Feature lines serve as the foundation for surface modeling, directly influencing the surface shape in orthopedic implant design (He et al., 2014). This approach integrates anatomical features (points, curves, and surfaces) while circumventing the labor-intensive, bottom-up design process. Through parametric design, the implant geometry can be dynamically adjusted to match individual patient anatomy, thereby enhancing compatibility (Li et al., 2023). The resulting surface morphology depends on the configuration of these feature lines and the generation algorithm. The bionic finger contour comprises medial and lateral lines, interconnected by a parametric control mechanism inspired by the functional hierarchy of the metacarpophalangeal structure. These connections ensure curvature adaptability and improve anatomical compatibility, addressing key limitations of traditional femoral condylar prosthesis design processes (Sun et al., 2024). Projecting the bionic finger contour onto the femoral condyle generates an attachment surface with excellent editability and significantly improved fit.

The strategic placement of bionic finger key points is critical, with each point corresponding to specific anatomical landmarks (Figure 3A). These key points encompass a starting point, first-level key point, second-level key point, third-level key point, and final point. The starting point and the first-level key point constitute the first-level phalanx line, corresponding to the articular sesamoid in the hand structure. Subsequent phalanx lines are similarly defined, with the first-level key point and second-level key point forming the second-level phalanx line (proximal phalanx), the second-level key point and third-level key point forming the third-level phalanx line (middle phalanx), and the third-level key point and the final point forming the fourth-level phalanx line (distal phalanx).

To ensure a high degree of fit between the femoral condylar prosthesis attachment surface and the recipient, the bionic hand-inspired structure is simplified into a surface composed of four finger contour lines. As illustrated in Figure 3B, these lines include the index finger contour line, middle finger contour line, ring finger contour line, and little finger contour line. Further details are provided in Sections 2.2.3 and 2.2.4.

For the medial bionic hand-inspired structure, the finger contour feature lines, from inside to outside, are the index finger contour feature line (i = 1), middle finger contour feature line (i = 2), ring finger contour feature line (i = 3), and little finger contour feature line (i = 4). The key points for constructing each finger contour are the starting point A _i , first-level key point P _i1, second-level key point P _i2, third-level key point P _i3, and final point B _i . The determination of P _i1, P _i2, and P _i3 is as follows: P _i1 is positioned at the same height as M _high, the highest point of the medial femoral condyle, and extends along the negative direction of the coronal axis. The distance between P _i1 and M _medial is denoted as H _im1. P _i2 is situated at the same height as M _medial, the most medial point of the medial femoral condyle, and extends along the negative direction of the coronal axis, with the distance between P _i2 and M _medial denoted as H _im2. P _i3 is located at the same height as M _low, the most medial point of the medial femoral condyle, and extends along the negative direction of the coronal axis, with the distance between P _i3 and M _medial recorded as H _im3. The distances H _im1, H _im2, and H _im3 are calculated using Equation 1. H i m 1 = i ‐ 1 × M m e d i a l   M l a t e r a l → 3 × δ 1 H i m 2 = i ‐ 1 × L m e d i a l   L l a t e r a l → 3 × δ 2 H i m 3 = i ‐ 1 × L m e d i a l   L l a t e r a l → 3 × δ 3   (1) where M _medial represents the most medial point of the medial femoral condyle, and M _lateral represents the most lateral point of the medial femoral condyle. These coefficients ( δ 1 - δ 3 , ε 1 - ε 3 ) were empirically calibrated from an analysis of 20 CT scans representing diverse femoral morphologies (as described in Section 2.1), ensuring population-level adaptability to anatomical variations such as Asian-specific condylar dimensions (Fan et al., 2017). The initial values were refined through an iterative process to minimize the average Hausdorff distance across the calibration set.

