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Prosthetic impingement is important to consider during total hip arthroplasty planning to minimise the risk of joint instability. Modelling impingement preoperatively can assist in defining the required component alignment for each individual. We developed an analytical impingement model utilising a combination of mathematical calculations and an automated computational simulation to determine the risk of prosthetic impingement. The model assesses cup inclination and anteversion angles that are associated with prosthetic impingement using patient-specific inputs, such as stem anteversion, planned implant types, and target Range of Motion (ROM). The analysed results are presented as a range of cup inclination and anteversion angles over which a colour map indicates an impingement-free safe zone in green and impingement risk zones in red. A validation of the model demonstrates accuracy within +/- 1.4° of cup inclination and anteversion. The study further investigated the impact of changes in stem anteversion, femoral head size, and head offset on prosthetic impingement, as an example of the application of the model.

Dislocation is one of the most common complications leading to revision surgery after Total Hip Arthroplasty (THA), accounting for almost one-quarter (21%) of all revision procedures [

In a cup retrieval study performed by Marchetti et al., 80% of cups revised due to dislocation showed evidence of prosthetic impingement [

Acetabular “safe zones” have been introduced by various authors to assist with cup alignment and to minimise post-operative complications. Well-known safe zones, such as those published by Lewinnek [

Motion capture, laboratorial simulators, and computational models are common methods of measuring range of motion of the hip [

An analytical ROM model has been proposed by Yoshimine et.al. [

The aim of this study is to develop and validate a robust and accurate analytical model to assess the cup inclination and anteversion angles that are associated with prosthetic impingement using patient-specific inputs.

Hisatome and Doi proposed a mathematical formula to calculate the theoretical range of motion using seven factors including head radius (r), cup depth (d), cup inclination (

Hisatome provided a mathematical formula to calculate the prosthetic hip range of motion in certain activities, i.e., pure flexion, extension, internal rotation at 90° flexion, and external rotation. The impingement model in this study allows for customised inputs to define the target ROM test conditions. The proposed model offers two combined target ROM conditions: (1) user-defined degree of Internal Rotation (IR) at any Flexion (FL) and (2) user-defined degree of External Rotation (ER) at any Extension (EX). The IR_FL test is associated with anterior prosthetic impingement in flexion, and the ER_EX test is associated with posterior prosthetic impingement in extension. The derivation of how to calculate the cup orientations that satisfy the user-defined target ROM (IR_FL and ER_EX) is detailed in the Appendix.

An automated computational simulation is used to calculate the stem neck width (n) at the impingement level (Figure

Stem neck width (n) at the impingement level.

Even with an automated simulation, and running only discrete values of stem anteversion, this is a time-consuming process. In order to run the impingement analysis at any stem anteversion, ‘Thin Plate Spline Interpolation’ was used to calculate the neck width at all cup and stem positions, utilising the simulated neck width values. The simulated data was plotted with cup inclination and anteversion on the X and Y axes, and neck width on the Z axis in Matlab (Mathworks, US) (Figure

Surface interpolation of stem neck width.

The proposed impingement model generates two impingement boundaries for any given set of target ROM conditions (IR@FL and ER@EX). Figure

Impingement plot at 30° IR @ 90° FL and 10° ER @ 10° EX.

Using the formula proposed in the Appendix, the cup orientations that satisfy any target ROM conditions can be calculated. The proposed model was investigated with the target ROM of 30°IR@90°FL and 10°ER@10°EX as an example. In order to test the application of the model in preoperative planning scenarios, three parameters (stem anteversion, femoral head size, and femoral head offset) were investigated to see how each parameter affects the prosthetic ROM. All other input parameters were set to the default values: neck-shaft angle = 125°, stem flexion = 0°, and stem adduction = 6°.

An alternative CAD model was used to verify that the proposed analytical model can accurately calculate the cup inclination and anteversion at impingement. The worst-case implant combinations that would provide the least accurate results were selected to validate the proposed model.

The worst-case implant size was determined with a combination of maximum head size which engaged with the shortest head offset. This resulted in the impingement to occur at the most lateral position of the stem (i.e., closer to the stem shoulder and therefore with the greatest difference in stem neck geometry (Figure

40mm polyethylene liner engaging at -4mm head offset compares to engaging at +4mm offset.

The implant geometries were imported into Solidworks and placed at the positions defined above. The liner was free to rotate about its centre of rotation. Using the interference detection function in Solidworks, the cup inclination and anteversion at which the acetabular component impinges with the stem can be recorded. The recorded cup inclination and anteversion in Solidworks were compared with the simulated results to determine the accuracy of the proposed model.

The accuracy of the analytical model was assessed against the CAD model with worst case implant combinations. The cup orientation boundaries that were created by the proposed model and the CAD model were compared. The results show the maximum difference between the two models is 1.4° in both cup inclination and anteversion (Table

Maximum difference in cup orientation, at impingement in flexion and impingement in extension, between the proposed impingement model and an independent CAD model.

