Available via license: CC BY 4.0
Content may be subject to copyright.
Physiological Measurement
PAPER • OPEN ACCESS
Anatomical atlas of the upper part of the human
head for electroencephalography and
bioimpedance applications
To cite this article: Fernando S Moura et al 2021 Physiol. Meas. 42 105015
View the article online for updates and enhancements.
You may also like
High density carbon fiber arrays for
chronic electrophysiology, fast scan cyclic
voltammetry, and correlative anatomy
Paras R Patel, Pavlo Popov, Ciara M
Caldwell et al.
-
Spinal pedicle screw planning using
deformable atlas registration
J Goerres, A Uneri, T De Silva et al.
-
Review on biophysical modelling and
simulation studies for transcranial
magnetic stimulation
Jose Gomez-Tames, Ilkka Laakso and
Akimasa Hirata
-
This content was downloaded from IP address 89.249.56.102 on 25/11/2022 at 14:36
Physiol. Meas. 42 (2021)105015 https://doi.org/10.1088/1361-6579/ac3218
PAPER
Anatomical atlas of the upper part of the human head for
electroencephalography and bioimpedance applications
Fernando S Moura
1,2
, Roberto G Beraldo
1
, Leonardo A Ferreira
1
and Samuli Siltanen
2
1
Engineering, modelling and Applied Social Sciences Center, Federal University of ABC São Bernardo do Campo, São Paulo, Brazil
2
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
E-mail: fernando.moura@ufabc.edu.br
Keywords: anatomical atlas, cerebral circulation, electrical properties, human head model, electrophysiology, electrical impedance
tomography, electroencephalography
Abstract
Objective. The objective of this work is to develop a 4D (3D+T)statistical anatomical atlas of the
electrical properties of the upper part of the human head for cerebral electrophysiology and
bioimpedance applications. Approach. The atlas was constructed based on 3D magnetic resonance
images (MRI)of 107 human individuals and comprises the electrical properties of the main internal
structures and can be adjusted for specific electrical frequencies. T1w+T2w MRI images were used to
segment the main structures of the head while angiography MRI was used to segment the main
arteries. The proposed atlas also comprises a time-varying model of arterial brain circulation, based on
the solution of the Navier–Stokes equation in the main arteries and their vascular territories. Main
results. High-resolution, multi-frequency and time-varying anatomical atlases of resistivity, con-
ductivity and relative permittivity were created and evaluated using a forward problem solver for EIT.
The atlas was successfully used to simulate electrical impedance tomography measurements indicating
the necessity of signal-to-noise between 100 and 125 dB to identify vascular changes due to the cardiac
cycle, corroborating previous studies. The source code of the atlas and solver are freely available to
download. Significance. Volume conductor problems in cerebral electrophysiology and bioimpedance
do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its
electrical properties for solving the associated PDEs numerically. Ideally, the model should be made
with patient-specific information. In clinical practice, this is not always the case and an average head
model is often used. Also, the electrical properties of the tissues might not be completely known due to
natural variability. Anatomical atlases are important tools for in silico studies on cerebral circulation
and electrophysiology that require statistically consistent data, e.g. machine learning, sensitivity
analyses, and as a benchmark to test inverse problem solvers.
1. Introduction
Electrophysiology is the branch of physiology that investigates the electrical properties of biological tissues. The
analysis is based on electrical measurements, voltages, or electric currents, generated by the tissue or in response
to external electric stimuli.
One special group is clinical neurophysiology, where the bioelectrical activity is recorded to assess central
and peripheral nervous systems. Electroencephalography (EEG)is an important monitoring and diagnostic
method in this speciality to record brain electrical activity that can be used to diagnose thalamocortical rhythms,
such as assessing seizure disorders, epilepsy, sleep disorders, coma, schizophrenia, Parkinson disease, and brain
death (Michel and Brunet 2019, Jatoi and Kamel 2017).
Electroencephalography measures voltage variations using multiple electrodes typically placed along the
scalp of the patient. The measured voltages are the result of ionic currents inside the brain, therefore they are
caused by spontaneous electrical activity.
OPEN ACCESS
RECEIVED
7 July 2021
REVISED
16 October 2021
ACCEPTED FOR PUBLICATION
21 October 2021
PUBLISHED
26 November 2021
Original content from this
work may be used under
the terms of the Creative
Commons Attribution 4.0
licence.
Any further distribution of
this work must maintain
attribution to the
author(s)and the title of
the work, journal citation
and DOI.
© 2021 The Author(s). Published on behalf of Institute of Physics and Engineering in Medicine by IOP Publishing Ltd
In the case of epilepsy diagnostics, EEG is employed to determine the type, location, and extension of the
lesion causing seizures. This is a challenging task since it depends on measurements taken on the surface of the
scalp to infer the internal source of the disorder, a process called source reconstruction (Hallez et al 2007, Grech
et al 2008).
Bioimpedance analysis is another group of methods used to assess the electrical properties of biological
tissues. Measurements are made in response to external stimuli, such as measuring voltages caused by external
current sources attached to the surface of the body or vice-versa.
Electrical impedance tomography (EIT)is a medical image technique in which electrical measurements on
the surface of the body are used to create an image of conductivity distribution (or admittivity, the complex-
valued equivalent)within the body. The image can then be associated with the physiological conditions of the
patient. EIT has been used successfully in many areas, such as in lung applications to monitor acute respiratory
distress syndrome, obstructive lung diseases or perioperative patients (Martins et al 2019), monitoring
mechanical ventilation, heart activity (Frerichs et al 2016), cardiac function and detecting cancerous tissues
(Adler and Boyle 2019). It is also being investigated to monitor brain activity and to distinguish between
ischemic and hemorrhagic stroke (Adler and Boyle 2019).
Many electrophysiology applications require solving a nonlinear ill-posed inverse problem associated with
the volume conductor. Reliable and stable solutions depend on prior information about the geometry and
electrical properties of the tissues and knowledge about measurement uncertainty. In the case of source
reconstruction, prior information about the electrical properties of the tissues is required for composing the
forward volume conduction model needed in the process. Small errors in the electrical properties inside the head
can obfuscate the effects of deep brain activity. In the case of EIT, anatomical and electrical prior information is
also required to restrict the solution search space.
In addition, the brain is not a static structure. The flow of blood varies periodically during each cardiac cycle
(Wagshul et al 2011). Intracranial pulsatility has been evaluated using magnetic resonance imaging (Vikner et al
2019, Holmgren et al 2019), or transcranial Doppler sonography (Kneihsl et al 2020), and tissue pulsatility
imaging (Kucewicz et al 2008, Desmidt et al 2018).
Blood flow centre-line velocity and artery radius influence the electrical impedance of blood in that artery
(Gaw et al 2008, Shen et al 2016,2018). This makes it promising to use electrical conductivity measurements,
such as in EIT or impedance cardiography, in haemodynamic monitoring using surface electrodes on the skin.
In fact, there have been several works recently aiming to monitor blood flow and/or pressure waveforms using
them, e.g. common carotid arteries (Zhang et al 2020), aortic artery (Badeli et al 2020), pulmonary artery (Braun
et al 2018), radial artery (Pesti et al 2019), and cerebral arteries (Beraldo and Moura 2020). There are works about
impedance cardiography to determine stroke volume (Bernstein 2010), electrical bioimpedance sensing to
determine the central aortic pressure curves (Min et al 2019), and pulmonary artery pressure estimation using
EIT (Proença et al 2020). There is an increasing interest in brain monitoring using electrical measurements, such
as to monitor ventricular volume (Wembers et al 2019), rheoencephalography to assess cerebral blood flow
(Bodo et al 2018, Meghdadi et al 2019), brain perfusion of rats (Dowrick et al 2016, Song et al 2018), and stroke
identification (Goren et al 2018, Agnelli et al 2020, Candiani and Santacesaria 2020, Candiani et al 2019).