Similarly, for the lateral bionic hand-inspired structure, the finger contour lines, from outside to inside, are the index finger contour (j = 1), middle finger contour (j = 2), ring finger contour (j = 3), and little finger contour (j = 4). The key points for constructing each finger contour of the lateral bionic hand-inspired structure are the starting point C _j , first-level key point Q _j1, second-level key point Q _j2, third-level key point Q _j3, and final point D _j . Q _j1 is positioned at the same height as L _high, the highest point of the lateral femoral condyle, and extends along the positive direction of the coronal axis. The distance between Q _j1 and L _lateral is denoted as H _jl1. Q _j2 is situated at the same height as L _medial, the highest point of the lateral femoral condyle, and extends along the positive direction of the coronal axis, with the distance between Q _j2 and L _medial denoted as H _jl2. Q _j3 is located at the same height as L _low, the most lateral point of the lateral femoral condyle, and extends along the positive direction of the coronal axis, with the distance between Q _j3 and L _medial recorded as H _jl3. The distances H _jl1, H _jl2, and H _jl3 are calculated using Equation 2. H j l 1 = j ‐ 1 × L m e d i a l   L l a t e r a l → 3 × ε 1   H j l 2 = j ‐ 1 × L m e d i a l   L l a t e r a l → 3 × ε 2   H j l 3 = j ‐ 1 × L m e d i a l   L l a t e r a l → 3 × ε 3   (2)

Here, L _medial represents the most medial point of the lateral femoral condyle, and L _lateral represents the most lateral point of the lateral femoral condyle. The coefficients ε ₁, ε ₂ and ε ₃ are empirical values obtained from an analysis of a dataset of femur samples. The selection of A _i and B _i is based on the osteotomy d ₀ performed by orthopedic surgeons, satisfying the conditions: P i 1 A i   → = d 0 P i 3 B i → = d 0 and Q j 1   C j → = d 0 Q j 3   D j → = d 0 .

The adjustment coefficients (δ and ε) are dimensionless scaling factors that translate anatomical dimensions of the femoral condyle (e.g., |M _medial M _lateral|) into offsets (H _im1, H _im2, etc.) for positioning the bionic key points. These coefficients are essential for ensuring the generated contour feature lines are anatomically proportional and adaptable to population variations. Since they define the proportional relationship between bone morphology and the bionic model, the coefficients cannot be derived from first principles and must be empirically calibrated using a representative anatomical dataset. The calibration aimed to optimize anatomical fit, quantified by the Hausdorff distance between the resulting attachment surface and the native condylar surface.

The calibration procedure used a set of femur CT scans with diverse morphological characteristics as the calibration set. The average Hausdorff distance between the prosthesis attachment surface—generated from a candidate set of coefficients—and the native condylar surface was defined as the objective function to minimize. The Nelder-Mead simplex algorithm was employed for iterative optimization, which converged to values of δ ₁–δ ₃ and ε ₁–ε ₃ approximately equal to 0.76.

This data-driven calibration ensures the parametric model captures essential statistical relationships between bone size and the curvature distribution required for a conformal fit. The value 0.76 serves as a population-average starting point; for patient-specific applications, these coefficients can be further fine-tuned using individual CT data to achieve superior fit.

The bionic fitting bending parameters are determined by the finger key bending angles of the bionic hand-inspired structure. As shown in Figure 4, each finger contour line has three key bending angles: the first-level key bending angle (α _i1), second-level key bending angle (α _i2), and third-level key bending angle (α _i3). The first-level key bending angle (α _i1) is the angle between A _i P _i1 and P _i1 P _i2. The second-level key bending angle (α _i2) is the angle between P _i1 P _i2 and P _i2 P _i3. The third-level key bending angle (α _i3) is the angle between P _i2 P _i3 and P _i3 B _i . The bending angles are calculated using Equation 3. α i 1 = arccos P i 1 A i → · P i 1 P i 2 → P i 1 A i → × P i 1 P i 2 → α i 2 = arccos P i 2 P i 1 → · P i 2 P i 3 → P i 2 P i 1 → × P i 2 P i 3 → α i 3 = arccos P i 3 P i 2 → · P i 3 B i → P i 3 P i 2 → × P i 3 B i → (3)

The lateral bionic fitting bending parameters are similarly defined. The first-level key bending angle (β _j1) is the angle between C _j Q _j1 and Q _j1 Q _j2. The second-level key bending angle (β _j2) is the angle between Q _j1 Q _j2 and Q _j2 Q _j3. The third-level key bending angle (β _j3) is the angle between Q _j2 Q _j3 and Q _j3 D _j . The bending angles are calculated using Equation 4. β j 1 = arccos Q j 1 C j → · Q j 1 Q j 2 → Q i 1 C j → × Q j 1 Q j 2 → β j 2 = arccos Q j 2 Q j 1 → · Q j 2 Q j 3 → Q j 2 Q j 1 → × Q j 2 Q j 3 → β j 3 = arccos Q j 3 Q j 2 → · Q j 3 D j → Q j 3 Q j 2 → × Q j 3 D j → (4)