Cup Anteversion | Cup Inclination | |
---|---|---|

Maximum difference in flexion | 1.1° | 1.4° |

Maximum difference in extension | 1.4° | 1.0° |

In order to show how the neck width can vary at different impingement levels on the neck, four different stems were analysed within the neck width database. As shown in Table

Neck width range for four stems investigated in this study.

Stems | Neck width range in mm (Avg) |
---|---|

Stem 1 | 11.3 – 22.2 (14.7) |

Stem 2 | 10.9 – 17.3 (13.5) |

Stem 3 | 11.0 – 18.2 (13.7) |

Stem 4 | 10.9 – 20.3 (13.7) |

Figures

Impingement with different stem anteversion for Stem 2.

Impingement with different head sizes. At stem anteversion of 10° for stem 2.

Impingement with different head offset for stem 2.

As can been seen from Figure

The impingement safe zone generated by the proposed model is also affected by femoral head size. As the femoral head increases, the green zone gets larger, suggesting that a larger femoral head results in more cup component positions which satisfy the impingement testing condition (Figure

Femoral head offset is a common parameter to consider when planning patient’s leg length, offset, or soft tissue tension during THA. However, it can be overlooked during impingement analysis. The proposed model allows the impact of different head offsets on the prosthetic impingement to be considered. In the case of the stem tested (Stem 2), short (-4mm) and extra-long (+8mm) head offsets showed a smaller impingement-free zone (green area) compared to neutral (+0mm) and long (+4mm) head offsets (Figure

(Left) Liner impinges at stem neck with a +4mm offset head. (Right) Liner impinges at stem trunnion with a +8mm offset head.

The present study introduced an analytical model for analysing prosthetic impingement in THA. The model involves a mathematical formula in combination with an automated neck width simulator which allows the model to take into account implant-specific neck width variations to accurately determine optimal cup orientations that are free from risk of prosthetic impingement. The model requires a one-off pre-generation of the neck width profile database for the stem of interest using the automated neck width simulator prior to the use of the model. Combined with the pre-generated neck width database and the proposed formula, the model is able to provide a zone of cup orientations that satisfy any user defined flexion and extension testing conditions, combined with any internal rotation or external rotation. The output of the model is presented as a colour map for ease of visualisation.

Even though the proposed model is capable of testing the prosthetic impingement at any user defined target ROM conditions, the question of which target ROM suits each individual patient is yet to be solved. Different target ROMs have been suggested by different groups. Incavo et al. studied passive ROM of eight cadaveric hips and suggested subjects can reach an average of 20° in extension and 24° in external rotation [

Similar to findings from previous studies, our model also highlights the importance of considering combined anteversion of the acetabular and femoral components. Widmer provided a simplified formula to achieve optimal ROM which suggests the sum of cup anteversion and 0.7 times the stem anteversion should be equal to 37° [

There are a few limitations to the proposed model. First, the neck width simulator requires the specific implant geometry to be analysed prior to use. This limits the model to be used only with the implants available in the pregenerated database. More implants can be added into the database upon availability of the implant geometry. Secondly, the combined motion provided in this model is limited to the two mentioned above (IR@FL and ER@EX). Abduction and adduction of the femur were not considered in this model as it was believed that the amount of abduction and adduction was small during daily activities such as sitting and walking, in comparison to the other movements. Lastly, it is acknowledged that the functional outcome of a THA is multi-factorial and not only based on risk of prosthetic impingement. The cause of other phenomena, such as bony impingement, contact joint force, and component wear, will also significantly impact the functional outcome and longevity of the THA [

This study describes an analytical model that determines a cup orientation “safe zone” for avoiding prosthetic impingement, based on accurately derived implant parameters. The model tests combined rotations of flexion/internal rotation and extension/external rotation, the limits of which can be customised. The model has demonstrated improved accuracy over other published impingement models and can be used as an investigational tool to assess the impact of varying implant parameters, in additon to preoperative planning in THA.

The concept of creating the IR_FL formula is to calculate the maximum rotation of the stem at a defined degree of flexion via finding the intersection point I (INTRflx, INTRfly, INTRflz) of the cup rotation cone and stem rotation cone (Figure ^{−1}(n/2r)-(180°- 2^{−1}((r-d)

Cup cone and stem cone overlap.

Cup cone.

The stem rotation cone is another right circular cone with a unit generatrix formed by rotating the stem at defined flexion angle (Figure

Stem cone.

The maximum internal rotation angle is equal to

The same concept can be applied to calculate the maximum external rotation of the stem at any defined extension angle.

The data used to support the findings is contained within the article.

The author or one or more of the authors have received or will receive benefits for personal or professional use from a commercial party related directly or indirectly to the subject of this article.