Volume conductor problems in electrophysiology and bioimpedance do not have analytical solutions for
nontrivial geometries and rely on numerical methods, e.g. finite element method (FEM)to discretize the head in
small elements and solve the associated PDEs. Ideally, the FEM model should be built with patient-specific
information, taken from MRI or CT scans to capture precisely the geometry of the head, its internal structures,
and electrode positions. Unfortunately, in clinical practice, this is not the case. Often, an oversimplified
geometry is employed for all patients due to the lack of computational tools and time.
The effects of mismodelling have been investigated before. EEG source localization errors increase
substantially when individual-specific head models are not at disposal (Acar and Makeig 2013). The authors also
show that errors in the conductivity of the skull cause large estimate errors. The latter is especially challenging
because the electrical properties of the skull are highly heterogeneous and have large variability inter-individual.
Cerebrospinal fluid (CSF)has a big impact on the results due to its high conductivity that forms a conductive
layer surrounding the brain effectively shielding the interior (Vorwerk et al 2014, Cho et al 2015). Also, the
authors show that distinguishing white and grey matters also impact the head volume conductor model.
The objective of this work is to develop a statistical anatomical atlas of electrical properties of the upper part
of the human head for electrophysiology and bioimpedance applications. The atlas is constructed based on MRI
images of human individuals and comprises the electrical properties of the main structures for
electrophysiology. The proposed atlas also comprises a time-varying model of the brain circulation, based on the
solution of the Navier–Stokes equation for blood flow in the main arteries (Melis et al 2017, Melis 2018). The
atlas can be used to generate synthetic data statistically consistent with the population to compose learning sets
for machine learning methods, for sensitivity analyses, and as a benchmark to test algorithms. The atlas can also
2
Physiol. Meas. 42 (2021)105015 F S Moura et al
be used as statistical prior information for inverse problems in electrophysiology. Anatomy-based priors are
found in the literature, such as for thorax applications (Martins et al 2019, Kaipio and Somersalo 2005).
2. Anatomical atlas description and construction
The anatomical atlas is composed of a static component A
s
with the electrical properties of the main tissues
found in the upper part of the human head and a dynamic component A
d
(t)to account for blood perfusion
dynamics in the human head. The two components of the atlas are considered Gaussian and independent,
therefore the final statistics of the atlas Ais composed by
G~ANx,, 1
sss
(¯)()
G~At Nxt t,, 2
ddd
() (
¯() ()) ()
GG~+ +At Nx x t t,. 3
sd sd
() ( () ()) ()
The two components of the atlas are presented in details in the following subsections.
2.1. Static component
The static component of the atlas distinguishes five main compartments of importance for electrophysiology of
the human head: grey matter (GM), white matter (WM), cerebrospinal fluid (CSF), bones (BO)and other soft
tissues (OT). Figure 1depicts the general procedure to calculate the static component of the anatomical atlas.
3D Magnetic Resonance (MR)images of 107 healthy human individuals, made available by the CASILab at
the University of North Carolina at Chapel Hill, were used to build the atlas (Bullitt et al 2005). The MR images
were obtained in a three-tesla equipment with a resolution of 1 ×1×1 mm. An equal number of male and
female individuals were used, with an average age of 43 ±15 years old. The dataset contains T1w and T2w MR
images of each patient and are both used to improve skull segmentation (Nielsen et al 2018)as described below.
The symmetric image normalization (SyN)method was applied to the images to diminish differences due to
misalignment, aspect ratio, and sizes between the heads (Avants et al 2008). For this purpose, the advanced
normalization tools was used, under the Neuroimaging in Python Pipelines and Interfaces (Nipype)framework
(Gorgolewski et al 2011). Detailed information regarding the normalization can be found in Avants et al
(2008,2009).
Each of the 214 (2×107)images was transformed aiming to maximize its similarity with a reference image.
The reference image is the MNI ICBM 152
3
, a nonlinear symmetric atlas with 1 ×1×1 mm resolution
(Grabner et al 2006, Fonov et al 2009). The reference image is presented in figure 2. Using an average head
geometry as reference avoids having to choose one of the images in the dataset as reference, eliminating the
possibility of choosing as a reference an individual with any abnormal geometric feature. Each transformation is
Figure 1. Main steps necessary to compute the static component of the anatomical atlas. Each image is normalized to a reference
image, segmented into the main compartments. Each segment is assigned with the corresponding electrical property and, finally, the
statistics of the atlas can be estimated.
3
Available at http://nist.mni.mcgill.ca/?p=858
3
Physiol. Meas. 42 (2021)105015 F S Moura et al
performed in two stages, first a rigid transformation to roughly align the geometries, followed by an affine
transformation.
The normalization process assumes the heads have similar shapes and proportions. Therefore, the atlas
represents a head with size and proportions similar to the reference head used for the normalization. If
necessary, the resulting atlas can be transformed to accommodate other geometries, for example when the
geometry of the head of the patient is available or if an average head model is preferred. This procedure will be
described in section 3.3.
After the spatial normalization, the images were segmented into six classes: background, WM, GM, CSF, BO,
and OT. The statistical parametric mapping (SPM)was used to segment the images (Frackowiak et al 2004).
Compact bones produce very low MR signals, causing difficulties for skull segmentation. A recent study by
Nielsen et al (2018)presents an analysis on the performance of bone segmentation using various toolboxes
commonly employed to segment the human head against CT-based skull segmentation. The authors show that
SPM outperforms other methods in the study when the multi-channel (T1w+T2w)strategy is employed. The
inclusion of T2w increases the contrast between scalp, compact bone and CSF and greatly reduces the presence
of outliers with bad segmentation, substantially reducing the variance across subjects. This combination also
increases the contrast between soft tissues (Misaki et al 2014). The authors also describe that SPM’s multi-
channel segmentation (T1w+T2w)inaccuracies compared to CT segmentation manifest mainly as false
positives around the air cavities and false negatives around the vertebrae. For the proposed atlas, segmentation
errors between bone and air is not an issue due to their high resistivities while the vertebrae region is out of the
scope of the atlas proposed in this work.
We employed SPM’s multi-channel segmentation (T1w+T2w)following the guidelines from Nielsen et al
(2018). The method is composed of a preprocessing step where T1w and T2w images are coregistered
maximizing mutual information, followed by circular optimization of three components: (i)modelling of the
intensities of the images using a Gaussian mixture model; (ii)normalization of tissue probability maps of the five
parts of the head with the images; and (iii)a bias field correction. Further details about the implementation can
be found in Ashburner and Friston (2005). At the end of this phase, each voxel of the images is assigned to the
label with the highest probability.
Three additional steps were also performed to improve segmentation. (i)Any segmentation holes inside the
head were filled with the nearest tissue in the image. This procedure was applied to all 2D slices in the three
anatomical planes of each image, (ii)small segmentation artefacts outside the human head were removed by
isolating the largest connected group in the image using a six-connected neighbourhood strategy. (iii)Four
iterations of morphological opening operation to the binary mask of the head to smooth the external surface of
the head.
2.1.1. Electrical properties of the segments
Each voxel of the segmented images was assigned to the electrical property of the corresponding tissue before
computing the statistics of the atlas. Tissues were modelled as isotropic, even though it is known that some
tissues are anisotropic. The electrical properties depend on the type, physiological conditions and frequency in
consideration (Gabriel et al 1996,1996a).
Given the angular frequency of the electrical signal ω=2πf, the complex relative permittivity
w
ˆ(
)
of a
tissue can be modelled as the sum of four Cole–Cole dispersion terms (Gabriel et al 1996b)
å
wwt
s
w
=+ D
++
a
¥
=
-
jj1,4
n
n
n
1
4
1
0
0
n
ˆ( ) () ()
where ò
0
is the permittivity of free space and all the other parameters depend on the tissue (Gabriel et al 1996b,
Andreuccetti et al 1997). The conductivity σand permittivity òof the tissue can be obtained from
w
ˆ(
)
Figure 2. Slices of the reference image MNI ICBM 152.