To rigorously verify the fit, we employed the Hausdorff distance (van Kreveld et al., 2022; Ellen et al., 2011), a metric renowned for its efficacy in evaluating surface reconstructions. Fit was quantitatively assessed by calculating the distance between the feature point set on the attachment surface of the femoral condylar prosthesis and the corresponding feature point set on the surface of the femoral condyle. Specifically, the set of feature points collected on the attachment surface (plate) was denoted as A _plate, while the set of feature points collected on the femoral condyle surface was denoted as B _femur. In the acquisition process, we primarily focused on collecting points that reflect the surface characteristics, including those on the finger contour feature line and the internal auxiliary feature line. The Hausdorff distance between the sets A _plate and B _femur, denoted as H (A _plate, B _femur), is mathematically expressed as follows:

The Hausdorff distance between the sets A _plate and B _femur, denoted as H (A _plate, B _femur), is defined by Equation 7. H A plate , B femur = max max a ∈ A plate min b ∈ B femur a − b , max b ∈ B femur min a ∈ A plate b − a (7)

The point clouds were sampled at a density of 10 points/mm³ to ensure accurate representation of the surface curvature. It is worth noting that the clinical acceptability threshold of 0.5 mm for interface micromotion, derived from foundational studies on bone ingrowth (Pilliar et al., 1986), is a recognized benchmark for cementless femoral components (Springer et al., 2009). The mean Hausdorff distance achieved in this study (0.29 ± 0.03 mm) is significantly below this threshold, indicating high geometric fidelity. Potential sources of measurement error include CT image resolution and surface reconstruction algorithms, but the low coefficient of variation (10.3%) across parametric groups suggests the method is robust against these variations.

The experimental validation, resulting in a Hausdorff distance of 0.29 mm, confirms that the proposed design achieves high anatomical alignment precision while reducing design complexity compared to conventional CAD-based approaches. The key innovation of this work is its functional biomechanical adaptation, enabled by a hierarchical curvature control framework. This framework facilitates dynamic conformity to the femoral condyle anatomy by integrating three technical aspects: (1) proximal condyle apex mapping for longitudinal curvature modulation, (2) intercondylar fossa alignment for transverse bending adaptation, and (3) distal phalangeal parameterization for condylar base curvature optimization. The achieved precision of 0.29 mm validates this tri-level mapping mechanism, demonstrating the ability of the prosthetic surface to conform dynamically to the underlying bone. By translating principles of biological adaptation into a clinical design methodology, this work establishes a practical approach for enhancing implant-bone integration and shows potential for improving functional outcomes through patient-specific optimization.

The achieved sub-millimeter precision is a critical prerequisite for reducing micromotion and stress shielding, which are key biomechanical factors in long-term implant stability (Pilliar et al., 1986; Springer et al., 2009). However, it is important to note that superior geometric fit, while necessary, must be complemented by biomechanical validation to fully ascertain its clinical impact.

The geometric fidelity of the femoral bone model directly influences the resulting fit of the attachment surface. To investigate this relationship, we evaluated two mesh resolutions with explicit consideration of computational efficiency:

1. Mesh Configuration & Computational Load

Coarse mesh (8 mm element size, 791 elements total/183 condyle) was generated in 2.1 min on a standard workstation, while the fine mesh (3 mm element size, 5,990 elements total/1,337 condyle) required 18.7 min.

Curvature analysis (Figure 10) revealed that the fine-mesh model achieved a 62% improvement in curvature transition smoothness (quantified by a reduction in the standard deviation of curvature along the profile from 0.012 mm^-1 to 0.0045 mm^-1) with reduced curvature comb fluctuations over the coarse-mesh model, but demanded 9× longer computation time, establishing a clear precision-efficiency tradeoff where coarse mesh suffices for preliminary δ/ε coefficient calibration whereas fine mesh is essential for final anatomical adaptation.

2. Practical Balancing Strategy

For clinical deployment, we recommend a two-tier approach: initial coefficient calibration using coarse mesh (≤8 mm) for rapid iteration in pilot cases, followed by patient-specific optimization with fine mesh (≤3 mm) and validated δ/ε coefficients. This hierarchical workflow reduces total computation time by 73% while maintaining Hausdorff distance <0.35 mm across 20 retrospective cases, with coefficient variations remaining below 5%.