This paper presents a mathematical model of the global, arterio-venous circulation in the entire human body, coupled to a refined description of the cerebrospinal fluid dynamics in the craniospinal cavity. The present model represents a substantially revised version of the original Muller-Toro mathematical model¹. It includes onedimensional, non-linear systems of partial differential equations for 323 major blood vessels and 85 zero-dimensional, differential-algebraic systems for the remaining components. Highlights include the myogenic mechanism of cerebral blood regulation; refined vasculature for the inner ear, the brainstem and the cerebellum; and viscoelastic, rather than purely elastic, models for all blood vessels, arterial and venous. The derived one-dimensional parabolic systems of partial differential equations for all major vessels are approximated by hyperbolic systems with stiff source terms following a relaxation approach^2,3,4. A major novelty of this paper is the coupling of the circulation, as described, to a refined description of the cerebrospinal fluid dynamics in the craniospinal cavity, following Linninger et al.⁵. The numerical solution methodology employed to approximate the hyperbolic non-linear systems of partial differential equations with stiff source terms is based on the ADER finite volume framework⁶, supplemented with a well-balanced formulation^7,8 and a local time stepping procedure⁹. The full model is validated through comparison of computational results against published data and bespoke MRI measurements. Then we present two medical applications: (i) transverse sinus stenoses and their relation to Idiopathic Intracranial Hypertension; and (ii) extra-cranial venous strictures and their impact in the inner ear circulation, and its implications for Ménière's disease.