Rheumatoid arthritis (RA) is affecting 1.5 million adults in United States, and 75% of the

patients with upper limb RA show syndrome in the wrist joint. Total joint replacement with properly designed implant prosthesis is the optimal treatment to such disease. Elderly patients with lower limb disabilities are selected as target patient group due to the fact that they need the wrist to support significant amount of their body weight in daily life. The current designs of implants are evaluated with respect to their materials, fixations, and clinical success. The advantages of current designs are adopted for the proposed design and the proposed design is validated through theoretical calculations.

**Design Rationale**

Current products for wrist total joint replacement have certain drawbacks and revisions and failures have been reported. Furthermore, the target patient group has high requirements on the implant due to the heavy reliance of the wrist joint. We would like to provide elderly people with high quality of daily life without pain from wrist RA. As such, the new design of the implant is proposed, adopting the advantages of current design and making improvements, in order to satisfy the requirement of target patient group.

**Geometry**

The final implant consists of 2 major components: a metallic radial stem and a polymer distal head with molded fixation screws. The specified design utilizes a modified ball-and-socket joint in order to meet the design criteria for ROM. The angular dimensions of the fixation screws and radial stems were determined through analysis of current successful implants with image software.

Once the screw and stem geometry was determined, a preliminary CAD model was created for the development of the articulating surfaces. Motion studies were then conducted to analyze the resulting ROM. The curvature of the articulating ball and socket were then adjusted until the desired ROM was achieved. While the design was able to exceed the abduction and adduction of a physiological wrist joint, flexion and extension ranges are somewhat limited.

**Materials**

Due to the high level of loading in the radial stem of the implant, cobalt chromium molybdenum alloy was chosen for the radial socket and stem material. Research on current implants showed that cast ISO 5382-4:2014 alloy would be a good choice for the implant material, due to the high levels of stiffness, corrosion resistance, and biocompatibility that is acceptable for implanted devices [11]. The stem will also be plasma coated with titanium to promote osseointegration. The ISO standards specify a tensile strength of 665 MPa.

Ultra high molecular weight polyethylene (UHMW) was chosen to the articulating ball of the implant since it has high rate of success in joint replacement implants.

**Fixation**

The fixation in the proximal end will be cementless as it shows lower possibility of revision. Beyond that, small cavities of the bone make it difficult to achieve a uniform cement mantle of sufficient thickness between implant and bone. The distal head of the implant will be screwed to Scaphoid and Lunate.

**Testing and Stress Analysis**

When analyzing the fatigue stresses in the implant, a few assumptions must be made in order to simplify calculations. When looking at the proximal portion of the implant, it is assumed that the stem is properly and securely fixated in the radius. A bending moment would be exerted on the stem if a load were to be applied perpendicular to the stem. Since our patient group is focused on adults with lower limb disabilities, there will be multiple times throughout the day that the patient would be supporting their body weight on either a chair, walker, cane or other assistive device. This could result in anywhere from a half to full body weight load on the implant. For simplification, it will be assumed that half of a patient’s body weight will be applied perpendicular to the proximal stem. This assumption combined with the assumption that the stem is securely fixed in the radius would result in a maximum bending moment in the stem where it meets the cup. The moment arm in this situation would be caused by the half body weight load over the distance of the height of the cup.

In order to calculate the impact of the stem geometry configuration on the implant strength, the concentration factor (Kt) was calculated. Given a maximum diameter ratio between the stem in implant was 16mm/4mm, and given the ratio between the connecting radius and stem was 1mm/4mm, in the connection between the components, the stress concentration factor was found to be 1.36.

Assuming a body weight of 65 kg, a stem diameter of 1.5 cm, a cup height of 2.5 cm, and a radius of curvature that results in a stress concentration Kt = 1.36, the bending moment of 7.97 N-m at the base of the cup can be determined as 7.97 Nm. And with this moment combined with the previously determined stress concentration, a maximum bending stress of 32.78 MPa.

In order to determine an estimated life and safety factor, the fatigue strength must first be determined. A few assumptions must also be made to do this. For one, all fatigue factors to be determined are based upon steel, whereas our implant will be made of Cobalt Chromium Molybdenum alloy. Cobalt Chromium has an ultimate strength of 665 MPa. Due to the loading resulting in a bending stress, its load factor is CL = 1. A diameter of 1.5 cm makes the gradient factor CG = 0.9. The surface finish factor is the toughest to determine and requires a conservative estimate. Looking at the corroded in salt water line on a tensile strength vs surface finish factor graph for steel puts the surface finish factor at about CS = 0.3. The temperature factor is CT = 1 since the implant will be under body temperature conditions. Finally, a 99.9% reliability factor of CR = 0.753 was chosen in order to have a conservative fatigue strength estimate. Combining these factors with the ultimate strength results in a fatigue strength of 67.60 MPa.

Now that both the fatigue strength and the maximum stress have been determined, a life time estimate can be calculated. Using an equation derived from a logarithmic S-N curve, a life of about 9,901,000 cycles.

A safety factor can also be calculated using the ultimate strength and fatigue strength coupled with the alternating and mean stress. The maximum stress experienced by the stem is 32.78 MPa when fully loaded, and 0 MPa when unloaded, so the mean and alternating stresses are both equal to half of the maximum stress. This results in a safety factor of 3.74.

If the warranty of the proposed design is 10 years, with 20 times of supporting half body weight everyday, the load is applied 73,000 times, which is much lower than the calculated life cycles. The safety factors of the proposed design is much more than 1, so the proposed design is desirable from simplified calculation.

**CoCrMo Fatigue Testing**

In order to evaluated the potential for fatigue faliures in the metallic portion of the impact, axial fatigue testing will be performed on sample coupons of the desired ISO 5834-4 CoCrMo alloy. The test will be performed in *in vitro* conditions and test constraints of the ASTM F1801-97 standard. To simulate the corrosive conditions of implantation, the sample will be immeresed in a test chamber filled with a 0.9% saline solution held at 37 °C. An axial loading with a mean load of 1000N and an alternating load of 900N will then be applied in order to mimic gripping forces. The test will be repeated for 107 cycles in accordance with standard guidelines.