This growing medium has been used for years and works well. Many or the earlier hydroponic systems that were commercially available to the public were gravel based ebb / flow (flood and drain) type systems.
Gravel supplies plenty of air to the roots, but doesn't retain water, which means that the plants roots can dry out quickly if they are not watered enough. Another drawback to gravel is its weight, it's very heavy, and toting it around is difficult.
Gravel is usually fairly cheap (depending on where you live) and easy to find. You can easily reuse gravel as long as you wash and sterilize well between crops. After you harvest your crop you can wash the gravel to remove all the old roots and then sterilize them with a 10% bleach and water mix (one part bleach to 9 parts water). The gravel can also be sterilized by using a mixture of Hydrogen Peroxide and water (use 1 or 2 teaspoons of 35% food grade hydrogen peroxide per gallon of water).
When most people think of hydroponics they think of plants with their roots suspended in water with the nutrients dissolved in it. This is a very popular method of growing hydroponically and there are several types of systems that use water as the growing medium (deep flow N.F.T., shallow flow N.F.T. and water culture are among the most popular).
Water is a critical element in the growth of plants anyway, so using it as the growing medium makes a lot of sense. Care must be taken when selecting a system that uses water as the only growing medium, to ensure that the plant(s) are compatible. For example: Water-loving plants like "Bibb" type lettuce does best in a water-culture system where the plants float directly on the surface with their roots hanging into the water, but the same system will not work as well for most other plants because there is too much water and not enough oxygen. These other plants will do much better in a N.F.T. system where more oxygen is available to the roots because the plants are suspended above the level of the water.
This growing medium has had limited success. There are many variables that determine how well saw dust will work, most predominantly is the KIND of wood that the dust is made from. Some kinds of wood can give off chemicals that are detrimental to the health of the plant(s). Another problem with saw dust is that it will decompose, which can cause problems. Saw dust also retains a lot of moisture so care must be taken not to over water.
The best thing about saw dust is that it's usually free. I don't recommend using saw dust unless you are into experimenting.
Lava rock has been used successfully for years, it is light-weight and retains a fair amount of water in it's holes and pores. It is used most often in ebb & flow (fill & drain) systems with frequent watering cycles.
With a good selection of first rate growing mediums available lava rock is used much less often these days. The drop in popularity is due mostly to the fact that the sharp edges of the rock can cause root damage to the plants, and in most areas of the world it can be hard to find lava rock that is not chemically treated.