The most appropriate synthesis method to prepare a biodegradable polymer with controlled degradation rate and mechanical properties suitable for biomedical applications is ring-opening polymerization ROP . This method allows for the synthesis of biodegradable polymers such as polyesters, polycarbonates, and polyanhydrides, which are commonly used in biomedical applications.ROP is a versatile and well-controlled polymerization technique that enables the synthesis of polymers with a narrow molecular weight distribution, controlled chain length, and tailored end-groups. This control over the polymer structure allows for the fine-tuning of degradation rates and mechanical properties, making it suitable for various biomedical applications, such as drug delivery systems, tissue engineering scaffolds, and medical implants.In ROP, cyclic monomers are opened by a suitable initiator, and the polymer chain grows by the successive addition of monomers. The choice of monomer, initiator, and reaction conditions can be adjusted to achieve the desired polymer properties. For example, lactide and glycolide are commonly used monomers for the synthesis of biodegradable polyesters, such as poly lactic acid PLA and poly glycolic acid PGA , which have been widely used in biomedical applications due to their biocompatibility and tunable degradation rates.In summary, ring-opening polymerization is the most appropriate synthesis method to prepare biodegradable polymers with controlled degradation rates and mechanical properties suitable for biomedical applications.