A comparison of brain retraction mechanisms using finite element analysis and the effects of regionally heterogeneous material properties

Abstract

Finite element (FE) simulations of the brain undergoing neurosurgical procedures present us with the great opportunity to better investigate, understand, and optimize surgical techniques and equipment. FE models provide access to data such as the stress levels within the brain that would otherwise be inaccessible with the current medical technology. Brain retraction is often a dangerous but necessary part of neurosurgery, and current research focuses on minimizing trauma during the procedure. In this work, we present a simulation-based comparison of different types of retraction mechanisms. We focus on traditional spatulas and tubular retractors. Our results show that tubular retractors result in lower average predicted stresses, especially in the subcortical structures and corpus callosum. Additionally, we show that changing the location of retraction can greatly affect the predicted stress results. As the model predictions highly depend on the material model and parameters used for simulations, we also investigate the importance of using region-specific hyperelastic and viscoelastic material parameters when modelling a three-dimensional human brain during retraction. Our investigations demonstrate how FE simulations in neurosurgical techniques can provide insight to surgeons and medical device manufacturers. They emphasize how further work into this direction could greatly improve the management and prevention of injury during surgery. Additionally, we show the importance of modelling the human brain with region-dependent parameters in order to provide useful predictions for neurosurgical procedures.

Full text

Vol.:(0123456789)
Biomechanics and Modeling in Mechanobiology (2024) 23:793–808
https://doi.org/10.1007/s10237-023-01806-2
ORIGINAL PAPER
A comparison ofbrain retraction mechanisms using finite element
analysis andtheeffects ofregionally heterogeneous material
properties
EmmaGriths1· JayaratnamJayamohan2· SilviaBudday1
Received: 3 August 2023 / Accepted: 14 December 2023 / Published online: 15 February 2024
© The Author(s) 2024
Abstract
Finite element (FE) simulations of the brain undergoing neurosurgical procedures present us with the great opportunity to
better investigate, understand, and optimize surgical techniques and equipment. FE models provide access to data such as
the stress levels within the brain that would otherwise be inaccessible with the current medical technology. Brain retrac-
tion is often a dangerous but necessary part of neurosurgery, and current research focuses on minimizing trauma during
the procedure. In this work, we present a simulation-based comparison of different types of retraction mechanisms. We
focus on traditional spatulas and tubular retractors. Our results show that tubular retractors result in lower average predicted
stresses, especially in the subcortical structures and corpus callosum. Additionally, we show that changing the location of
retraction can greatly affect the predicted stress results. As the model predictions highly depend on the material model and
parameters used for simulations, we also investigate the importance of using region-specific hyperelastic and viscoelastic
material parameters when modelling a three-dimensional human brain during retraction. Our investigations demonstrate
how FE simulations in neurosurgical techniques can provide insight to surgeons and medical device manufacturers. They
emphasize how further work into this direction could greatly improve the management and prevention of injury during
surgery. Additionally, we show the importance of modelling the human brain with region-dependent parameters in order to
provide useful predictions for neurosurgical procedures.
Keywords Human brain· Neurosurgery· Finite element method· Material modelling· Regional heterogeneity
1 Introduction
Retraction of the brain is often necessary during neurosur-
gery to access problematic areas of the brain. It traditionally
involves manoeuvring brain tissue using a spatula retractor
to access deep parts of the brain in order to remove or repair
tumours or lesions. Secondary damage is often an unfortu-
nate result of retraction (Andrews and Bringas 1993; Zhong
etal. 2003). This is considered damage to the surround-
ing tissue that was not planned or accounted for initially.
Damage to nearby subcortical structures (Iyer and Chai-
chana 2018), excessive severing of white matter (Raza etal.
2011; Bander etal. 2016), and tissue creep (Kassam etal.
2015) can result in secondary neurological complications
resulting in functional impairment of patients.
Using tubular retractors instead of traditional spatulas has
been suggested to reduce the amount of secondary brain
damage (Okasha etal. 2020; Jamshidi etal. 2020; Shap-
iro etal. 2020; Eichberg etal. 2020; Mansour etal. 2020).
Tubular retractors consist of a cylinder or cone with either a
circular or elliptical cross section. These tubes are inserted
in the brain tissue and provide a surgical corridor through
which the deep parts of the brain can be accessed. These
retractors offer two obvious advantages over traditional spat-
ulas: smaller incisions of the brain tissue (reducing primary
damage) and an even distribution of pressure on retracted
brain tissue compared to the hard edges of spatulas (reduc-
ing secondary damage due to shearing forces on the brain)
(Zagzoog and Reddy 2020; Evins 2017; Raza etal. 2011).
* Emma Griffiths
emma.griffiths@fau.de
1 Department ofMechanical Engineering, Institute
ofContinuum Mechanics andBiomechanics, Friedrich-
Alexander-Universität Erlangen-Nürnberg, 91058Erlangen,
Germany
2 Department ofPediatric Neurosurgery, John Radcliffe
Hospital, OxfordOX39DU, UK
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