4
Physiol. Meas. 42 (2021)105015 F S Moura et al
sw w w=-
Im , 5
0
() (ˆ()) ()
ww=
Re . 6
0
() (ˆ()) ()
Biological tissues are naturally inhomogeneous, due to their complex macroscopic and microscopic
structure, function and physiological condition. To account for this, the uncertainty level of the estimates from
the above equations was set to ±20% following reported results in Gabriel et al (1996a).
The Electrical properties of BO were modelled as the average between cortical and cancellous bones, while
OT was modelled as muscle tissue.
2.1.2. Atlas statistics computation
Let Î
u
NVbe a vector representing a 3D image of the human head after normalization and segmentation,
where N
V
is the number of voxels, excluding those representing the background around the head. Let the image
be segmented into N
T
nonintersecting regions (tissues), each one with associated characteristic function
c
Î
tNV, for t=1, 2, L,N
T
. Also, let p
t
be the electrical property of each tissue under consideration. The
property can be real (e.g. resistivity or conductivity)or complex-valued (e.g. impeditivity or admitivity). We can
write the 3D image of this property ÎxNV(or real with the same dimension)as
å
c==
=
xXpp,7
t
N
tt
1
T
()
where ÎpNTis a vector composed by the electrical properties of the tissues and δ
XNN
VT
is a matrix where
each column is a characteristic function.
Assume images from N
I
individuals are used to build the atlas. Formally this number should be very large to
represent the statistics of the population. In practice, this number is limited by the size of the dataset. To reduce
this limitation each individual will be considered N
S
times, each time with a different value for p, following the
statistics of the tissues. This implies that the N
I
individuals represent the general shape of the head of the
population while allowing the electrical properties of the tissues to be more diverse. In addition, we assume the
same number of samples N
S
per individual, making them equally probable.
Using these hypotheses the average and covariance of the population can be estimated efficiently. For the
covariance matrix Γin special, the formulation allows the computation in factorized form Γ=KK
T
, reducing
storage requirements and simplifying algorithms that depend on factorizations of Γ.
Samples of the ith individual can be composed by sampling the properties of the tissues p
s
and applying (7)
==xXp sN,for 1,2,,, 8
si i sS,
()
where the samples p
s
can be generated from data fitted models or measurements. In this work, the electrical
properties of the tissues are considered Gaussian with average resulting from the model (4)and standard
deviation of 20% of the average, following reported results (Gabriel et al 1996a).
Let x
s,i
represent a sample of the ith individual. The average over all individuals can be estimated with
åå å å å
== =
== = = =
xXpXxNN N N N p
1111
,9
SI
i
N
s
N
si
Ii
N
i
Ss
N
sIi
N
i
11
,
11 1
IS I S I
¯¯()
where, again, N
S
is fixed and represent the number of samples with the same head geometry X
i
and
p
¯
is the
average electrical properties of the tissues.
The covariance matrix can be computed using the usual sample estimator
åå
G=---
==
xx
NN xx
1
1,10
IS i
N
s
N
si si
11
,,
H
IS
(¯)( ¯)()
where Gδ
NN
VV
and M
H
denotes conjugate transpose of M. For real valued p, the conjugate transpose is the
transpose M
H
=M
T
Adding -xx
ii
(
¯¯
)to both terms between parenthesis and rearranging the terms,
åå
G=--+- - +-
==
xx
NN xxx x xx
1
1,11
IS i
N
s
N
si i i si i i
11
,,
HH
IS
[( ¯)(
¯¯
)][( ¯)(
¯¯
)] ( )
where
=å
=
xxN
is
Nsi S
1,
S
¯
is the average of the ith individual. Proceeding with the products,
å
aaaaG=-+++
=
NN
1
1,12
IS i
N
1
123 4
I
() ()
å
aG=--=-
=
xxxxN1, 13
s
N
si i si i S i1
1
,,
H
S
(¯)( ¯)( ) ()
5
Physiol. Meas. 42 (2021)105015 F S Moura et al
åå
a=--= - -=
==
xxxx x x x x 0, 14
s
N
si i i
s
N
si i i2
1
,H
1
,H
SS
⎡
⎣
⎢⎤
⎦
⎥
(¯)(¯¯
)(
¯)(
¯¯
)()
åå
a=--=- -=
==
xxxx x xx x 0, 15
s
N
isii i
s
N
si i3
1
,H
1
,H
SS
⎡
⎣
⎢⎤
⎦
⎥
(¯¯
)( ¯)(
¯¯
)( ¯)()
å
a=--=--
=
xxxx Nxxxx.16
s
N
ii Sii4
1
HH
S
(¯¯
)(¯¯
)(
¯¯
)(¯¯
)()
Finally, taking the limit N
S
→∞
åå
GG=+ --
==
NN
xxxx
11 .17
Ii
N
i
Ii
N
ii
11
H
II
(¯¯
)(¯¯
)()
Defining
D
=-xx
x
ii
¯¯¯
and observing the linear relation (7)we can rewrite this last expression as
åå
GG=+DD=
==
XX WW
Nxx
1,18
Ii
N
ipiii
i
N
ii
1
HH
1
H
II
[¯¯
]()
G=DWX
Nx
1,19
i
I
ip i
⎡
⎣⎤
⎦
¯()
where
Î
´+
W
iNN1
VT
()
and Gδ
pNN
TT
is the covariance matrix of the electrical properties of the tissues.
Furthermore, the expression can be simplified to
G==WW
W
W
KK ,20
I
I
1
1
H
H
H
⎡
⎣
⎢
⎢⎤
⎦
⎥
⎥
[] ()
where δ+
K
NN N1
VT I
[( ) ]. Note that both the average (9)and the covariance (20)estimates do not require
explicit sampling procedure presented in (8).
In case of complex-valued p, the pseudo-covariance Gδ
NN
VV
˜can be computed in a similar way
G=KK .21
T
˜()
The atlas in this work is assumed Gaussian, therefore
x
¯and Γ(and
G
˜
for complex-valued p)completely
specify its probability density function.
2.2. Dynamic component
Flow in the cranial cavity is pulsatile, following the cardiac cycle. Arterial blood flows in waves, forcing part of the
venous blood and CSF to move, following the Monro-Kellie hypothesis (Wagshul et al 2011). Venous blood is
drained to the jugular veins via cerebral sinuses, while CSF moves in the subarachnoid space and leaves/returns
to the cavity via the foramen magnum to balance intracranial pressure waves during the cardiac cycle (Greitz et al
1992, Sakka et al 2011). Recently, pulsatility was also observed in small cortical veins (Driver et al 2020), and
studies in rats show that the flow in microvessels is quasi-steady laminar flow, following Hagen–Poiseuille law
expected in low Reynolds and Womersley numbers (Seki et al 2006).
Arterial blood enters the cranial cavity through its base via two pairs of arteries, the (right/left)vertebral and
internal carotid arteries. After entering, these arteries form the circle of Willis, a circulatory anastomosis
responsible for providing backup routes for cerebral blood supply (Bradac 2017, Chandra et al 2017). From the
circle of Willis four main pairs of arteries branch out, the (right/left)anterior, middle, posterior cerebral, and
superior cerebellar arteries.
The dynamic component of the atlas comprises the circulation in the main cerebral arteries. The procedure
follows the same main steps presented in section 2.1 with a few modifications. (i)Magnetic Resonance
Angiography (MRA)images of 109 healthy human individuals were used (Bullitt et al 2005). The images were
obtained in a three tesla equipment with a resolution of 0.5 ×0.5 ×0.8 mm. An equal number of male and
female individuals were used, with an average age of 43 ±14 years old. (ii)Segmentation was performed first by
applying a total variation filter to the images followed by a threshold segmentation. Only the lumen of the vessels
with contrast agent were segmented. (iii)Electrical property assignment follows the procedure described in the
following subsection.
