KEYWORDS: Biomechanics; OptiStruct; Opensim; Multi-load conditions; Bone

adaptation.

Hip bone is a complex and robust skeletal structure in the human body. The presence of
a hole in the hip bone, unlike other bones, has motivated us to design it using topology

optimization problem. Hip bone bears loads while doing daily activities such as walk-
ing, running, etc. The evolution of hip bone in humans might have played a definite role

in the evolution of bipedal gait and consequently in the evolution of humans from apes.
In this work, we design the hip bone for various activities of daily living, i.e., walking,
running, sit-to-stand and crouching using topology optimization. Hip bone is rigidly
fixed at sacro-iliac joint and pubic symphysis while the hip joint load is applied at the
acetabulum. Muscle forces are also included in boundary conditions and applied on the
hip bone through muscle attachment sites. This work is the first attempt to design the
hip bone for activities of daily living using topology optimization.
The topology optimization problem is posed as a compliance minimization problem
with volume constraint and solved using topology optimization software (OptiStruct).

Optimal designs are compared with natural hip bone by measuring shape similarity us-
ing Procrustes analysis. Based on the literature, we divided the activities into individual

phases and design the hip bone. First, the topology optimization problem is solved
for the individual phases of each activity. Next, we include muscle attachment areas
and the upper portion of the hip bone (iliac-crest) into non-design domains to preserve
the biological functionality and design the hip bone. Since each activity is divided

into phases, we use a multi-load approach that considers the effect of all phases simul-
taneously to design the hip bone. The objective function of the multi-load approach

is weighted compliance, hence we explore the multi-load approach for various cases
based on the weights. Next, we design the hip bone based on the user-guided method
as an inverse problem that identifies the best combination of phases (within an activity)
with the highest shape similarity. This is solved by applying the loads of a phase on the modified input obtained from another phase of the activity. This is again extended for
the combination of walking with other activities to design the hip bone. This is solved
by applying the loads of a phase from an activity on the modified input obtained from
another phase of other activity.
>From results, we observe that no hole is created in the lower portion and the material
removal occurs at the upper portion and muscle attachment areas since these areas have
low stresses for all four activities. After the inclusion of muscle attachment areas and
iliac-crest as non-design domains, stance phases of each activity create a hole in the
lower portion similar to natural hip bone. This is due to the low magnitude or the
high number of inactive lower muscles and these phases have high shape similarity

compared to other phases of the activities. The optimal designs obtained from the multi-
load approach have moderate to good shape similarity that is highly dependent on the

weights. We identify the optimal design with high shape similarity for each activity
using the combination of phases. Further, the combination between walking and other
activities gives the highest value of shape similarity.
Since this work is the first attempt to study the effect of mechanical forces on the

shape and topology of hip bone by redesigning it, we conduct experiments to vali-
date the OptiStruct results. A detailed experimental validation using similar material,

loading, and boundary conditions may be substituted by testing the hypothesis that

the conclusions drawn using the computational procedure remain valid also in experi-
ments. All the designs are based on compliance minimization and claim that they are

stiffer than the natural hip bone. The experimental testing hypothesis is: The geometric
model of any optimal design is stiffer than the geometric model of natural hip bone for
same material and boundary conditions. We select the optimal design obtained from

the combination of phases of walking and combination of phases of running and fab-
ricated using additive manufacturing. We conducted experiments for simple boundary

conditions, i.e., fixed boundary at the upper part of the hip bone and compression load
is applied at bottom of the hip bone and found that the testing hypothesis is valid and
the OptiStruct results are in good agreement with experimental results.

We select the optimal designs with the highest shape similarity and discuss the pos-
sible application as pelvic prosthesis. The high shape similarity designs may result in

less complications in terms of adjustment of the body to the prosthesis. This is the first work to include the muscle forces while designing the hip bone prosthesis and compar-
ing it with natural hip bone by measuring shape similarity.