To start, a sketch of the knee joint I made:
In the journal article "Clinical results of isolated reconstruction of the medial patellofemoral ligament for recurrent dislocation and subluxation of the patella" by Yoshinori MIKASHIMA, Masashi KIMURA, Yasukazu KOBAYASHI, Motoko MIYAWAKI, and Taisuke TOMATS, methods of surgical treatment for recurring patella luxation are investigated. The primary ligament focused on is the medial patellofemoral ligament (MPFL), which is a ligament that connects to the MCL and prevents lateral movement of the patella.
The paper studies the results of 24 patients who underwent surgical reconstruction of the MPFL with the use of an autogenous tendon, namely, the semitendinosus, which is femoral in origin. After knee immobilization and subsequent rehabilitation, patients were allowed full movement after 4 - 6 months. 2 years later they were re-evaluated.
There are many methods to perform this procedure, with a good amount making use of artificial tendons. It was found that with the proper implementation, the use of autogenous ligament is the most beneficial, especially when using a method of bone tunneling to affix the tendon.
To prevent patella luxation, I found that the DonJoy Tru-Pull Lite is a quality brace. It prevents medial movement of the patella, thereby preventing luxation.