*2.3. Morphological Study*

Morphological study of the proximal femur is essential because it is the region that undergoes long-term bone resorption in most state-of-the-art implants [18]. During preoperative planning of THR, the surgeon chooses a suitable stem from among the prostheses manufactured in advance. For this purpose, he/she evaluates the patient's morphology using radiographs; however, the femur has specific and individual characteristics, and this

technique does not provide detailed information about the femoral cavity, so the chosen stem may fill it poorly or exceed its dimensions, causing periprosthetic fractures. this technique does not provide detailed information about the femoral cavity, so the chosen stem may fill it poorly or exceed its dimensions, causing periprosthetic fractures.

Morphological study of the proximal femur is essential because it is the region that undergoes long-term bone resorption in most state-of-the-art implants [18]. During preoperative planning of THR, the surgeon chooses a suitable stem from among the prostheses manufactured in advance. For this purpose, he/she evaluates the patient's morphology using radiographs; however, the femur has specific and individual characteristics, and

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In addition, the geometric parameters neck–shaft angle, anteversion and offset would be inadequate, which could result in a dislocated stem [19–24]. The three-dimensional femoral model obtained from the CT scan (Figure 1A) provides more accurate information that allows the morphological study of each patient because it is essential for the customized design of cementless stems, since precise dimensions of the femoral canal guarantee mechanical stability and avoid *SS* [25]. In addition, the geometric parameters neck–shaft angle, anteversion and offset would be inadequate, which could result in a dislocated stem [19–24]. The three-dimensional femoral model obtained from the CT scan (Figure 1A) provides more accurate information that allows the morphological study of each patient because it is essential for the customized design of cementless stems, since precise dimensions of the femoral canal guarantee mechanical stability and avoid [25].

### 2.3.1. Neck–Shaft and Mechanical Angle 2.3.1. Neck–Shaft and Mechanical Angle

*2.3. Morphological Study* 

To measure the neck–shaft angle, modifications of the techniques described by Wang et al. [26] and Zhang et al. [27] were used. Previously, the femoral head was simulated as a sphere; thus, its centers are coincident. If this estimation is not possible due to the fracture of the femoral neck, the acetabulum can be used to define the sphere. Three reference planes are located: the first at the femoral neck isthmus (FNI), a plane parallel to the XY plane and rotated 45◦ clockwise with respect to the X-axis—45◦ is the supplement of the average neck–shaft angle according to the study by Gilligan et al. [28]; the second and third planes are located at the end of the lesser trochanter (LT) and 10 mm (LT-10) below and both are parallel to the XY plane (Figure 3A). To measure the neck–shaft angle, modifications of the techniques described by Wang et al. [26] and Zhang et al. [27] were used. Previously, the femoral head was simulated as a sphere; thus, its centers are coincident. If this estimation is not possible due to the fracture of the femoral neck, the acetabulum can be used to define the sphere. Three reference planes are located: the first at the femoral neck isthmus (FNI), a plane parallel to the XY plane and rotated 45° clockwise with respect to the X-axis—45° is the supplement of the average neck–shaft angle according to the study by Gilligan et al. [28]; the second and third planes are located at the end of the lesser trochanter (LT) and 10 mm (LT-10) below and both are parallel to the XY plane (Figure 3A).

**Figure 3.** Steps to measure the neck–shaft and mechanical angle. (**A**) Estimation of the femoral head with a sphere and location of the FNI, LT and LT-10 planes. (**B**) Sampling of bone sections. The adjustment made by the app for sections (**C**) FNI, (**D**) LT and (**E**) LT-10. (**F**) Neck and shaft axis. (**G**) Neck–shaft and mechanical angle. **Figure 3.** Steps to measure the neck–shaft and mechanical angle. (**A**) Estimation of the femoral head with a sphere and location of the FNI, LT and LT-10 planes. (**B**) Sampling of bone sections. The adjustment made by the app for sections (**C**) FNI, (**D**) LT and (**E**) LT-10. (**F**) Neck and shaft axis. (**G**) Neck–shaft and mechanical angle.

The proximal femur is cut through all three planes, generating bone sections. As described in the section *Elliptical adjustment app* (Section 2.2), the center of the bone section can be found by sampling it with NX® (Figure 3B). The fit performed by the app for the FNI, LT and LT-10 sections is shown in Figure 3C–E, respectively. The femoral neck axis The proximal femur is cut through all three planes, generating bone sections. As described in the section *Elliptical adjustment app* (Section 2.2), the center of the bone section can be found by sampling it with NX® (Figure 3B). The fit performed by the app for the FNI, LT and LT-10 sections is shown in Figure 3C–E, respectively. The femoral neck axis passes through the centers of the sphere and the FNI section, and the shaft axis passes through the centers of the LT and LT-10 sections (Figure 3F). Both axes are orthogonally projected on the XZ plane and the angle between them is the neck–shaft angle. The mechanical axis is parallel to the Z-axis, and the angle between the neck and the mechanical axes is the mechanical angle (Figure 3G). Therefore, the neck–shaft and mechanical angle (MA) for GC1 are 126.4◦ and 141.9◦ , and for GC2 are 133.1◦ and 143◦ .

