Marathoners, hill (mountain) runners often state that their weakest link is the downhill running portion of the race. This is understandable since the training for downhill running should be substantially different from uphill or track running. The physiological demands in downhill running are very different from those involved in uphill or flat running
For example, uphill or running on flat terrain involves mainly the concentric type muscle contraction. Downhill running involves mainly the eccentric type muscle contraction. Because of this the strength training for downhill running must be substantially different from the training involved in improving your uphill or track running.
What is especially interesting here is that the same muscles are involved in uphill and downhill running. The muscles just undergo a different type of muscle contraction. What is important here is to determine what percentage of your run will be downhill and what percent will be uphill or flat.
With this data you can learn to differentiate your strength training program so that you have adequate strength development for all phases of the run. However, the development should never be equal since the eccentric contraction is much more demanding on the body and requires more recovery. This is one of the reasons why it is the culprit in creating muscle soreness after a run.
For concentric muscle training you can do common exercises such as the squat and standing leg extensions with Active Cords. These exercises emphasize the main function of extension executed by the quadriceps muscle. For eccentric muscle training you can do negative squats in which the bar is loaded heavier for the down phase and lighter for the up phase. If you use Active Cords then you should emphasize the return movement with very slow execution.
In essence, you must train in a specific manner to improve your performance in each phase of the run. Doing exercises for general fitness or general strength will not suffice. This may be good for a recreational or slow runner but not for a runner who wants to race. With proper preparation you will not have any weak aspects of your run.
For more information see Explosive Running.