A pharmacological compound characterized by the conjugation of a fatty acid such as butyric, caproic, caprylic, lauric, myristic, palmitic, stearic, arachidic, behenic, oleic, linoleic, alpha-linolenic, arachidonic, eicosapentaenoic, docosahexaenoic acid, euric acid with Hyodeoxycholic acid or other systemic biocompatible lipid solubilizer/detergent compounds, as opposed to biocompatible lipid solubilizers/detergents sequestered in the entero-hepatic circulation, said conjugated compound being capable of producing a sustained bioavailability in the systemic circulation to access atherosclerotic plaques and cause ubiquitous dissolution of the cholesterol crystals and of the other cholesterol/lipids aggregations forming the lipidic component of an atherosclerotic plaque and also the ubiquitous dissolution of adipose tissue.