I know that is normal to use titanium in medical applications, but in case of circonium only in nuclear uses.
Titanium is biocompatible, with a good corrosion resistance because the microstructure is austenitic, good mechanical resistance in little volumen, and low density.
Titanium is generally accepted as biocompatible and has excellent corrosion resistance. Ti and Ti-based alloys generically possess high specific fracture toughness (toughness-weight ratio), specific tensile strength, and fatigue strength. Ti-based alloys have found orthopaedic or dental prosthetic applications as load-bearing implant materials. Their relatively low density also favours their biomedical application. Zirconium also possesses superior corrosion resistance (even higher than that of Ti for most highly corrosive environments) but is considerably denser than Ti (6.4 vs. 4.5 g/cm3). Zr costs about twice the cost of Ti. The mechanical properties of Ti alloys generally compare favourably to that of Zr alloys, except for hardness and wear resistance. Zr alloys have found some biomedical applications, but Ti alloys are more extensively applied, in general.
Prof. Carlos Araújo QueirozI has summarized the use of Ti and Zr alloys for medical applications. Please note that I do not work in this area. But I know as a metallurgist that stainless steels, cobalt alloys, commercially pure titanium, and Ti-6Al-4V alloys are generally used as implants They posses mechanical strength, corrosion resistance and the release of harmful toxins is small when exposed to body fluids and can be left inside the body for a longer period of time. So, the topic of metal release from metallic bio-materials is an important subject. I have read that Ti–15Zr–4Nb–4Ta alloy with its low metal release is considered advantageous for long-term implants. You may please see the following references. (a) "Comparison of metal release from various metallic biomaterials in vitro", Yoshimitsu Okazakia,,Emiko Gotoh, Biomaterials 26 (2005) 11–21. (b) "Review of materials in medical applications", David Bombač ET AL., RMZ – Materials and Geoenvironment, Vol. 54, No. 4, pp. 471-499, 2007. (c) A Review Paper by H. Michelle Grandin ET AL., in "Materials 2012, 5, 1348-1360; doi:10.3390/ma5081348". Best wishes.
Zr as a pure metal is not recommended for biomedical applications mainly due to its availability and cost while Ti serves the purpose better. It is used as an additive to replace V & Al in Ti6AL4V along with other noble elements. Whereas its oxide ZrO2 is a good bioinert ceramic.