ISNVD Abstract Book

POLITECNICO DI MILANO
mlagana@dongnocchi.it
stefania.marcotti@mail.polimi.it
A lumped-parameter model for the study of
cerebrospinal venous flow
Marcotti S 1 , Marchetti L 1 , Laganà MM 2 , Fiore GB 1 , Barberio A 2 , Viotti S 3 , Votta E 1 ,
Redaelli A 1 , Cecconi P 2
1
Bioengineering Department, Politecnico di Milano, Milan, Italy;
2
Magnetic Resonance Laboratory, Fondazione Don Gnocchi ONLUS, IRCCS Santa Maria Nascente,
Milan, Italy;
3
Università degli Studi di Milano, Milan, Italy.
Introduction
An impaired cerebrospinal venous drainage, defined as chronic
cerebrospinal venous insufficiency (CCSVI), has been recently
hypothesized to be one of the possible causes of Multiple Sclerosis (MS) [1]. It
is possible to delve into this hypothesis modeling the venous drainage in
brain and spinal column areas and simulating the intracranial flow changes due
to extracranial morphological stenoses. This study aims at:
1. constructing a lumped parameter model of the cerebrospinal venous
district, based on anatomical data
2. using the model for the simulation of different venous impairment
patterns
3. comparing the output of the model with in vivo controls’ data from
healthy subjects
4. comparing the CCSVI simulations with MS patients’ data
Material and Methods
1. A lumped parameter model of the neck and brain venous flow was created,
grounding on anatomical knowledge. Morphology and vessels’ diameters
and lengths were taken from literature [2].
• Each venous vessel was modeled as a hydraulic resistance, calculated
through Poiseuille law
• The inputs of the model were inlet arterial flow rates of the intracranial,
vertebral and lumbar districts
• The outputs were pressures and flows of each vessel, obtained solving the
attained linear system with a Matlab® script
2. Four pathological patterns observed in MS [1] were simulated through
the model, properly modifying the diameters of those specific vessels
which are supposed to be impaired by CCSVI and adding collateral
vessels
3. 12 healthy controls (HC) (Male/Female = 11/3; median age (range) =
24.5 (22-52) years) were examined using a 1.5 T Magnetic Resonance (MR)
Siemens Magnetom Avanto scanner. Neck and intracranial veins’ flow rates
were estimated with Phase Contrast MR. MeanflowsoftheHCgroup
were compared with the physiological output flows computed with the
model. MR Time of Flight (TOF) images were also acquired to visualize and
compare vessels’ morphologies
The standard protocol for the CCSVI diagnosis [1] was used and neck
vessels’ flow rates were estimated with Pulsed Wave Doppler ECD.
Flow rates resulting from these simulations were compared with the
clinical observations of the MS group.
Fig. 3 ECD image of an internal
jugular vein’s reflux in a MS
patient
Results
Fig. 4 TCCD image of a superior petrosal
sinus’ reflux in a MS patient
• MRI images of the HC showed a high inter-subject morphological
variability
• Average values obtained in HC matched with good agreement the
outputs of the model
Fig. 5 Model of physiological pattern (arrows indicate flow directions). Short forms
stand for: ophthalmic veins OVl, OVr; basal veins of Rosenthal Rl, Rr; internal
cerebral veins ICVl, ICVr; inferior and superior sagittal sinus ISS, SSS; great vein of
Galen GV; straight sinus SS; transverse sinus TSl, TSr; anterior and posterior occipital
sinus POS, POSl, POSr, AOSl, AOSr; cavernous sinus CSl, CSr; superior and inferior
petrosal sinus SPSl, SPSr, IPSl, IPSr; sigmoid sinus SSl, SSr; internal jugular veins
IJVl, IJVr; vertebral veins VVl 1…6, VVr 1…6; cervical plexus CPa, CPp, CP 1…7;
linkage vessels between cervical plexus and vertebral veins CPVVl 1…6, CPVVr 1…6;
thoracic plexus TP 1…12; azygos vein AZ 1…12; linkage vessels between thoracic
plexus and azygos vein TPAZ 1…12; inferior vena cava CV, CV1, CV2; lumbar plexus
LP 1…2; lumbar vein LV 1…2; linkage vessels between lumbar plexus and lumbar vein
LPLV 1…2.
• As regards the pathological simulations, the model showed inverted flow
direction in the venous vessels which have been usually found to be
affected by reflux in real clinical MS cases
Fig. 1 RM-TOF images of 3 healthy controls. Is it possible to notice the differences
in disposition, morphology and vessels’ number
SSIGM right
SSIGM left
TS left
TS right
SSS
SS
Fig. 6 Example of model of pathological pattern: by reducing diameter of IJVs and
AZ, the model predicts inverted flow in SPS and TP, as observed in MS group
Discussion
Fig. 2 RM-Phase Contrast images analyzed to estimate flow rates of sigmoid sinus
(SSIGM), transverse sinus (TS), straight sinus (SS) and superior sagittal sinus (SSS)
4. 184 MS patients (Male/Female = 103/81; median age (range) = 42 (14-
75) years) were evaluated by an expert radiologist with ECD and
Transcranial Color Doppler (TCCD) Esaote MyLabVinco.
The proposed model can predict physiological and pathological
behaviors with good fidelity. Nevertheless, it could be improved taking into
account vessels' compliance and the thoracic pump effect. Moreover,
due to the high variability of vessel morphology among subjects, the
collection of a larger number of healthy controls is mandatory, so to assess
which hemodynamic and morphological patterns characterize this group and
better discriminate with respect to the MS population. In general, this model
could represent the first step towards the definition of patient specific
models , from MRI exams.
References
[1] Zamboni P, Galeotti R, Menegatti E, Malagoni AM, Tacconi G, Dall'Ara S, Bartolomei I, Salvi F. Chronic cerebrospinal venous insufficiency in patients with multiple sclerosis. J Neurol Neurosurg Psychiatry. 2009; 80:392-399.
[2] Newton TH, Potts DG. Radiology of the skull and brain – Angiography (Volume two/book 3; part XIII: Veins). MediBooks, Great Neck, NY 1974.