794 E.Griffiths et al.
There are several clinical reports describing the success-
ful use of tubular retractors on tumours and lesions that are
intra-axial (tumour or lesions found within the parenchyma
that is likely to be near subcortical structures) (Kelly etal.
1988; Raza etal. 2011; Recinos etal. 2011; Bander etal.
2016; Gassie etal. 2018; Mansour etal. 2020; Marenco-
Hillembrand etal. 2018, 2020; Echeverry etal. 2020), deep-
seated high-grade gliomas (Iyer and Chaichana 2018), and
lesions within the ventricles of the brain (Cohen-Gadol
2013; Shoakazemi etal. 2015). Additionally, they have been
used for the biopsies of deep-seated tumours (as they allow
for larger biopsy samples to be collected thus allowing for
better diagnostic suitability) (Jackson etal. 2017; Bander
etal. 2018) and aneurysm clippings (Jamshidi etal. 2018;
O’Connor etal. 2019; Jamshidi etal. 2020). These types
of surgical procedures have a high degree of risk, but are
necessary for many patients’ well-being. Thus, taking every
measure to reduce secondary neurological deficits is impor-
tant. There are many accounts in the literature that promote
the use of tubular retractors and acknowledge their benefits
(Raza etal. 2011; Shapiro etal. 2020; Mansour etal. 2020;
Eichberg etal. 2020; Evins 2017).
However, without studies comparing the use of spatula
and tubular retractors, one cannot confidently conclude that
tubular retractors reduce the incidence of secondary brain
injury (Raza etal. 2011; Bander etal. 2016; Eichberg etal.
2020) and further comparative studies are necessary to do
so. Making clinical comparison between retraction methods
is, however, very difficult to achieve due to several factors
such as,
• Variability in patients: Age, gender, and the patient’s cur-
rent condition can affect brain tissue stiffness. Addition-
ally, there exists anatomical variability in the shape and
size of each patient’s brain.
• Variability in surgery: Location, depth and size of lesion/
tumour will be different for each patient.
• Variability in surgeons: Techniques, preferences and sur-
gical experience will differ.
FE simulations can provide a means to overcome, and even
probe, many of these variabilities. FE simulations also allow
for a high risk procedure to be performed with no risk to
patients. Additionally, the incidence of secondary brain
injury can be difficult to determine (Evins 2017). The result-
ing impairment to subcortical structures may only show up
several days after surgery. FE simulations could provide data
on the loading experienced by these subcortical structures
during planning in order to minimize the corresponding risk.
FE simulations have previously been used for a variety
of neurosurgical applications. Miga etal. (2001) performed
a computational study using a linear elastic model com-
putational brain model to simulate a procedure involving
retraction and tumour resection so as to improve the patient-
to-image registration necessary for surgical image guidance
systems. Li etal. (2016) used a hyper-viscoelastic model
in conjunction with the extended finite element method
(XFEM) to model a similar procedure of a porcine brain
based on boundary conditions extracted from in vivo exper-
iments. Hansen etal. (2004) included the FE method to
enhance haptic feedback of a virtual reality system used to
simulate retraction. These systems aim to reduce brain tis-
sue damage by training new surgeons and improve neuro-
surgical planning. Research has continued in this direction
in order to enhance the realism and speed of these virtual
reality surgical simulators (Platenik etal. 2002; Fukuhara
etal. 2014a, b; Sase etal. 2015). Simulating a retraction
surgery, Awasthi etal. (Awasthi etal. 2020) investigated
the reaction force and pressure on spatulas using a hyper-
viscoelastic heterogeneous canine brain model. They probed
how intermittent verse continuous retraction, the number
of spatulas used, and the speed of retraction affect these
measures. Adachi etal. (2007) simulated the deformation
of a patient-specific three-dimensional FE brain model dur-
ing a retraction surgery using a traditional spatula. Using a
porcine brain model, Lamprich and Miga (2003) modelled
retraction using FE in order to update preoperative images
during surgery.
In order to provide accurate predictions of stress and
strain in FE simulated brains, a sufficiently accurate mate-
rial model of brain tissue is required. However, the brain is
a highly complex organ. Brain tissue is extremely soft and
compliant and is viscoelastic and/or poro-elastic depend-
ing on the time scale of interest and the loading conditions
(Budday etal. 2019). In addition, the brain exhibits clear
microstructural heterogeneity due to different functional
demands in different regions of the brain (Reiter etal. 2021).
This results in regionally different macroscopic mechanical
properties (Hinrichsen etal. 2023).
Region-specific properties in FE brain models have been
used when modelling traumatic head injuries (Viano etal.
2005; Mao etal. 2013; Miller etal. 2016). However, inves-
tigation into the importance of this is still in its infancy. In
recent investigations, the effects of region-specific hyper-
elastic parameters by Griffiths etal. (Griffiths etal. 2023)
showed that hyperelastic regional heterogeneity produced
significantly different results when compared to an homo-
geneous model, especially in the region of the corpus cal-
losum. This region has been shown to be significantly more
compliant than the other regions of the brain (Budday etal.
2019). To the best of our knowledge, the effects of regional
heterogeneity of viscoelastic properties for full-scale brain
simulations have not been explored.
Creating a model of the brain that can capture the anatomi-
cal and material characteristics of the brain under neurosurgi-
cal loadings with suitable accuracy is important. It can help
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