The neck–shaft angles of GC1 and GC2 are within the normal range of 90◦ to 135◦ ; if the inclination is greater than 125◦ , it is called *coxa valga*, and if it is less than 120◦ , *coxa vara* [29]. If the stem selected by the orthopedist or designed by the engineer alters the patient's neck–shaft angle, valgus or varus position, a muscular imbalance is generated and, as a consequence, affects the load to which the joint is subjected after THR, favoring the loosening of the implant [30–32]. The neck–shaft angles of GC1 and GC2 are within the normal range of 90° to 135°; if the inclination is greater than 125°, it is called *coxa valga*, and if it is less than 120°, *coxa vara* [29]. If the stem selected by the orthopedist or designed by the engineer alters the patient's neck–shaft angle, valgus or varus position, a muscular imbalance is generated and, as a consequence, affects the load to which the joint is subjected after THR, favoring the loosening of the implant [30–32].

passes through the centers of the sphere and the FNI section, and the shaft axis passes through the centers of the LT and LT-10 sections (Figure 3F). Both axes are orthogonally projected on the XZ plane and the angle between them is the neck–shaft angle. The mechanical axis is parallel to the Z-axis, and the angle between the neck and the mechanical axes is the mechanical angle (Figure 3G). Therefore, the neck–shaft and mechanical angle

### 2.3.2. Anteversion 2.3.2. Anteversion

Yadav et al. [33] measure femoral anteversion three-dimensionally as the angle between the condylar plane, formed by the condylar and neck axes, and the femoral neck plane, composed of the neck and shaft axes. However, the virtual model of the proximal femur (Figure 1) does not include the condyles, and a new strategy to quantify anteversion is proposed, which consists of taking the XZ plane as a reference and redefining the femoral neck plane as the one formed by the neck and mechanical axes, since both planes are formed by an axis parallel to Z, favoring the measurement of anteversion: the angle between the new femoral neck plane and the XZ plane (Figure 4). The approximate anteversion for GC1 and GC2 is 13.5◦ and 3.6◦ , respectively. Yadav et al. [33] measure femoral anteversion three-dimensionally as the angle between the condylar plane, formed by the condylar and neck axes, and the femoral neck plane, composed of the neck and shaft axes. However, the virtual model of the proximal femur (Figure 1) does not include the condyles, and a new strategy to quantify anteversion is proposed, which consists of taking the XZ plane as a reference and redefining the femoral neck plane as the one formed by the neck and mechanical axes, since both planes are formed by an axis parallel to Z, favoring the measurement of anteversion: the angle between the new femoral neck plane and the XZ plane (Figure 4). The approximate anteversion for GC1 and GC2 is 13.5° and 3.6°, respectively.

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(MA) for GC1 are 126.4° and 141.9°, and for GC2 are 133.1° and 143°.

**Figure 4.** Anteversion. **Figure 4.** Anteversion.

Anteversion aims to restore the femoral center of rotation [34]. Its reduction leads to increased external rotation of the leg, increases torsional moments on the prosthesis [35– 37] and may be associated with an increased risk of loosening [38]. Moreover, it has a strong influence on hip contact forces [39]; therefore, the correct anteversion angle allows an optimal range of motion with minimal risk of instability [40,41]. Anteversion aims to restore the femoral center of rotation [34]. Its reduction leads to increased external rotation of the leg, increases torsional moments on the prosthesis [35–37] and may be associated with an increased risk of loosening [38]. Moreover, it has a strong influence on hip contact forces [39]; therefore, the correct anteversion angle allows an optimal range of motion with minimal risk of instability [40,41].

### 2.3.3. Offset 2.3.3. Offset

The offset is the perpendicular distance between the shaft axis and the center of the femoral head. Because the femoral head was simulated as a sphere to measure the neck– shaft angle (Figure 3A), it has implicit offset information, so it is not necessary to quantify the offset on the condition that the sphere is used in the custom design. This parameter improves physical function, increases hip stability, maintains postoperative pelvic balance and minimizes the risk of dislocations [31,42,43]. Several studies have shown that an increase in offset correlates with a reduced neck–shaft angle, increased range of motion, increased lever arm and abductor strength. If not restored, it increases the reactive force of the joint, consequently causing wear and leading to implant failure [42–45]. The offset is the perpendicular distance between the shaft axis and the center of the femoral head. Because the femoral head was simulated as a sphere to measure the neck– shaft angle (Figure 3A), it has implicit offset information, so it is not necessary to quantify the offset on the condition that the sphere is used in the custom design. This parameter improves physical function, increases hip stability, maintains postoperative pelvic balance and minimizes the risk of dislocations [31,42,43]. Several studies have shown that an increase in offset correlates with a reduced neck–shaft angle, increased range of motion, increased lever arm and abductor strength. If not restored, it increases the reactive force of the joint, consequently causing wear and leading to implant failure [42–45].