2.2.1. Electrical properties of the segments
The influence of blood flow centre-line velocity and vessel radius over the electrical impedance of blood is
modelled and included in the atlas (Gaw et al 2008, Shen et al 2016,2018).
We simulated blood flow in the main arteries of the brain using the openBF solver (Melis et al 2017,
Melis 2018), a 1D blood flow solver based on monotonic upstream-centered scheme for conservation laws
6
Physiol. Meas. 42 (2021)105015 F S Moura et al
(MUSCL)finite-volume numerical scheme. The solver assumes the blood is an incompressible Newtonian fluid,
flowing through narrow and long circular vessels with linear compliant walls. The Navier–Stokes equations are
reduced to 1D by imposing axisymmetry, linearized and solved for pulsatile flows using the finite difference
method. Detailed description can be found in Melis (2017).
Brain circulation simulation encompasses the superior aortic system, from the ascending aorta to the main
arteries providing blood to the brain. The arteries considered in the simulation can be seen in figure 3.
Blood was assumed Newtonian with density ρ=1050 kg m
−3
and dynamic viscosity μ=4.5 ×10
−3
Pa s.
The geometry and mechanical properties of the vessels are presented in table 1, based on Alastruey et al (2007)
and complemented with data collected by Dodo et al (2020), Fomkina et al (2016), Schmitter et al (2013). The
terminal vessels were coupled with 3-element Windkessel models to mimic the perfusion of downstream vessels
and avoid numerical oscillations. Heart flow output in one cardiac cycle was set to
p
tt
=<
Qt Qttsin
0otherwise
,22
M
⎧
⎨
⎩
⎛
⎝⎞
⎠
() ( )
where Q
M
=485 ml s
−1
is peak flow rate, τ=0.3 s and the cardiac cycle period is 1 s, following (Alastruey et al
2007).
Lasting one cardiac cycle, the simulated pulsatile blood flow of each vessel must be converted to the electrical
property of interest. Visser’s model, a nonlinear function that relates blood resistivity changes to the average
blood velocity in a cylindrical vessel, can be used for this purpose (Visser 1989,1992, Hoetink et al 2004)
r
r
D=- - -Hv
R
0.45 1 exp 0.26 , 23
0
0.39
⎜⎟
⎡
⎣
⎢⎛
⎝⎞
⎠⎤
⎦
⎥
¯()
ℓ
where Δρ
ℓ
is the longitudinal resistivity change to the reference (still blood)resistivity ρ
0
,His the hematocrit
(volume percentage of red blood cells in the blood),v
¯is the average cross-sectional velocity and Ris the radius of
the vessel. Visser’s model presents a similar expression for the conductivity, however no expression was derived
for other electrical properties. We will hypothesize the conductivity expression can be applied to the permittivity
of blood.
Visser’s model applies to blood flowing in a rigid vessel and in a defined orientation. Measurements taken
from impedance cardiography studies in humans showed relative variations Δρ
ℓ
/ρ
0
smaller (15% maximum)
than predicted from Visser’s model in the same conditions (25% maximum), 60% reduction (Raaijmakers et al
1996). The difference can be explained by the fact that the vessels are not straight and have different orientations.
To accommodate this discrepancy, changes in blood resistivity were scaled to 60% of Visser’s model (23),as
reported in the literature.
For each time step, the electrical property of the blood in each main artery is calculated using Visser’s model
and used to compute the statistics of the atlas at that time instant.
Figure 3. Superior aortic system considered in the simulations. The names of the vessels are presented in table 1.
7
Physiol. Meas. 42 (2021)105015 F S Moura et al
The volume occupied by the main arteries is small compared to the volume of the brain, however its area of
influence is considerable. Each artery is responsible for providing blood to specific areas of the brain, known as
brain arterial vascular territories (Kim et al 2019). Six main supratentorial vascular territories were modelled,
(right/left)MCA, ACA, and PCA, also the (right/left)superior cerebellar artery. The main brain territories can
be seen in figure 4. In addition to these, the (right/left)external carotid territories were also included due to the
proximity to the electrodes that can impact measurements. The dynamic model does not consider collateral
circulation other than the redundancy coming from the circle of Willis.
Blood supply inside each territory is assumed to be proportional to the waveform of the associated main
artery. To the best of our knowledge, there are not many studies on electrical property variations of brain tissues
along the cardiac cycle. The majority of the studies focus on electrical property changes in response to sensorial
or motor activity or epilepsy events (Newell et al 2002, Tidswell et al 2001, Towers et al 2000, Holder et al 1996).
The net electrical property change is caused by a dynamic balance between the amount of blood, extracellular
Figure 4. Main cerebral vascular territories. Acronyms: anterior cerebral artery (ACA), middle cerebral artery (MCA), posterior
cerebral artery (PCA), superior cerebellar artery (SCA).
Table 1. Geometrical and mechanical properties of the arteries. Based on Alastruey et al (2007)and
complemented with data collected by Dodo et al (2020), Fomkina et al (2016), Schmitter et al (2013).ℓ: length,
r
0
: Proximal lumen radius, E: Young’s modulus, R
T
: Terminal resistance, and C
T
: Terminal capacitance.
#Artery
a
ℓr
0
ER
T
C
T
(mm)(mm)(kPa)(10
9
Pa s m
−3
)(10
−10
m
3
Pa
−1
)
01 Ascending aorta 40 12.00 400 ——-
02 Aortic arch I 20 11.20 400 ——-
03 Brachiocephalic 34 6.20 400 ——-
04 Aortic arch II 39 10.70 400 ——-
05 L CCA 208 2.50 400 ——-
06 R CCA 177 2.50 400 ——-
07 R Subclavian 34 4.23 400 ——-
08 Thoracic aorta 156 9.99 400 0.18 38.7
09 L Subclavian 34 4.23 400 ——-
10/13 ECA 177 1.50 800 5.43 1.27
11/12 ICA I 177 2.00 800 ——-
14/17 Vertebral 148 1.36 800 ——-
15/16 Brachial 422 4.03 400 2.68 2.58
18/21 ICA II 5 2.00 1600 ——-
19/20 PCoA 15 0.73 1600 ——-
22 Basilar I 25 1.62 1600 ——-
23/24 MCA 119 1.43 1600 5.97 1.16
25/26 ACA I 12 1.17 1600 ——-
27/28 PCA I 5 1.07 1600 ——-
29/30 ACA II 103 1.20 1600 8.48 0.82
31 ACoA 3 0.74 1600 ——-
32/33 PCA II 86 1.05 1600 11.08 0.62
34 Basilar II 1 1.62 1600 ——-
35 Basilar III 3 1.62 1600 ——-
36/37 SCA 86 0.65 1600 25.0 0.62
a
Acronyms:Anterior cerebral artery (ACA), Anterior communicating artery (ACoA), Common carotid artery
(CCA), External carotid artery (ECA), Internal carotid artery (ICA), Middle cerebral artery (MCA), Posterior
cerebral artery (PCA), Posterior communicating artery (PCoA), Superior cerebellar artery (SCA).
8
Physiol. Meas. 42 (2021)105015 F S Moura et al
fluids, and cell swelling in a given location and at a given time instant. In this study, the dynamic component of
this variation is set to 0.5% of the main artery of the territory (Tidswell et al 2001).
2.2.2. Atlas statistics computation
Based on the segmentation of the vessels, explained in section 2.2, and the location of the vascular territories,
presented in figure 4, it is possible to define two characteristic functions per territory, the main vessels in a given
territory
c
Î
mNVand its area of influence
c
Î
m
cNV(the complement within the vascular territory).