795
A comparison ofbrain retraction mechanisms using finite element analysis andtheeffects of…
us predict how these procedures affect the stress levels within
the brain and thus assist in surgical planning. It can also help
understand how to improve these procedures and the equip-
ment used in order to prevent or reduce injury (Kyriacou etal.
2002).
To the best of our knowledge, there are no studies compar-
ing different retraction mechanisms utilizing the FE method in
conjunction with a brain based on medical images that is seg-
mented into regions with different material properties. Addi-
tionally, the effects of retraction on surrounding subcortical
structures have not been probed. Both of these investigations
would be difficult, if not impossible, to performed with current
medical technology. This paper will simulate the retraction of
brain tissue using three different types of retractors: (1) tra-
ditional spatulas, (2) tubular retractors with an circular cross
section and (3) tubular retractors with a elliptical cross section.
We compare the effects of each mechanisms on the surround-
ing cortical and subcortical structures as well as the sensitiv-
ity of these methods to the retraction location. Additionally,
we investigate the importance of region-specific hyperelastic
and viscoelastic parameters. We use a three-dimensional fully
segmented brain with a hyper-viscoelastic model, which con-
siders region-specific parameters of four regions of the brain,
the cortex, corona radiata, basal ganglia, and corpus callosum
(Budday etal. 2017b, a).
2 Methods
2.1 Modelling finite viscoelasticity
2.1.1 Kinematics
To model the deformation of the brain, we use nonlinear
continuum mechanics and consider a deformation mapping
𝝋(X,t)
that maps the undeformed, unloaded configuration
with positional vectors
X
at time
t0
to the deformed, loaded
configuration with position vectors
x=𝝋(X,t)
at time t.
The spectral representation of the deformation gradient,
F=d𝝋∕dX=∇x𝝋
, in terms of the eigenvalues
𝜆a
is
where
na
=F
⋅
Na
and
Na
are the eigenvectors in the
deformed and undeformed configurations.
We also introduce the spectral representation of the left
Cauchy–Green deformation tensor,
(1)
F
=∇x𝝋=
3
∑
a=1
𝜆ana⊗Na
,
(2)
𝐛
=𝐅⋅𝐅t
=
3
∑
a=1
𝜆a𝐧a⊗𝐧a
.
To model the viscous nature of brain tissue, the deformation
gradient is decomposed into an elastic and viscous part,
where i denotes the parallel arrangement of m viscoelastic
elements (Sidoroff 1974). To characterize the rate of defor-
mation, we introduce the spatial velocity gradient,
which is decomposed into an elastic
le
i
=

F
e
⋅(F
e
i
)−
1
, and a
viscous part
l
v
i
=Fe
i
⋅

Fv
i
⋅(Fv
i
)−1
⋅(Fe
i
)−
1
. It proves conveni-
ent to introduce the elastic left Cauchy–Green strain tensor
for each mode
with eigenvalues
𝜆e
ia
and eigenvectors
ne
ia
, which are, in
general, not identical to the eigenvectors of the total left
Cauchy–Green deformation tensor,
ne
ia≠na
. The material
time derivative of the elastic left Cauchy–Green deforma-
tion tensor
be
i
introduces its Lie-derivative
along the velocity field of the material motion.
2.1.2 Constitutive modelling
Previously, it has been shown that the Ogden model rep-
resents the time-independent, hyperelastic response of the
brain tissue under various loading modes (Budday etal.
2017a; Mihai etal. 2015; Miller and Chinzei 2002). The
viscoelastic extension of this model has, thereafter, been
shown to capture the conditioning and hysteresis effects.
Based on previous experimental evidence, we assume an
isotropic material response for both the elastic and viscoe-
lastic behaviour (Budday etal. 2019, 2017b).
The viscoelastic free energy function
𝜓
is given as the
sum of an equilibrium part
𝜓eq
given in terms of the total
principal stretches
𝜆a
and a non-equilibrium term in terms
of the sum of the elastic principal stretches
𝜓neq
=
∑m
i−1
𝜓
i
for each viscoelastic mode
i,…,m
.
Following the standard arguments of thermodynamic, the
Kirchhoff stress
𝝉
consists of two terms, the equilibrium
term
𝝉eq
and the non-equilibrium term
𝝉neq
which is the sum
of the Kirchhoff stress for each viscoelastic mode,
(3)
𝐅=𝐅e
i
⋅
𝐅v
i∀i=1, …,m,
(4)
𝐥
=∇
𝐗𝐯=

