B-hydroxybutyrate is one of the three ketone bodies that the body makes from fatty acids. Chemically, it is not actually a ketone, but it is made, along with acetoacetate and acetone, as part of the process of fatty acid metabolism (ketones are partially-metabolised fatty acids, just as charcoal is partially-burnt wood). In fact, β-hydroxybutyrate is the principal ketone body, and researchers therefore use it as the primary marker of nutritional ketosis.
If you have a blood meter that measures your GKI, then you are already measuring your serum β-hydroxybutyrate, because it is the “K” in the GKI, your glucose/ketone index. I’d be willing to bet that your meter has a setting that will give the glucose and ketone readings separately.
Under conditions of very low carbohydrate intake, the brain still needs to be fed. So the liver takes fats and turns them into ketone bodies. The liver also makes a small amount of glucose, to feed the red blood corpuscles (which cannot use ketones at all) and those parts of the brain that absolutely require glucose (the brain requires a certain small amount of glucose, but it can get nearly all the energy it needs from ketones). These twin processes of ketogenesis and gluconeogenesis are the hallmarks of nutritional ketosis.
In conditions of dietary glucose above a certain amount, the liver stops making ketones and glucose, and the brain feeds almost entirely on glucose. The problem is that excessive glucose and insulin levels (hyperglycaemia and hyperinsulinaemia) are very damaging to the body, which is the rationale for a low-glucose diet to prevent hyperinsulinaemia.
If you are concerned about low ketone levels, make sure to get plenty of fat, since fatty acids are the raw materials for ketone bodies. You will naturally be eating quite a bit of meat, so make sure not to trim off any of the fat, cook with butter, lard, tallow, or bacon grease, and you can even butter your meat, if you want. When we eat like this, the resulting low insulin allows the metabolic rate to increase, so we can metabolise both the fat we eat and some of the excess stored fat in our adipose tissue (fat cells).