Let N
M
be the number of vascular territories. We can write a 3D image of the electrical property of the
dynamic component ÎxtN
T
() as
åcc=+
=
xtptpt,24
m
N
mB mmB
c
m
c
1
,,
M
() () () ( )
where p
m,B
(t)and
pt
mB
c
,
(
)
are the electrical properties of blood in the respective segments. The effect of blood in
the complements
pt
mB
c
,
(
)
is modelled as a percentage of p
m,B
(t)
åå
cc ca=+=
a
==
xtpt pt,25
m
N
mB mmm
c
m
N
mB m
1
,
1
,,
MM
() ()( ) () ( )
where α
m
0 adjusts the effect. The vector χ
α,m
represents the influence region of each vascular territory and
can be used to compose images as in (7). The statistics of the dynamic component is computed following the
same procedure presented in section 2.1.2 with the modified characteristic function χ
α,m
.
Figure 5. Static atlas computations. (a)Processing steps of two representative individuals of the dataset. The first two row shows T1w
and T2w images after normalization and the third row the result SPM’s multi-channel segmentation (T1w+T2w). GM: red, WM:
blue, CSF: green, BO: white, and OT: grey. (b)Average of the characteristic functions χ
t
for each tissue.
9
Physiol. Meas. 42 (2021)105015 F S Moura et al
3. Results
3.1. Static component of the atlas
Figure 5(a)shows two representative individuals in the segmentation steps to compute the static component of
the atlas. The first two rows present T1w and T2w images after normalization and the third row show the
segmented tissues using SPM’s multi-channel segmentation (T1w+T2w). Figure 5(b)shows the average over the
characteristic functions of all individuals and for each segmented tissue. A voxel with a value equal to 1.0
indicates it was classified as the same tissue across all subjects.
The static component of the atlas at 1 kHz is presented in figure 6. The figure shows transversal slices of the
average (figure 6(a)) and standard deviation (figure 6(b)). It is possible to see high resistivity regions in the
forehead, caused by the thick bone and the frontal sinus, in the zygomatic bones and the petrous part of the
temporal bone in the base of the skull.
Figure 7shows slices of the atlas built in terms of conductivity, resistivity, and relative permittivity in
different frequencies. The figure shows that the average resistivity and permittivity decrease with increases in
frequency while conductivity increases. Although the average process tends to eliminate small features of the
Figure 6. Transversal slices of the static component of the atlas (resistivity)at 1 kHz. (a)average; (b)standard deviation.
10
Physiol. Meas. 42 (2021)105015 F S Moura et al
images, it is still possible to see small and thin structures inside the brain, like the longitudinal fissure, third and
fourth ventricles and central canal.
3.2. Dynamic component
The dynamic component of the atlas was computed following the procedure described in section 2.2.
Transversal slices of the average at 1 kHz are presented in figure 8. The main vessels that compose the circle of
Willis in the base of the cranial cavity, the dense arterial vascularization in the insular cortex, and the superior
sagittal sinus are visible.
Figure 9presents the waveforms obtained from the Navier–Stokes solver simulating one cardiac cycle (60
bpm), with hematocrit H=0.5. From left to right, the figure presents flow rate, average cross-sectional velocity,
static pressure and resistivity changes to still blood following Visser’s model (23). Peak velocity occurs
approximately 0.25 s after the beginning of the cardiac cycle. Resistivity changes lie within −17% and −21% to
still blood, indicating the resistivity in these vessels differs considerably from the electrical properties of still
blood.
Figure 7. Statistics of the atlas in different frequencies. (a)Average; (b)standard deviation.
11
Physiol. Meas. 42 (2021)105015 F S Moura et al
3.3. Effects of the cardiac cycle on surface measurements for electrical impedance tomography
As one example of application, the atlas was employed to simulate EIT surface electrode measurements at 1 kHz
during one cardiac cycle (60 bpm)using the FEM to solve the complete electrode model for EIT (Cheney et al
1999, Holder 2005). This type of in silico study is important to investigate the possibility of monitoring blood
perfusion anomalies in patients.
A segmented head image of an average young adult
4
was selected to create the geometry (Hammond et al
2017, Hou et al 2017, Song et al 2013). This geometry is not among those used to create the atlas, avoiding
statistical biases. The boundary surfaces of the segments were extracted and cleaned to remove artefacts.
A FEM mesh was created using Gmsh software (Geuzaine and Remacle 2009). The mesh, presented in
figure 10(a), is composed of 2.06 million linear tetrahedral elements, split into six segments and 32 electrodes
with diameter of 15 mm were placed in two parallel planes with 20 mm of separation. Electrode numbers can be
seen in the figure.
The atlas was projected into the FEM mesh using the SyN (Avants et al 2008). The method requires two 3D
binary images with the characteristic functions of the same volume, one in the atlas reference system and one in
Figure 8. Transversal slices of the average image of the segmented vessels filled with still blood at 1 kHz. Small values were masked in
grey to emphasize the structure of the main vessels.
Figure 9. Waveforms of the main arteries over one cardiac cycle. From left to right: flow rate, average cross-sectional velocity, static
pressure and resistivity changes.
4
https://pedeheadmod.net/pediatric-head-atlases/
12
Physiol. Meas. 42 (2021)105015 F S Moura et al
the FEM mesh reference system. The volumes used for the normalization comprise the soft tissues inside the
cranial cavity (CC=GM+WM+CSF).
For the atlas, the characteristic function of the cranial cavity χ
CC
is found by taking the average of the sum of
the characteristic functions of these tissues over all individuals that compose the atlas, followed by thresholding
at 75%
cccc=++E,26
WM GM CSF
¯{} ()
cc
=
ijk ijk
,, 1if ,, 0.75
0otherwise ,27
CC
⎧
⎨
⎩
() ¯() ()
where (i,j,k)is the coordinates of each voxel. For the FEM mesh, a 3D image can be created from the segmented
internal structures of the mesh, seen in figure 10(b),bydefining a 3D grid of points that encloses the head and
checking if each voxel belongs to the cranial cavity segment CC.
The affine transformation resulting from the normalization was applied to all voxels of the atlas, projecting
them into the FEM mesh reference system. Finally, the values of the atlas were interpolated into the centroids of
the tetrahedron. The projection can be seen in figure 10(b).
EIT measurement simulation was performed by imposing sinusoidal bipolar current injection of 1 mA at
1 kHz and computing the electrode voltage measurements. Current pattern follows a skip-8 scheme to allow
diametral current injection (two planes with 16 electrodes each)(Silva et al 2017). This choice mitigates the
electrical shunting effect of the skull that causes the majority of the current to flow along the scalp only if the pair
of injecting electrodes are too close. The simulated measurements are presented in figure 11 in four time instants
along the cardiac cycle.
Figure 11(a)presents the measurements at t=0s, used as reference measurement v
0
. Figure 11(b)shows
relative differences Δv(t), in dB, between measurements in three other time instants v(t)and the reference v
0
,
defined as
D= -
vvv
v
tt
20 log , 28
10
0
0
⎜⎟
⎛
⎝⎞
⎠
() () ()
where the division is computed element-wise. Figure 11(c)is a plot of the same differences for the first 32
measurements and show that the largest differences are measured at t=0.25 s, time instant when we have peak
velocities, as presented before in figure 9. Figure 11(d)presents histograms of the differences Δv(t). In the same
Figure 10. Finite element mesh used to simulate EIT measurements. (a)Internal structure and electrode locations; (b)slices of the
projected atlas into the FEM mesh.
13
Physiol. Meas. 42 (2021)105015 F S Moura et al
histograms, the vertical lines represent the percentiles 10%, 50% (median), and 90% together with their numeric
values (p10, p50, and p90).