𝐅⋅𝐅
−1
=𝐥
e
i
+𝐥
v
i
(5)
b
e
i=Fe
i
⋅(Fv
i)t=
3
∑
a=1
(𝜆e
ia)2ne
ia⊗ne
ia
,
(6)

be
i
=2[l
e
i
⋅b
e
i
]
sym
=2[l⋅b
e
i
]
sym
−2[l
v
i
⋅b
e
i
]
sym,
(7)
Lvbe
i=−2[lv
i
⋅
be
i]sym,
(8)
𝜓=𝜓eq +𝜓neq.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

796 E.Griffiths et al.
The equilibrium free energy part is modelled using a one-
term Ogden model whereby the strain energy function is
split into an isochoric and a volumetric part (Ogden 1972),
The isochoric part is defined in terms of the isochoric princi-
pal stretches

𝜆a=J−1∕3
𝜆
a
, where J denotes the volume ratio
J=detF
, and is given by
The shear modulus
𝜇
and the nonlinearity parameter
𝛼
are
determined by fitting the model to experimental data. The
volumetric part is defined as
where
𝜅
, the bulk modulus, is determined from the shear
modulus and the Poisson’s ratio,
𝜈
, through the relation
Following (9) the equilibrium stress is calculated from
To determine the Kirchhoff stress for each viscoelastic
mode,
𝝉i
, the same Ogden type strain energy function is
adopted with a similar split into an isochoric and volumetric
part as in (10). The isochoric part is now given in terms of
the isochoric elastic principal stretches

𝜆e
i
=(J
e
i
)
−1∕3
𝜆
e
i
and
is given by,
and the volumetric part follows from (12),
The Kirchhoff stress for each viscoelastic mode is expressed
analogously to14 as,
(9)
𝝉
=2
𝜕𝜓
𝜕b
⋅b=𝝉eq +𝝉neq
with 𝝉neq =
m
∑
i=1
𝝉i
.
(10)
𝜓eq =
𝜓
iso +
𝜓
vol .
(11)
𝜓iso
=2𝜇
∞
∕𝛼
2
∞
(

𝜆
𝛼
1
+

𝜆
𝛼
2
+

𝜆
𝛼
3
−3)
.
(12)
𝜓
vol =𝜅
1
4
(J2−1−2lnJ)
,
(13)
𝜅
=𝜇
2(1+𝜈)
3(1−2𝜈)
.
(14)
𝝉
eq =2𝜕𝜓eq
𝜕b
⋅b=
3
∑
a=1
𝜕𝜓eq
𝜕𝜆a
𝜆ana⊗na
.
(15)
𝜓i(iso)
=2𝜇
i
∕𝛼
2
i
[(

𝜆
e
i1
)
𝛼
i+(

𝜆
e
i2
)
𝛼
i+(

𝜆
e
i3
)
𝛼
i−3]
,
(16)
𝜓
i(vol) =𝜅i
1
4
(J2−1−2lnJ)
,
It remains to specify the temporal evolution of the viscoelas-
tic kinematics. To satisfy the reduced dissipation inequality
for each mode (Govindjee and Reese 1997; Budday etal.
2017c), we choose the following evolution equation for the
internal variable
be
i
,
The update of the non-equilibrium part of the constitutive
equation in time is performed using an implicit time integra-
tion with exponential update, of which details can be found
in Budday etal. (2017b).
2.2 FE model
2.2.1 FE mesh generated fromsegmented brain image
A three-dimensional brain model that captures the major
sulci and gyri was created from magnetic resonance imaging
(MRI) data of a woman’s brain at the age of 30. FreeSurfer
image analysis suite1 was used to segment the MRI images
and MATLAB R2021b (MathWorks Inc, US) was used to
clean the resulting voxel image, convert it into a mesh of
hexahedral elements and apply smoothing to this mesh. Fur-
ther details on its creation can be found in Griffiths etal.
(2023). Figure1 shows the segmentation of this model into
(17)
𝝉
i=2
𝜕𝜓
i
𝜕be
i
⋅be
i
=
3
∑
a=1
𝜕𝜓i
𝜕𝜆e
ia
𝜆e
ia ne
ia ⊗ne
ia
=
3
∑
a=1
𝜏ia ne
ia ⊗ne
ia .
(18)
−
Lvbe
i
⋅(be
i)−1=
1
2𝜂i
𝝉i
.
Cortex
Corpus
callosum
Internal brain
structures
Corona radiata
Fig. 1 Segmentation of the three-dimensional brain consisting of four
regions
1 https:// surfer. nmr. mgh. harva rd. edu/
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

