Figure 6b presents those related to the anatomical model. The two sets of results showed that, as the stiffness of the osteotomy material increased, the displacement at the osteotomy decreased; hence, both lines show negative slopes. Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 17 the subdivision of specific faces was recalculated with smaller sizes to assure a more refined mesh in areas requiring higher precision of the results. The Delaunay free-form meshing algorithm guaranteed discretization of the domains, generating an eight-node hexahedral element. Additional displacement degrees of freedom were allowed by selecting the incompatible modes option. The total number of nodes and elements of each model are detailed in Table 4. Table 4. Description of the total number of elements and nodes per model. Simplified Anatomic Elements 272075 373624 Nodes This study assumed isotropic linear elastic properties for all components, and their mechanical properties were those previously presented in Table 1. The loading, representing the electromechanical stimulus, was included by prescribing a 2 mm displacement at the holes of the free clamp, where the elongator was connected, as indicated in Figure 4. 3. Results 3.1. Experimental Results Figure 6 compares the results for the several types of Sawbones® (10, 15, 20, 30, 40, 50) blocks using the notation presented in Equation (1). The sawbones stiffness for the different blocks is shown in the graphic with the orange line; Figure 6a presents the results related to the simplified models, whereas Figure 6b presents those related to the anatomical model. The two sets of results showed that, as the stiffness of the osteotomy material increased, the displacement at the osteotomy decreased; hence, both lines show negative slopes. (a) (b) Figure 6. Displacement at the osteotomy in the two experimental models: (a) the simplified model; (b) the anatomic model. Figure 6 shows that if the osteotomy material with the lower stiffness was under an imposed displacement of 2 mm through the worm screw, it received only 18% of the 2 mm. This percentage of displacement was calculated by comparing the displacement measured in osteotomy with the displacement imposed in the micromotor. Figure 7a compares the osteotomy displacement for the Sawbones®20 material when three different values of prescribed displacement were defined at the worm screw of both fixator models. The behavior of both models was quite similar, and the differences were mainly related to the geometrical dimensions of the two models. Moreover, these results confirmed that, as the osteotomy’s stiffness increased, the discharge of the force between the bone and the y = -0.0105x + 0.5854 R² = 0.9678 y = -0.0078x + 0.3948 R² = 0.9611 0 0.2 0.4 0.6 0.8 1 1.2 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 10 20 30 40 50 Stiffness [GPa] Displacement [mm] Sawbones® material d2 d1.5 Sawbones® data Linear (d2) Linear (d1.5) Figure 6. Displacement at the osteotomy in the two experimental models: ( a ) the simplified model; (b) the anatomic model. Figure 6shows that if the osteotomy material with the lower stiffness was under an imposed displacement of 2 mm through the worm screw, it received only 18% of the 2 mm. This percentage of displacement was calculated by comparing the displacement measured in osteotomy with the displacement imposed in the micromotor. Figure 7a compares the osteotomy displacement for the Sawbones ® 20 material when three different values of prescribed displacement were defined at the worm screw of both fixator models. The behavior of both models was quite similar, and the differences were mainly related to the geometrical dimensions of the two models. Moreover, these results confirmed that, as the osteotomy’s stiffness increased, the discharge of the force between the bone and the fixator was different, as described by several works [ 30 – 32 ]. Table 5contains the values of Figure 7a and the prescribed displacement ratio measured at the osteotomy. The tests carried out on the simplified and anatomical models allowed recording the energy consumption of the micromotor (CEMotor) in the variations of displacement versus stiffness at the osteotomy. Figure 7b shows the values of the CEMotor variable for the simplified and anatomy models to assure a prescribed displacement of 2 mm at the worm screw and using a 2 mm/min velocity. Figure 7b allows the quantification of the CEMotor variable for several osteotomy stiffnesses. In the initial phase of healing, particularly, there was a higher increase in the stiffness and, simultaneously, in the value of the CEMotor variable. After this initial phase, the CEMotor variable showed a stabilization with slight variations. Appl. Sci. 2022,12, 2328 9 of 17 Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 17 fixator was different, as described by several works [30–32]. Table 5 contains the values of Figure 7a and the prescribed displacement