Transforaminal lumbar interbody fusion (TLIF) using an implanted cage is the gold standard surgical treatment for disc diseases such as disc collapse and spinal cord compression, when more conservative medical therapy fails. Titanium (Ti) alloys are widely used implant materials due to their superior biocompatibility and corrosion resistance. A new Ti-6Al-4V TLIF cage concept featuring an I-beam cross-section was recently proposed, with the intent to allow bone graft to be introduced secondary to cage implantation. In designing this cage, we desire a clear pathway for bone graft to be injected into the implant, and perfused into the surrounding intervertebral space as much as possible. Therefore, we have employed shape optimization to maximize this pathway, subject to maintaining stresses below the thresholds for fatigue or yielding.

The TLIF I-beam cage (Fig. 1(a)) with an irregular shape was parametrically designed considering a lumbar lordotic angle of 10°, and an insertion angle of 45° through the left or right Kambin's triangles with respect to the sagittal plane. The overall cage dimensions of 30 mm in length, 11 mm in width and 13 mm in height were chosen based on the dimensions of other commercially available cages. The lengths (l_a, l_p) and widths (w_a, w_p) of the anterior and posterior beams determine the sizes of the cage's middle and posterior windows for bone graft injection and perfusion, so they were considered as the design variables for shape optimization. Five dynamic tests (extension/flexion bending, lateral bending, torsion, compression and shear compression, as shown in Fig. 2(b)) for assessing long term cage durability (10⁷ cycles), as described in ASTM F2077, were simulated in ANSYS 15.0. The multiaxial stress state in the cage was converted to an equivalent uniaxial stress state using the Manson-Mcknight approach, in order to test the cage based on uniaxial fatigue testing data of Ti-6Al-4V. A fatigue factor (K) and a critical stress (σ_cr) was introduced by slightly modifying Goodman's equation and von Mises yield criterion, such that a cage design within the safety design region on a Haigh diagram (Fig. 2) must satisfy K ≤ 1 and σ_cr ≤ S_Y = 875 MPa (Ti-6Al-4V yield strength) simultaneously.

After shape optimization, a final design with l_a = 2.30 mm, l_p = 4.33 mm, w_a = 1.20 mm, w_p = 2.50 mm, was converged upon, which maximized the sizes of the cage's windows, as well as satisfying the fatigue and yield strength requirements. In terms of the strength of the optimal cage design, the fatigue factor (K) under dynamic torsion approaches 1 and the critical stress (σ_cr) under dynamic lateral bending approaches the yield strength (S_Y = 875 MPa), indicating that these two loading scenarios are the most dangerous (Table 1). Future work should further validate whether or not the resulting cage design has reached the true global optimum in the feasible design space. Experimental validation of the candidate TLIF I-beam cage design will be a future focus.

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