797
A comparison ofbrain retraction mechanisms using finite element analysis andtheeffects of…
4 regions: cortex, corona radiata, corpus callosum and the
remaining internal structures consisting of the amygdala,
basal ganglia, brain stem, cerebellum, hippocampus and
midbrain.
2.2.2 Material parameters
A compressible, viscoelastic material model is considered
suitable to model neurosurgical procedures with sufficient
accuracy (Kyriacou etal. 2002; Budday etal. 2017b). Using
the material model described in Sect.2.1 and based on the
previous work of Budday etal. (2015, 2017b), we use two
viscoelastic elements (
m=2
) to capture the viscoelastic
response of brain tissue. We use the constitutive material
parameters identified by Budday etal. (2017b) for condi-
tioned brain tissue in four brain regions (shown in Table1).
A Poisson’s ratio of 0.49 is used throughout.
2.2.3 Boundary conditions
Using the FE generated brain model from Sect.2.2.1 and the
hyper-viscoelastic material model described in Sect.2.2.2,
we aim to simulate a transsulcal brain retraction using
three different mechanisms: two spatulas moving apart,
an expanding circular retractor and an expanding elliptical
retractor. The boundary conditions applied are taken from
Awasthi etal. (2020), where the non-retracted hemisphere
and the brain stem are fixed while the retracted hemisphere
remains traction free. To improve the quality of the results
and allow for a smooth transition between the element
sizes at the retraction sites, an octree mesh refinement was
applied (Schneiders 1998). This refinement method subdi-
vides a hexahedral element into eight hexahedral elements.
Elements of varying size are created in the transition zone
between the refined and non-refined region. Fig.2 shows
a magnified view of the refined initial mesh setup for each
retraction method. A summary of a mesh convergence study
at the retraction site can be found in AppendixA.
In order to investigate the effects of location on the sur-
rounding brain structures we chose four retraction locations,
as shown in Fig.3.
For the spatula retraction, an initial slit of 12mm length
and 1mm gap was created to simulate the initial incision.
This incision was made to a depth of 32mm. The retrac-
tion of two spatulas of 4mm width at a depth of 30mm
was simulated by prescribing the displacement of the nodes
associated with these dimensions in the x- and y-direction.
For the tubular retractions, an initial circular or elliptical
puncture of 3mm diameter was created in the brain mesh.
The puncture replicates the catheter needle used to guide the
retractors. This incision was made to a depth of 40mm to
account for a 30-mm tubular retractor and a 10-mm conical
introducer located at the end of the retractors. The retrac-
tion was simulated by prescribing the radial displacement of
nodes on the punctured surface to a depth of 30mm.
The circular tubular retractors were expanded to a width
of 10mm and the elliptical retractor to a final major diam-
eter of 10mm and minor diameter of 6.67mm. Unlike
tubular retractors, the retraction displacement of spatulas
is not fixed. This displacement can vary between surgeries
and surgeons but is most often larger than that for a tubular
retractor (Evins 2017). In our simulations, the final spatula
retractor displacement was set to 12.5mm. All simulations
were performed at a retraction rate of 5mm/min Budday
etal. (2017c), Awasthi etal. (2020). After the final retraction
displacement was reached the brain tissue was held at this
displacement for 30min to simulate the length of a typical
Table 1 Constitutive properties
identified by Budday etal.
(2017b) for the conditioned
viscoelastic material of the four
brain regions
Ogden
1st
Maxwell element
2nd
Maxwell element
𝜇∞
𝛼∞
𝜇1
𝛼1
𝜂1
𝜇2
𝛼2
𝜂2
[kPa] [–] [kPa] [–] [kPa·s] [kPa] [–] [kPa·s]
Cortex 0.42
−
21.27 1.40
−
14.66 3.05 0.56
−
23.76 289.37
Corona radiata 0.16
−
25.66 0.97
−
25.35 2.19 0.25
−
29.22 299.79
Internal structures 0.17
−
21.52 0.68
−
15.50 2.27 0.27
−
22.76 240.17
Corpus callosum 0.04
−
28.41 0.63
−
27.01 1.62 0.16
−
30.80 232.53
Spatula Circle Ellipse
x
y
Fig. 2 Magnified view of the initial mesh for each retraction mecha-
nism (traditional spatula, tubular retractor with circular cross section,
tubular retractor with an elliptical cross section), generated based on
an octree mesh refinement is shown at the retraction location
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