ratio measured at the osteotomy. The tests carried out on the simplified and anatomical models allowed recording the energy consumption of the micromotor (CEMotor) in the variations of displacement versus stiffness at the osteotomy. Figure 7b shows the values of the CEMotor variable for the simplified and anatomy models to assure a prescribed displacement of 2 mm at the worm screw and using a 2 mm/min velocity. Table 5. Ratio of the prescribed displacements at the osteotomy for the Sawbones®20 material. Prescribed [mm] PA6 Model AN Model Osteotomy [mm] Ratio [%] Osteotomy [mm] Ratio [%] 2 0.33 17% 0.37 19% 1.5 0.19 13% 0.21 14% 1 0.1 10% 0.16 16% (a) (b) Figure 7. (a) Displacement at the osteotomy in the two experimental models using the Sawbones® 20 material at the osteotomy; (b) variation of CEMotor variable with the stiffness of the material at the osteotomy. Figure 7b allows the quantification of the CEMotor variable for several osteotomy stiffnesses. In the initial phase of healing, particularly, there was a higher increase in the stiffness and, simultaneously, in the value of the CEMotor variable. After this initial phase, the CEMotor variable showed a stabilization with slight variations. 3.2. Numerical Results The simulations of the two models completed all time steps. The displacements over each axes directions and its magnitude were analyzed. The first analysis was based on the displacement distribution in the osteotomy when 2 mm of prescribed displacement were defined at the worm screw. Since the y-axis is parallel to the solicitation direction and the fixator axes, the average y displacements at the osteotomy face firstly loaded are presented in Table 6. The average values were evaluated considering all nodes of the osteotomy face of both models. In addition, the maximum displacement value on the same face is also presented. It is possible to observe that as the stiffness of the osteotomy material increased, the displacement decreased, with both models showing similar behavior. For both models, Figures 8 and 9 show the distribution of y-displacement at the interface wherein the contact appeared firstly. The distribution pattern varied with the material’s stiffness. The homogeneity of the displacements increased as the osteotomy stiffness increased, suggesting that stimulation would be more challenging to implement as 0 0.1 0.2 0.3 0.4 1.0 1.5 2.0 Osteotomy displacement [mm] Worm screw displacement [mm] AN PA6 70 75 80 85 90 95 100 105 110 115 120 58 258 458 658 858 1058 CEMotor [mA] Osteotomy stiffness [MPa] ANv2d2E PA6v2d2E Figure 7. ( a ) Displacement at the osteotomy in the two experimental models using the Sawbones ® 20 material at the osteotomy; ( b ) variation of CEMotor variable with the stiffness of the material at the osteotomy. Table 5. Ratio of the prescribed displacements at the osteotomy for the Sawbones®20 material. Prescribed [mm] PA6 Model AN Model Osteotomy [mm] Ratio [%] Osteotomy [mm] Ratio [%] 2 0.33 17% 0.37 19% 1.5 0.19 13% 0.21 14% 1 0.1 10% 0.16 16% 3.2. Numerical Results The simulations of the two models completed all time steps. The displacements over each axes directions and its magnitude were analyzed. The first analysis was based on the displacement distribution in the osteotomy when 2 mm of prescribed displacement were defined at the worm screw. Since the y-axis is parallel to the solicitation direction and the fixator axes, the average ydisplacements at the osteotomy face firstly loaded are presented in Table 6. The average values were evaluated considering all nodes of the osteotomy face of both models. In addition, the maximum displacement value on the same face is also presented. It is possible to observe that as the stiffness of the osteotomy material increased, the displacement decreased, with both models showing similar behavior. Table 6. Average and maximum Y-displacement in the face of the osteotomy firstly loaded. Osteotomy Material PA6 Model [mm] AN Model [mm] Average Maximum Average Maximum S10 0.35 0.49 0.55 0.59 S15 0.30 0.43 0.48 0.52 S20 0.29 0.38 0.42 0.46 S30 0.20 0.29 0.30 0.34 S40 0.12 0.18 0.14 0.17 S50 0.11 0.16 0.11 0.14 For both models, Figures 8and 9show the distribution of y-displacement at the interface wherein the contact appeared firstly. The distribution pattern varied with the material’s stiffness. The homogeneity of the displacements increased as the osteotomy stiffness increased, suggesting that stimulation would be more challenging to implement as bone regeneration occurred. The image on the right-hand side of both figures shows the Appl. Sci. 2022,12, 2328 16 of 17 Acknowledgments: This research was sponsored by national funds through FCT—Fundação para a Ciência e a Tecnologia, under the project UIDB/00285/2020. Conflicts of Interest: The authors declare no conflict of interest. References 1. Perren, S.M. Evolution of the internal fixation of long bone fractures. 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