title: An anatomy-based lumped parameter model of cerebrospinal venous circulation: can an extracranial anatomical change impact intracranial hemodynamics?
abstract: BACKGROUND
  The relationship between extracranial venous system abnormalities and central nervous system disorders has been recently theorized. In this paper we delve into this hypothesis by modeling the venous drainage in brain and spinal column areas and simulating the intracranial flow changes due to extracranial morphological stenoses.
  
  
  METHODS
  A lumped parameter model of the cerebro-spinal venous drainage was created based on anatomical knowledge and vessels diameters and lengths taken from literature. Each vein was modeled as a hydraulic resistance, calculated through Poiseuille's law. The inputs of the model were arterial flow rates of the intracranial, vertebral and lumbar districts. The effects of the obstruction of the main venous outflows were simulated. A database comprising 112 Multiple Sclerosis patients (Male/Female = 42/70; median age ± standard deviation = 43.7 ± 10.5 years) was retrospectively analyzed.
  
  
  RESULTS
  The flow rate of the main veins estimated with the model was similar to the measures of 21 healthy controls (Male/Female = 10/11; mean age ± standard deviation = 31 ± 11 years), obtained with a 1.5 T Magnetic Resonance scanner. The intracranial reflux topography predicted with the model in cases of internal jugular vein diameter reduction was similar to those observed in the patients with internal jugular vein obstacles.
  
  
  CONCLUSIONS
  The proposed model can predict physiological and pathological behaviors with good fidelity. Despite the simplifications introduced in cerebrospinal venous circulation modeling, the key anatomical feature of the lumped parameter model allowed for a detailed analysis of the consequences of extracranial venous impairments on intracranial pressure and hemodynamics.
authors.affiliation: Department of Electronics, Information and Bioengineering, Politecnico di Milano, Piazza Leonardo Da Vinci, 32, 20133, Milan, Italy. stefania.marcotti@mail.polimi.it.
authors.forename: Stefania
authors.initials: S
authors.lastname: Marcotti
authors.affiliation: Department of Electronics, Information and Bioengineering, Politecnico di Milano, Piazza Leonardo Da Vinci, 32, 20133, Milan, Italy. lara.marchetti@mail.polimi.it.
authors.forename: Lara
authors.initials: L
authors.lastname: Marchetti
authors.affiliation: Magnetic Resonance Laboratory, Fondazione Don Carlo Gnocchi ONLUS, IRCCS Santa Maria Nascente, Via Capecelatro 66, 20148, Milan, Italy. pcecconi@dongnocchi.it.
authors.forename: Pietro
authors.initials: P
authors.lastname: Cecconi
authors.affiliation: Department of Electronics, Information and Bioengineering, Politecnico di Milano, Piazza Leonardo Da Vinci, 32, 20133, Milan, Italy. emiliano.votta@polimi.it.
authors.forename: Emiliano
authors.initials: E
authors.lastname: Votta
authors.affiliation: Department of Electronics, Information and Bioengineering, Politecnico di Milano, Piazza Leonardo Da Vinci, 32, 20133, Milan, Italy. gianfranco.fiore@polimi.it.
authors.forename: Gianfranco Beniamino
authors.initials: GB
authors.lastname: Fiore
authors.affiliation: Magnetic Resonance Laboratory, Fondazione Don Carlo Gnocchi ONLUS, IRCCS Santa Maria Nascente, Via Capecelatro 66, 20148, Milan, Italy. antonellobar@yahoo.it.
authors.forename: Antonello
authors.initials: A
authors.lastname: Barberio
authors.affiliation: Magnetic Resonance Laboratory, Fondazione Don Carlo Gnocchi ONLUS, IRCCS Santa Maria Nascente, Via Capecelatro 66, 20148, Milan, Italy. stefano.viotti@gmail.com.
authors.forename: Stefano
authors.initials: S
authors.lastname: Viotti
authors.affiliation: Department of Electronics, Information and Bioengineering, Politecnico di Milano, Piazza Leonardo Da Vinci, 32, 20133, Milan, Italy. alberto.redaelli@polimi.it.
authors.forename: Alberto
authors.initials: A
authors.lastname: Redaelli
authors.affiliation: Magnetic Resonance Laboratory, Fondazione Don Carlo Gnocchi ONLUS, IRCCS Santa Maria Nascente, Via Capecelatro 66, 20148, Milan, Italy. mlagana@dongnocchi.it.
authors.forename: Maria Marcella
authors.initials: MM
authors.lastname: Laganà
mesh_terms: D000328:Adult; D001921:Brain / Q000098:blood supply*; D016022:Case-Control Studies; D002560:Cerebrovascular Circulation / Q000502:physiology*; D005260:Female; D006439:Hemodynamics / Q000502:physiology; D006801:Humans; D007427:Intracranial Pressure / Q000502:physiology; D007601:Jugular Veins / Q000502:physiology; D008297:Male; D008875:Middle Aged; D009103:Multiple Sclerosis / Q000503:physiopathology*; D055815:Young Adult