4. Discussion
Conductor volume problems in electroencephalography and electrical bioimpedance cerebral monitoring
require a 3D model of the head and its electrical properties for solving the associated PDEs numerically. In many
situations, a 3D model of the head of the patient is not available or an average head model is preferred. Even in
cases when the model is available via MRI or CT images, the electrical properties of the tissues might not be
completely known due to natural variability. This work presents a novel 4D (3D+T)statistical anatomical atlas
of the electrical properties of the human head for electrophysiology applications created from MRI images of 107
subjects.
Satisfactory skull segmentation was achieved by employing SPM’s multi-channel MRI (T1w+T2w)
segmentation (Nielsen et al 2018). For the atlas, T1w and T2w MRI images were used to segment the tissues. This
choice resulted in good segmentation for the purpose of the atlas and reduced the number of artefacts compared
with segmentation based only on T1 images, especially near the anterior part of the frontal bone. The relatively
large number of subjects, 107 in total, also helps to mitigate the effects of eventual segmentation artefacts in the
final statistics.
The atlas was built for an average head shape and can be normalized to specific geometries. This process was
exemplified with one EIT application. The normalization step optimized the alignment of the cranial cavity,
volume comprising GM+WM+CSF segments. In our experiments, this choice produces a better match
between the atlas and the FEM mesh. However, this choice can cause small artefacts in the external surface of the
mesh due to the small thickness of the scalp and its proximity to the skull. These artefacts can be seen in
figure 10(b)where the resistivity of the scalp near the top of the cranial vault is affected by the skull.
Figure 11. Simulated electrode measurements. (a)Reference measurements v
0
;(b)relative differences Δv(t);(c)first 32 relative
differences Δv(t);(d)histograms of the differences Δv(t).
14
Physiol. Meas. 42 (2021)105015 F S Moura et al
The electrical properties of biological tissues are frequency dependent. The atlas can be built for different
frequencies as exemplified in figure 7. This flexibility expands the applicability of the atlas, such as in
multifrequency EIT (Horesh 2006, Malone et al 2014).
Cerebral circulation was also modelled and added to the atlas. The atlas is capable of simulating the pulsatile
blood flow in the main cerebral arteries and vascular territories and their effects on electrical measurements. As
one example of application, the atlas was employed in an in silico study to investigate the possibility of
monitoring blood perfusion using EIT. Among other objectives, this type of study is important to provide
information on measurement sensitivity necessary to detect perfusion anomalies and serve as a guide for future
EIT equipment developments for these applications. Figure 11(d)predicts that EIT equipment need a signal-to-
noise ratio between 100 and 125 dB to identify changes due to the cardiac cycle. This is in good agreement with a
previous study (Towers et al 2000)on clamped carotid arteries.
Conductor volume inverse problems are sensitive to modelling errors. The skull encloses the brain, and its
proximity to the surface and high resistivity imposes a strong barrier to electric current. In EIT, the skull causes
the majority of the current to flow along the scalp and not penetrate the skull cavity. This shielding causes drop in
sensitivity inside the the skull cavity. The high SNR ratio requirement obtained from the simulation is a direct
consequence of the intense shielding effect of the skull. In EEG, the skull causes difficulties to measure brain
activity due to the insulating effect and results in substantial errors in source localization problems. These
difficulties reinforce the necessity of accurate geometric models of the skull and accurate priors of the skull for
inverse problems in electrophysiology.
The statistical nature of the atlas also allows quantifying its uncertainty. Figure 6shows that the regions with
the largest standard variations are located along the boundary of the bones. This can be explained by the fact that
small anatomical differences between the skulls of the individuals cause large resistivity variations due to the
difference between the resistivity of bones and other tissues around them.
The proposed atlas has some limitations. It is known that ageing increases the stiffness of the vessels, however
the atlas does not include ageing effects on the stiffness of the walls of the arteries. Nevertheless, the atlas can be
adjusted by setting Young’s modulus of the vessels accordingly with the age of the population. Except for the
redundancy caused by the circle of Willis, collateral brain circulation was not modelled either caused by
preexisting vascular redundancy or neovascularization. The venous side of the circulation was not modelled.
Although only five main tissues were segmented, the method can be readily extended to accommodate more
tissues. All tissues were modelled as isotropic, even though it is known that some tissues are anisotropic.
Extending the atlas to anisotropic tissue is possible but increases the complexity substantially. Also, the scalp was
modelled as a uniform tissue, however it is a multi-layer tissue, composed of skin, connective tissue, epicranial
aponeurosis, and muscles that have different electrical properties. Due to its proximity to the electrodes, scalp
mismodellings can impact EIT recovered images. Finally, the dynamic effect of blood circulation in each
territory was modelled as proportional to the velocity of the blood in the main vessel. This approximation does
not take into consideration variations in the volume of blood in a given region, for example when the brain
responds to external stimuli. The current limitations of the atlas act as motivation for future research topics.
These challenging limitation will be the focus of future works to further improve the anatomical atlas.
The atlas was developed in Python 3, and the source code is available at https://github.com/fsmMLK/
openSAHE or archived at https://doi.org/10.5281/zenodo.5567086. The source code contains also the EIT
forward problem solver and meshes used in this work. The atlases created in this work are also available
precomputed at https://doi.org/10.5281/zenodo.5559624. Github repository contains a detailed description of
the files, installation, and usage.
5. Conclusion
We presented a novel anatomical atlas of the electrical properties of the human head. To the best of our
knowledge, the present model is the first model capable of simulating cerebral circulation and its effects on
electrical measurements. Despite the limitations, the atlas brings important implications to cerebral
electrophysiology studies. This novelty has the potential to become an important tool for in silico studies on
cerebral circulation and electrophysiology, such as electrical measurement sensitivity to vascular pathologic
conditions like stroke classification and monitoring, arterial vasospasms, and arteriovenous malformation. The
atlas can also be used as statistical prior information for inverse problems in EEG and EIT and to create training
sets for machine learning algorithms.
15
Physiol. Meas. 42 (2021)105015 F S Moura et al
Acknowledgments
The work was funded in part by the Jane and Aatos Erkko Foundation, project ‘Electrical Impedance
Tomography—a novel method for improved diagnosis of stroke’, the Academy of Finland (Centre of Excellence
in Inverse Modelling and Imaging, decision number 312 339), the São Paulo Research Foundation–FAPESP
(Process numbers: 2019/09154-7 and 2017/18378-0)and Coordenação de Aperfeiçoamento de Pessoal de
Nível Superior (CAPES)—Finance Code 001. The authors wish to thank the Finnish Grid and Cloud
Infrastructure (FGCI)for supporting this project with computational and data storage resources.
