The phytic acid content of whole grains is the main reason for their low mineral bioavailability. Brown rice, simply cooked, provides very little iron and essentially no zinc due to its high concentration of phytic acid. Milling brown rice, which turns it into white rice, removes most of the minerals but also most of the phytic acid, leaving mineral bioavailability similar to or perhaps even better than brown rice (the ratio of phytic acid to iron and zinc actually decreases after milling rice). If you're going to throw rice into the rice cooker without preparing it first, white rice is probably better than brown overall. Either way, the mineral availability of rice is low. Here's how Dr. Robert Hamer's group put it when they evaluated the mineral content of 56 varieties of Chinese rice:
This study shows that the mineral bio-availability of Chinese rice varieties will be [less than] 4%. Despite the variation in mineral contents, in all cases the [phytic acid] present is expected to render most mineral present unavailable. We conclude that there is scope for optimisation of mineral contents of rice by matching suitable varieties and growing regions, and that rice products require processing that retains minerals but results in thorough dephytinisation.It's important to note that milling removes most of the vitamin content of the brown rice as well, another important factor.
Potatoes and other tubers contain much less phytic acid than whole grains, which may be one reason why they're a common feature of extremely healthy cultures such as the Kitavans. I went on NutritionData to see if potatoes have a better mineral-to-phytic acid ratio than grains. They do have a better ratio than whole grains, although whole grains contain more total minerals.
Soaking grains reduces their phytic acid content, but the extent depends on the grain. Gluten grain flours digest their own phytic acid very quickly when soaked, due to the presence of the enzyme phytase. Because of this, bread is fairly low in phytic acid, although whole grain yeast breads contain more than sourdough breads. Buckwheat flour also has a high phytase activity. The more intact the grain, the slower it breaks down its own phytic acid upon soaking. Some grains, like rice, don't have much phytase activity so they degrade phytic acid slowly. Other grains, like oats and kasha, are toasted before you buy them, which kills the phytase.
Whole grains generally contain so much phytic acid that modest reductions don't free up much of the mineral content for absorption. Many of the studies I've read, including this one, show that soaking brown rice doesn't really free up its zinc or iron content. But I like brown rice, so I want to find a way to prepare it well. It's actually quite rich in vitamins and minerals if you can absorb them.
One of the things many of these studies overlook is the effect of pH on phytic acid degradation. Grain phytase is maximally active around pH 4.5-5.5. That's slightly acidic. Most of the studies I've read soaked rice in water with a neutral pH, including the one above. Adding a tablespoon of whey, yogurt, vinegar or lemon juice per cup of grains to your soaking medium will lower the pH and increase phytase activity. Temperature is also an important factor, with 50 C (122 F) being the optimum. I like to put my soaking grains and beans on the heating vent in my kitchen.
I don't know exactly how much adding acid and soaking at a warm temperature will increase the mineral availability of brown rice (if at all), because I haven't found it in the literature. The bacteria present if you soak it in whey, unfiltered vinegar or yogurt could potentially aid the digestion of phytic acid. Another strategy is to add the flour of a high-phytase grain like buckwheat to the soaking medium. This works for soaking flours, perhaps it would help with whole grains as well?
So now we come to the next problem. Phytic acid is a medium-sized molecule. If you break it down and it lets go of the minerals it's chelating, the minerals are more likely to diffuse out of the grain into your soaking medium, which you then discard because it also contains the tannins, saponins and other anti-nutrients that you want to get rid of. That seems to be exactly what happens, at least in the case of brown rice.
So what's the best solution for maximal mineral and vitamin content? Do what traditional cultures have been doing for millenia: soak, grind and ferment whole grains. This eliminates nearly all the phytic acid, dramatically increasing mineral bioavailiability. Fermenting batter doesn't lose minerals because there's nowhere for them to go. In the West, we use this process to make bread, which would probably be a good food if it weren't for the gluten. In Africa, they do it to make ogi, injera, and a number of other fermented grain dishes. In India, they grind rice and beans to make idli and dosas. In the Phillipines, they ferment ground rice to make puto. Fermenting ground whole grains is the most reliable way to improve their mineral bioavailability and nutritional value in general.
But isn't having a rice cooker full of steaming brown rice so nice? I'm still working on finding a reliable way to increase its nutritional value.