Customized Implant Design

Unlike previous methods that try to optimize current shape of the implant, the logic

behind this method is sort of out-of-the-box idea aiming at shaping a new implant starting

from scratch. Assuming that the endosteal canal of the distal humerus with its FE axis is

provided, the problem only focuses on the challenge of obtaining the shape of the implant

which best fits into this cavity while FE axes match perfectly. For starting point of the

solution, it can considered that the FE axis of the implant match exactly the FE axis of the

bone. Therefore, the problem can be easily narrowed down to finding the best shape for

the stem that fits well in the bone cavity. Once it is ensured that the stem inserts the

FE axis of the bone, minimum possible malalignment (ideally close to zero) is

guaranteed.

Finding an optimal shape for the stem that from a starting point out of the bone

canal can be transferred to a final point in the bone cavity with no penetration into the

walls seems to be challenging. In order to solve this problem, it can be presumed that a

final solution has been achieved and so there is a final position/posture for the implant

stem in which all the constraints are satisfied. Due to the fact that most of the common

implant stems have regular straight edges in the distal-proximal direction, the most

accessible starting point out of the bone cavity based on the achieved final position of the

implant stem, is a point that lies on the centerline of the implant stem. This centerline also

represents the optimal insertion trajectory that provides the surgeon a linear direction for

implantation. That being said, the problem can be converted to finding a 3D axis of the

canal that best represents the centerline of the implant stem and satisfies all constraints.

The optimal 3D axis lies where the largest volumetric envelope inside the bone cavity

occurs for the linear insertion of the implant stem.

To better calculate this volumetric envelope, it can be presumed that this envelope

is close to a cylinder with an irregular cross sectional shape while the 3D axis

characterizes the centerline of this cylinder. In order to maximize the volume of this

envelope, it is required to search for the biggest cross sectional area of the cylinder.

Indeed, this maximum irregular cross section of the cylinder-shape envelope is the

biggest common area of the projections of all inner boundaries of the distal humerus onto

a plane which is normal to the aforementioned optimal 3D axis, as shown in Figure 5.5.

(a) (b) Centroid of distal

cross section of the bone

3D axis along the resultant envelope

3D representation of the envelope

Figure ‎5.5: Customized implant design method representation: (a) finding the proper 3D axis that represents the largest common area of the bone cross sections, and (b) the resultant envelope along the 3D axis.

(b)

The method developed within this section searches for the optimal 3D axis that

maximizes the common area of projections of all inner boundaries of the bone onto the

plane normal to this axis. The algorithm employs a simple searching function to search

among all 3D axes that start from the geometric center of the distal cross section of the

bone

(X

BD

,Y

BD

,Z

BD

)

and ends on a sphere with the arbitrary radius of 1mm positioned

at the geometric center of the distal cross section. To decrease the computational

complexity of this search, the bounds were set in a way that only a portion of the sphere

that observes proximal cross section of the bone, was included in the search domain. The

3D axis

A

insertioncan be implemented as,

min max

[cos sin sin sin cos ]

0 2 insertion                A (5.12)

To find the projection ( _km)

plane

proj  of kth point on mth inner bone cross section



_kmonto

a plane with the

A

insertionas the normal vector and tangent to the sphere at

(X

_BD



,Y

_BD



,Z

_BD



)

point, the following calculations are needed,

cos sin sin sin cos                    BD BD i j BD BD i j BD BD j X X Y Y Z Z (5.13) P_BD [X_BD Y_BD Z_BD ] (5.14)

proj(

_km

)

_km

(

_insertion

.(

_km

P ))

_{BD insertion}

plane



_



_

_A



_



_A

(5.15)

Once all points on each inner bone cross section were projected on the plane, the problem

equation is converted to,

maximize(Area(proj( mD) ... proj( mP)))

k k

plane plane

  _(5.16)

Once this optimal axis is defined, there are couple of approaches that can be taken

for finding the shape of the stem. Among all possibilities, it was decided to follow the

cross sectional sizing of the current implant shape for this new method. By having this

optimal axis, the algorithm then starts to rotate the implant stem along that axis until it

finds an orientation for the implant stem that has no penetration into the bone.

If we put the resultant two sections of implant FE axis, which was supposed to

match bone FE axis and implant stem shape together, the new optimized shape of the

implant can be achieved which can ensure a minimum malalignment. In order to check

the efficiency of this method, the resultant shape of the implant was inserted into the bone

cavity form a starting point out of the cavity using the method described in the previous

section.

In document Computational Techniques to Predict Orthopaedic Implant Alignment and Fit in Bone (Page 190-194)