The MR brain images from healthy volunteers used in this paper were collected and made available by the
CASILab at The University of North Carolina at Chapel Hill and were distributed by the MIDAS Data Server at
Kitware, Inc. (https://insight-journal.org/midas/community/view/21)
ORCID iDs
Fernando S Moura https://orcid.org/0000-0002-0433-1224
Roberto G Beraldo https://orcid.org/0000-0001-6986-3435
Leonardo A Ferreira https://orcid.org/0000-0001-5303-2776
Samuli Siltanen https://orcid.org/0000-0002-5988-5232
References
Acar Z A and Makeig S 2013 Effects of forward model errors on EEG source localization Brain Topogr. 26 378–96
Adler A and Boyle A 2019 Electrical impedance tomography Wiley Encyclopedia of Electrical and Electronics Engineering ed J G Webster 2nd
edn (New Jersey, NJ: Wiley)pp 1–16
Agnelli J P, Çöl A, Lassas M, Murthy R, Santacesaria M and Siltanen S 2020 Classification of stroke using neural networks in electrical
impedance tomography Inverse Problems 36 115008
Alastruey J, Parker K H and Peiró J 2007 Modelling the circle of willis to assess the effects of anatomical variations and occlusions on cerebral
flows J. Biomech. 40 1794–805
Andreuccetti D, Fossi R and Petrucci C 1997 An internet resource for the calcu lation of the dielectric properties of body tissues in the
frequency range 10 hz - 100 ghz http://niremf.ifac.cnr.it/tissprop/
Ashburner J and Friston K 2005 Unified segmentation Neuroimage 26 839–51
Avants B, Grossman C E M and Gee J 2008 Symmetric diffeomorphic image registration with cross-correlation: evaluating automated
labeling of elderly and neurodegenerative brain Med. Image Anal. 12 26–41
Avants B, Tustison N, Song G and Gee J 2009 Ants: open-source tools for normalization and neuroanatomy https://sourceforge.net/
projects/advants/
Badeli V, Melito G M, Köstinger A R, Bíró O and Ellermann K 2020 Electrode positioning to investigate the changes of the thoracic
bioimpedance caused by aortic dissection—a simulation study J. Electr. Bioimpedance 11 38–48
Beraldo R G and Moura F S 2020 Time-difference electrical impedance tomography with a blood flow model as prior information for stroke
monitoring Proc. XXVII Brazilian Congress on Biomedical Engineering (Vitória, Brazil: SBEB)pp 280–5
Bernstein D P 2010 Impedance cardiography: pulsatile blood flow and the biophysical and electrodynamic basis for the stroke volume
equations J. Electr. Bioimpedance 12–17
Bodo M, Montgomery L D, Pearce F J and Armonda R 2018 Measurement of cerebral blood flow autoregulation with rheoencephalography:
a comparative pig study J. Electr. Bioimpedance 9123–32
Bradac G B 2017 Vascular Territories (Cham: Springer International Publishing)pp 105–7
Braun F, Proença M, Lemay M, Bertschi M, Adler A, Thiran J-P and Solà J 2018 Limitations and challenges of EIT-based monitoring of
stroke volume and pulmonary artery pressure Physiol. Meas. 39 014003
Bullitt E, Zeng D, Gerig G, Aylward S, Joshi S, Smith J K, Lin W and Ewend M G 2005 Vessel tortuosity and brain tumor malignancy: a
blinded study Acad. Radiol. 12 1232–40
Candiani V, Hannukainen A and Hyvonen N 2019 Computational framework for applying electrical impedance tomography to head
imaging SIAM J. Sci. Comput. 41 B1034–60
Candiani V and Santacesaria M 2022 Neural networks for classification of strokes in electrical impedance tomography on a 3d head model
Mathematics in Engineering 41–22
Chandra A, Li W, Stone C, Geng X and Ding Y 2017 The cerebral circulation and cerebrovascular disease I: Anatomy Brain Circ. 345–56
Cheney M, Isaacson D and Newell J C 1999 Electrical impedance tomography SIAM Rev. 41 85–101
Cho J-H, Vorwerk J, Wolters C H and Knösche T R 2015 Influence of the head model on EEG and MEG source connectivity analyses
NeuroImage 110 60–77
Desmidt T, Andersson F, Brizard B, Dujardin P-A, Cottier J-P, Patat F, Réméniéras J-P, Gissot V, El-Hage W and Camus V 2018 Ultrasound
measures of brain pulsatility correlate with subcortical brain volumes in healthy young adults Ultrasound Med. Biol. 44 2307–13
Dodo Y, Takahashi T, Honjo K, Kitamura N and Maruyama H 2020 Measurement of the length of vertebrobasilar arteries: a three-
dimensional approach J. Neurol. Sci. 414 116818
Dowrick T, Blochet C and Holder D 2016 In vivo bioimpedance changes during haemorrhagic and ischaemic stroke in rats: towards 3d
stroke imaging using electrical impedance tomography Physiol. Meas. 37 765–84
Driver I D, Traat M, Fasano F and Wise R G 2020 Most small cerebral cortical veins demonstrate significant flow pulsatility: a human phase
contrast mri study at 7t Front. Neurosci. 14 415
Fomkina O A, Nikolenko V N and Chernyshkova E V 2016 Morphology and biomechanical properties of cerebellar arteries in adults Russ.
Open Med. J. 5e0205
16
Physiol. Meas. 42 (2021)105015 F S Moura et al
Fonov V, Evans A, McKinstry R, Almli C and Collins D 2009 Unbiased nonlinear average age-appropriate brain templates from birth to
adulthood NeuroImage 47 S102
Frackowiak R S, Friston K J, Frith C D, Dolan R J, Price C J, Zeki S, Ashburner J T and Penny W D 2004 Chapter 31—experimental design
and statistical parametric mapping Human Brain Function 2nd edn (Burlington: Academic)pp 599–632
Frerichs I et al 2016 Chest electrical impedance tomography examination, data analysis, terminology, clinical use and recommendations:
consensus statement of the TRanslational EIT developmeNt stuDy group Thorax 72 83–93
Gabriel C, Gabriel S and Corthout E 1996 The dielectric properties of biological tissues: I. Literature survey Physics Med. Biol. 41 2231–49
Gabriel S, Lau R W and Gabriel C 1996a The dielectric properties of biological tissues: II. Measurements in the frequency range 10 hz to 20
ghz Phys. Med. Biol. 41 2251–69
Gabriel S, Lau R W and Gabriel C 1996b The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of
tissues Phys. Med. Biol. 41 2271–93
Gaw R L, Cornish B H and Thomas B J 2008 The electrical impedance of pulsatile blood flowing through rigid tubes: a theoretical
investigation IEEE Trans. Biomed. Eng. 55 721–7
Geuzaine C and Remacle J F 2009 Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities Int. J. Numer.
Methods Eng. 79 1309–31
Goren N, Avery J, Dowrick T, Mackle E, Witkowska-Wrobel A, Werring D and Holder D 2018 Multi-frequency electrical impedance
tomography and neuroimaging data in stroke patients Sci. Data 5180112
Gorgolewski K, Burns C, Madison C, Clark D, Halchenko Y, Waskom M and Ghosh S 2011 Nipype: a flexible, lightweight and extensible
neuroimaging data processing framework in python Front. Neuroinform. 513
Grabner G, Janke A L, Budge M M, Smith D, Pruessner J and Collins D L 2006 Symmetric atlasing and model based segmentation: an
application to the hippocampus in older adults Medical Image Computing and Computer-Assisted Intervention–MICCAI 2006 ed
R Larsen et al (Berlin, Heidelberg: Springer )pp 58–66
Grech R, Cassar T, Muscat J, Camilleri K P, Fabri S G, Zervakis M, Xanthopoulos P, Sakkalis V and Vanrumste B 2008 Review on solving the
inverse problem in eeg source analysis J. NeuroEng. Rehabil. 525
Greitz D, Wirestam R, Franck A, Nordell B, Thomsen C and StÅhlberg F 1992 Pulsatile brain movement and associated hydrodynamics
studied by magnetic resonance phase imaging Neuroradiology 34 370–80
Hallez H et al 2007 Review on solving the forward problem in eeg source analysis J. NeuroEng. Rehabil. 446
Hammond D, Price N and Turovets S 2017 Construction and Segmentation of Pediatric Head Tissue Atlases for Electrical Head Modeling
(Vancouver, Canada: OHBM)
Hoetink A E, Faes T J C, Visser K R and Heethaar R M 2004 On the flow dependency of the electrical conductivity of blood IEEE Trans.