798 E.Griffiths et al.
neurosurgical procedure (Zhong etal. 2003; Awasthi etal.
2020).
All simulations were performed using the open source
FE library deal.II2 previously implemented by Kaessmair
etal. (2021).3
3 Results anddiscussion
3.1 Comparison ofretraction mechanisms
To compare the three different retraction mechanisms, Fig.4
shows the predicted maximum principal strain distribu-
tion on a transverse slice of the brain taken 2cm below
the surface. A strain limit of 50% has been set as a damage
threshold. This value is based on the experimental results of
Franceschini etal. (2006).
All mechanisms show strains above the damage threshold
in the area immediately adjacent to the retraction. However,
the simulated brain retracted using a spatula shows a much
larger area of damage compared to either tubular retractor.
A noticeable strain can even be noted on the non-retracted
hemisphere. In comparison, the two tubular retractors show
a regular and contained strain distribution with no visible
strain on the non-retracted hemisphere.
Figure5 shows the corresponding simulated von Mises
stress distribution in the same location as in Fig.4 at two
time points: the first moment when the maximum retraction
displacement has been reached and 30min later whilst hold-
ing the maximum retraction displacement.
In all three models, a relaxation of the stress can be seen
between the two time points, especially in regions further
away from the retraction site. The relaxation observed for
the spatula is much greater than for either tubular mecha-
nism. The spatulas enforce the displacement over a relatively
small area along the initial incision based on the width of
the spatula. The tubular retractors enforce the displacement
along the entire area of puncture. Since there is a larger area
that is unprescribed in the spatula simulations, there is more
freedom in the model to relax, thus greater stress relaxation
can occur.
Similar to the strain in Fig.4, the stress distribution
resulting from using a spatula is both greater in area and
much less regular than that of the tubular mechanisms.
Significantly larger stress values are even noted in the non-
retracted hemisphere. As one would assume, the areas of
high stresses are areas, where secondary brain damage is
more likely to occur. Those are smaller for the tubular retrac-
tors, which could motivate their preferred use over spatulas.
There is a large amount of variability available to a surgeon
when using a spatula, such as their position and width. The
tubular retractors present almost no variability: the diam-
eter is chosen beforehand and they provide a relatively large
visually unobstructed surgical corridor through which the
surgeon can work (Zagzoog and Reddy 2020). Therefore,
the location and quantity of the high stress areas within the
brain are easier to predict. The variability of spatulas makes
predictions in these cases less reliable. The regularity of
both the stress and strain distributions of the tubular mecha-
nisms allows for a better prediction of which regions could
be affected by retraction at difference sites when conduct-
ing surgical planning. We now look into the effects of each
retraction mechanism on particular areas of the brain that are
not in direct contact with the surgical instrument. Figures6
and 7 show the maximum averaged predicted von Mises
stress and the average predicted von Mises stress over time
using each mechanism for (a) the internal structures of the
brain and (b) the corpus callosum (the softest region of the
brain (Budday etal. 2017b)). The results are shown for one
location loaded from top and one lateral retraction location.
In Fig.6, the spatula shows the largest produced maxi-
mum von Mises stress in the internal structures and the cor-
pus callosum at both loading locations. The internal brain
structures experience a 30–50% lower von Mises stress when
the tubular retractors are used compared to the spatulas. In
the corpus callosum, a 70% lower peak average stress is
shown when loaded from the top using a tubular retractor
compared to a spatula. For the lateral loading, the differ-
ence between the mechanisms is considerably smaller. The
lowest average peak stress in all locations and brain regions
Lateral locations
Superior locations
x
y
x
y
x
y
Fig. 3 The four locations (two from top and two lateral) at which
retraction is applied to the brain model. The retraction location is
indicated on the brain with a yellow circle
2 https:// www. dealii. org/
3 The code can be found at https:// github. com/ BRAIN IACS- Group/
efiSi m1F_ Brain_ Retra ction.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

799
A comparison ofbrain retraction mechanisms using finite element analysis andtheeffects of…
is experienced when using an elliptical tubular retractor.
This is expected due to the smaller minor diameter and thus
the less overall retraction. While the elliptical cross sec-
tion clearly reduces the area of visibility in retraction, the
reduced risk of secondary brain damage to surrounding areas
potentially prevails.
Figure7a shows a similar stress relaxation profile in
the internal structures at both locations. In the corpus cal-
losum, a slightly larger amount of stress relaxation occurs
when using a spatula compared to the other mechanisms
when loaded from the top. This is consistent with the results
shown in Fig.5, where the spatula led to the most pro-
nounced stress relaxation, particularly in areas far from the
retraction site. For the laterally loaded condition, the corpus
callosum shows slightly greater relaxation when using the
circular or elliptical retractor.
An important note to make on the different retraction
mechanisms is the variability that is allowed with the spat-
ula. The spatula mechanism can vary in width, placement,
stability, retraction displacement and number of spatulas
used. These factors can be both beneficial and harmful to
the surrounding tissue. For example, the use of intermittent
and multi-spatula reaction has been shown to produce lower
reaction forces on the brain surface (Andrews and Bringas
1993; Awasthi etal. 2020), but excessive retraction of the
brain or accidental slipping of the instrumentation may
cause unexpectedly high forces. On the other hand, tubular
retractors have very little variability: the diameter is chosen
beforehand and they provide a relatively large visually unob-
structed surgical corridor through which the surgeon can
work (Zagzoog and Reddy 2020). Tubular retractors can thus
be considered a more consistent and predictable mechanism.
This predictability allows for greater accuracy in the plan-
ning of complex and dangerous neurosurgical procedures
but also hinders potentially necessary variability to handle
unforeseen situations.
This is the first FE study where the effects of different
types of retraction mechanism on brain tissue loadings have
been considered. From our study, the tubular retractors pre-
dict lower maximum von Mises stresses when compared
to spatulas. The tubular retractors also showed smaller and
more confined areas above current known damage thresh-
olds close to the retraction site. This supports the clinical
SpatulaCircleEllipse
maximum principal strain [-]
0.0
0.5
0.1
0.2
0.3
0.4
Fig. 4 Simulated maximum principal strain distribution for a slice
of the brain 2cm below the surface of retraction for each retraction
mechanism, using a traditional spatula, a tubular retractor with circu-
lar cross section, and a tubular retractor with an elliptical cross sec-
tion. A strain limit of 50% has been set as a damage threshold based
on the results of Franceschini etal. (2006)
Fig. 5 Simulated von Mises
stress for a slice of the brain
2cm below the surface of
retraction for each retraction
mechanism, using a traditional
spatula, a tubular retractor
with circular cross section,
and a tubular retractor with an
elliptical cross section. Two
time points are shown: the first
moment when the maximum
retraction displacement has
been reached and 30min later
whilst holding the maximum
retraction displacement
Spatula Circle
Max retraction
Ellipse
After 30 mins
0
2.0
0.5
1.0
1.5
von Mises stress [kPa]
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