Biomed. Eng. 51 1251–61
Holder D S 2005 Electrical Impedance Tomography: Methods, History and Applications 1st edn (Cornwall, UK: IOP Publishing Ltd)
Holder D S, Rao A and Hanquan Y 1996 Imaging of physiologically evoked responses by electrical impedance tomography with cortical
electrodes in the anaesthetized rabbit Physiol. Meas. 17 A179–86
Holmgren M, WÅhlin A, DunÅs T, Malm J and Eklund A 2019 assessment of cerebral blood flow pulsatility and cerebral arterial compliance
with 4d flow MRI J. Magn. Reson. Imaging 51 1516–25
Horesh L 2006 Some novel approaches in modelling and image reconstruction for multi-frequency electrical impedance tomography of the
human brain PhD Thesis Department of Medical Physics—University College London
Hou J, Turovets S, Li K, Luu P, Tucker D and Larson-Prior L 2017 Spatially Resolved Pediatric Skull Conductivities for Inhomogeneous
Electrical Forward Modeling (Vancouver, Canada: OHBM)
Jatoi M A and Kamel N 2017 Brain Source Localization Using EEG Signal Analysis (Boca Raton, FL: CRC Press)
Kaipio J and Somersalo E 2005 Statistical and Computational Inverse Problems (New York, NY: Springer)
Kim D-E, Jang J, Schellingerhout D, Ryu W-S, Park J-H, Lee S-K, Kim D and Bae H-J 2019 Supratentorial cerebral arterial territories for
computed tomograms: a mapping study in 1160 large artery infarcts Sci. Rep. 911708
Kneihsl M et al 2020 Intracranial pulsatility in relation to severity and progression of cerebral white matter hyperintensities Stroke 51 3302–9
Kucewicz J C, Dunmire B, Giardino N D, Leotta D F, Paun M, Dager S R and Beach K W 2008 Tissue pulsatility imaging of cerebral
vasoreactivity during hyperventilation Ultrasound Med. Biol. 34 1200–8
Malone E, Jehl M, Arridge S, Betcke T and Holder D 2014 Stroke type differentiation using spectrally constrained multifrequency EIT:
evaluation of feasibility in a realistic head model Physiol. Meas. 35 1051–66
Martins T C et al 2019 A review of electrical impedance tomography in lung applications: theory and algorithms for absolute images Annu.
Rev. Control 48 442–71
Meghdadi A H, Popovic D, Rupp G, Smith S, Berka C and Verma A 2019 Transcranial impedance changes during sleep: a
rheoencephalography study IEEE J. Transl. Eng. Health Med. 71–7
Melis A 2017 Gaussian process emulators for 1D vascular models PhD Thesis University of Sheffield
Melis A 2018 openbf: Julia software for 1d blood flow modelling https://github.com/INSIGNEO/openBF
Melis A, Clayton R H and Marzo A 2017 Bayesian sensitivity analysis of a 1d vascular model with gaussian process emulators Int. J. Numer.
Methods Biomed. Eng. 33 e2882
Michel C M and Brunet D 2019 EEG source imaging: a practical review of the analysis steps Front. Neurol. 10 325
Min M, Kõiv H, Priidel E, Pesti K and Annus P 2019 Noninvasive acquisition of the aortic blood pressure waveform Wearable Devices—the
Big Wave of Innovation (Rijeka: InTech)
Misaki M, Savitz J, Zotev V, Phillips R, Yuan H, Young K D, Drevets W C and Bodurka J 2014 Contrast Enhancement by combining t1- and
t2-weighted structural brain MR images Magnetic Resonance in Medicine 74 1609–20
Newell J C, Blue R S, Isaacson D, Saulnier G J and Ross A S 2002 Phasic three-dimensional impedance imaging of cardiac activity Physiol.
Meas. 23 203–9
Nielsen J D, Madsen K H, Puonti O, Siebner H R, Bauer C, Madsen C G, Saturnino G B and Thielscher A 2018 Automatic skull segmentation
from MR images for realistic volume conductor models of the head: assessment of the state-of-the-art NeuroImage 174 587–98
Pesti K, Kõiv H and Min M 2019 Simulation of the sensitivity distribution of four- electrode impedance sensing on radial artery 2019 IEEE
Sensors Applications Symp. (SAS) pp 1–6
Proença M, Braun F, Lemay M, Solà J, Adler A, Riedel T, Messerli F H, Thiran J-P, Rimoldi S F and Rexhaj E 2020 Non-invasive pulmonary
artery pressure estimation by electrical impedance tomography in a controlled hypoxemia study in healthy subjects Sci. Rep. 10 21462
Raaijmakers E, Marcus J T, Goovaerts H G, Vries P M J M, Faes T J C and Heethaar R M 1996 The influence of pulsatile flow on blood
resistivity in impedance cardiography Proc. 18th Annual Int. Conf. IEEE Engineering in Medicine and Biology Society 5, pp 1957–8
17
Physiol. Meas. 42 (2021)105015 F S Moura et al
Sakka L, Coll G and Chazal J 2011 Anatomy and physiology of cerebrospinal fluid, European annals of otorhinolaryngology Head Neck Dis.
128 309–16
Schmitter S, Jagadeesan B, Grande A, Sein J, Ugurbil K and Moortele P V 2013 4d flow measurements in the superior cerebellar artery at 7
tesla: feasibility and potential for applications in patients with trigeminal neuralgia J. Cardiovascular Magn. Reson. 15 W21
Seki J, Satomura Y, Ooi Y and Seiyama T Y A 2006 Velocity profiles in the rat cerebral microvessels measured by optical coherence
tomography Clin. Hemorheol. Microcirc. 34 233–9
Shen H, Li S, Wang Y and Qin K-R 2018 Effects of the arterial radius and the center-line velocity on the conductivity and electrical
impedance of pulsatile flow in the human common carotid artery Med. Biol. Eng. Comput. 57 441–51
Shen H, Zhu Y and Qin K-R 2016 A theoretical computerized study for the electrical conductivity of arterial pulsatile blood flow by an elastic
tube model Med. Eng. Phys. 38 1439–48
Silva O L, Lima R G, Martins T C, Moura F S, Tavares R S and Tsuzuki M S G 2017 Influence of current injection pattern and electric
potential measurement strategies in electrical impedance tomography Control Eng. Pract. 58 276–86
Song J, Chen R, Yang L, Zhang G, Li W, Zhao Z, Xu C, Dong X and Fu F 2018 Electrical impedance changes at different phases of cerebral
edema in rats with ischemic brain injury BioMed Res. Int. 2018 1–10
Song J et al 2013 Anatomically accurate head models and their derivatives for dense array eeg source localization Funct. Neurol. Rehabil.
Ergon. 3275–93
Tidswell T, Gibson A, Bayford R H and Holder D S 2001 Three-dimensional electrical impedance tomography of human brain activity
NeuroImage 13 283–94
Towers C M, McCann H, Wang M, Beatty P C, Pomfrett C J D and Beck M S 2000 3d simulation of EIT for monitoring impedance variations
within the human head Physiol. Meas. 21 119–24
Vikner T, Nyberg L, Holmgren M, Malm J, Eklund A and WÅhlin A 2019 Characterizing pulsatility in distal cerebral arteries using 4d flow
MRI J. Cerebral Blood Flow Metab. 40 2429–40
Visser K R 1989 Electric properties of flowing blood and impedance cardiography Ann. Biomed. Eng. 17 463–73
Visser K R 1992 Electric conductivity of stationary and flowing human blood at low frequencies Med. Biol. Eng. Comput. 30 636–40
Vorwerk J, Cho J-H, Rampp S, Hamer H, Knösche T R and Wolters C H 2014 A guideline for head volume conductor modeling in EEG and
MEG NeuroImage 100 590–607
Wagshul M E, Eide P K and Madsen J R 2011 The pulsating brain: a review of experimental and clinical studies of intracranial pulsatility
Fluids Barriers CNS 85
Costelar C, Flürenbrock F, Korn L C, Benninghaus A, Misgeld B J E, Shchukin S I, Radermacher K and Leonhardt S 2019 FEM simulation of
bioimpedance-based monitoring of ventricular dilation and intracranial pulsation Int. J. Bioelectromagn. 21 7–20
Zhang H J, Shen H, Li Y J and Qin K R 2020 An in vitro circulatory device for studying blood flow electrical impedance in human common
carotid arteries 2020 IEEE 16th Int. Conf. on Control Automation (ICCA) pp 1518–22
18
Physiol. Meas. 42 (2021)105015 F S Moura et al