800 E.Griffiths et al.
observations that tubular retractors could be safer than spatu-
las in certain brain surgeries scenarios.
3.2 Effects oflocation changes
Oftentimes, during surgical planning different locations are
considered and the decision for the best location is made
based on the location of the entity to be accessed, the nearby
brain structures, and the distribution of the white matter
tracts (Hendricks and Cohen-Gadol 2016). We explore
the effects of location changes on the predicted von Mises
stress of the internal structures of the brain and the corpus
callosum.
Figure8 shows the maximum averaged von Mises stresses
for the internal structures and corpus callosum at the four
locations for each mechanism.
In Fig.8a, the von Mises stress is higher for the later-
ally loaded locations compared to the locations loaded from
the top for all mechanisms. Additionally, little difference is
seen between the two locations loaded from the top in either
region. Utilizing a spatula shows a larger von Mises stress
when loaded laterally. The tubular retractors have similar
maximum von Mises stresses when loaded from the top but
differing values when loaded laterally. Location three shows
lower stress values, similar to the ones loaded from top,
especially when using an elliptical tube. Location four has
the greatest peak von Mises stress when using any mecha-
nism. We attribute this to location four’s proximity to the
area. Location four is positioned directly above the internal
brain structures, while location three is slightly further away.
It should be noted, however, that the maximum von Mises
stress is higher for the spatulas than for the tubular retractors
at all locations.
The low stiffness of the corpus callosum causes it to be
much more sensitive to the location selection, as shown
in Fig.8b. Using the spatula, both lateral locations led
to lower average stress values compared to the locations
from the top. In the corpus callosum, an 80% difference
0
10
20
30
40
50
60
Spatula
Circle
Ellipse
Spatula
Circle
Ellipse
Internal Structures Corpus Callosum
Maximum von Mises Stress [Pa]
Superior Lateral Superior Lateral
Loading locations
a)
b)
Fig. 6 Maximum averaged simulated von Mises stress in two regions,
internal brain structures and the corpus callosum, for three retraction
mechanisms, a traditional spatula, a tubular retractor with circular
cross section, and a tubular retractor with an elliptical cross section.
The results are shown for two retraction locations: one lateral and one
loaded from top
Fig. 7 Normalized simulated
von Mises stress over time
in two regions, internal brain
structures and the corpus callo-
sum, for three retraction mecha-
nisms, a traditional spatula, a
tubular retractor with circular
cross section, and a tubular
retractor with an elliptical cross
section. The results are shown
for two retraction locations
and are indicated on the brain
inserts with a yellow circle
0500 1000 1500 2000
0
20
40
60
80
100
Spatula
Circle
Ellipse
0 500 1000 1500 2000
0
20
40
60
80
100
0500 1000 1500
2000
0
20
40
60
80
100
Spatula
Circle
Ellipse
0 500 1000 1500 2000
0
20
40
60
80
100
Time [s
]T
ime [s]
Time [s]Time [s]
Avg von Mises Stress [% of max]Avg von Mises Stress [% of max]
Corpus Callosum Internal structures
a)
b)
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

801
A comparison ofbrain retraction mechanisms using finite element analysis andtheeffects of…
in average stress is noted when comparing location one
and location three. The location sensitivity of stresses in
the corpus callosum can also be seen with regard to the
tubular retractors. Similar to the results shown in Fig.8a,
lateral location four shows higher average stresses than
lateral location three. However, this is shown to a greater
degree here with location three causing the lowest average
stress out of all four locations, and location four causes the
highest average stress.
Figure9 shows a comparison of the predicted aver-
age stress values over time at the four different loca-
tions (shown on the right hand side of Fig.9) for each
mechanism.
Figure9a shows a similar stress relaxation response for
the internal structures for all three mechanisms at all four
locations. Figure9b shows a more pronounced stress relaxa-
tion within the region of the corpus callosum for the load-
ings from the top when using a spatula. This, however, is
much less pronounced when using the tubular retractors.
This FE study is the first to consider different surgical
sites for retraction in a human brain. From these results, we
can see how the combined location and mechanism affect the
predicted von Mises stresses in different areas of the brain,
even far from the retraction site. It is not possible, however,
to conclude that one specific retraction device is superior
over the other when considering secondary damage. Figure8
shows that a spatula lead to lower stresses in location one
compared to a circular retractor in location three. This com-
plex interaction is not fully understood yet. But the effects of
location are clearly shown here to be an important parameter
to consider for retraction brain surgery in the future.
3.3 Effects ofincorporating regional heterogeneity
The brain consists of several anatomical regions that have
varying functional demands and also differ in their mechani-
cal properties (Budday etal. 2017b; Hinrichsen etal. 2023).
To show the necessity of taking these variations into account
in a full three-dimensional FE model of the brain, we com-
pare the model with four distinct regions (4R: cortex, corona
radiata, corpus callosum, and internal brain structures) to
a homogeneous (1R) model, whereby the parameters were
calculated from the volume average of the four regions.
The material parameters of the homogeneous model
are given in Table2. Additionally, the percentage differ-
ence of these parameters from their region-specific values
(given in Table1) is provided. In the homogeneous model,
the hyperelastic and viscoelastic values differ significantly
from their region-specific values. The corpus callosum is
modelled to be much stiffer in the 1R model than it is in the
4R model and the viscosity of this region is also highly over-
estimated by the 1R model. The cortex is the only region that
is modelled to be slightly softer than in the region-dependent
model.
Table3 summarizes the volume average time constants
(𝜏i=𝜂i∕𝜇i)
calculated from the volume average viscoelastic
material parameters and compares them with the region-
specific values. The time constant for the first viscoelas-
tic element
𝜏1
only shows a large difference for the internal
structures. The time constant for the second viscoelastic ele-
ment
𝜏2
shows more deviation in all regions. The greatest
difference appears for the corpus callosum.
Upon investigation of the regional responses, the cor-
tex and corona radiata did not show significantly different
responses. This may be due to the larger area of constraint on
this model on those areas and the larger areas of prescribed
displacement of these regions. For this reason, these regions
are not considered for comparison. Fig.10 shows the nor-
malized average von Mises stress over time in the internal
structures and corpus callosum between the 4R and the 1R
Superior Lateral
Circle
Spatula Ellipse
Circle
Spatula Ellipse
Maximum von Mises Stress [Pa]Maximum von Mises Stress [Pa]
Corpus Callosum Internal structures
a)
b)
0
10
20
30
40
50
60
0
5
10
15
20
25
30
Fig. 8 Maximum average simulated von Mises stress in the a internal
brain structures and b corpus callosum for four different locations and
each of the three retraction mechanisms. The retraction locations are
indicated on top
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

802 E.Griffiths et al.
model. Figure11 shows a comparison of the maximum aver-
age von Mises stress for these two regions.
There is no visible difference in the stress relaxation in the
internal structures, in spite of large difference between the vol-
ume averaged and regionally specific time constants. Slight dif-
ferences can be noted in the relaxation behaviour of the corpus
callosum, where the 4R model shows a more pronounced stress
relaxation for all three mechanisms. Differences, however, can
be noted in the predicted maximum von Mises stress in Fig.11.
In internal structures, differences of between 20 and 30%
are seen across all three mechanisms. Within the corpus
callosum, even larger differences between 45 and 60% are
noted, as expected from the large difference in the parameter
values reported in Table2.
Avg von Mises Stress
[% of max]
Avg von Mises Stress
[% of max]
Corpus Callosum Internal structures
Spatula Circle Ellipse
Time [s]
Time [s] Time [s]
Time [s] Time [s]
Time [s]
a)
b)
Superior
Lateral
0500 1000 1500 2000
0
25
50
75
0 500 1000 1500 2000
0
25
50
75
0 500 1000 1500 2000
0
25
50
75
0 500 1000 1500 2000
0
25
50
75
0 500 1000 1500 2000
0
25
50
75
0 500 1000 1500 2000
0
25
50
75
100
100
100
100 100 100
Fig. 9 Normalized average simulated von Mises stress over time in the a internal brain structures and b corpus callosum for four different loca-
tions and each of the three retraction mechanisms. The retraction locations are indicated on the right hand side
Table 2 Volume averaged material parameters used in the homo-
geneous (1R) model and the percentage difference of these material
parameter from those used in the region-specific (4R) model account-
ing for the distinct mechanical properties of the cortex, corona
radiata, corpus callosum, and internal brain structures
Equilibrium 1
st
Maxwell Element 2
nd
Maxwell Element
µ∞α∞µ1α1η1µ2α2η2
[kPa] [-] [kPa] [-] [kPa·s] [kPa] [-] [kPa·s]
Volume average 0.03 -22.97 0.11 -18.83 0.26 0.04 -25.63 28.40
Difference [%]
Cortex –34 8 –21 28 –15 –30 8 –2
CoronaRadiata 72 –10 14 –26 18 56 –12 –5
Internal structures 62 7 62 21 14 44 13 18
Corpus Callosum 590 –19 75 –30 59 144 –17 22
Table 3 Characteristic time constants
(𝜏i=𝜂i∕𝜇i)
near thermody-
namic equilibrium calculated from the volume average material
parameters and the percentage difference from the time constants cal-
culated for the region-specific (4R) model accounting for the distinct
mechanical properties of the cortex, corona radiata, corpus callosum,
and internal brain structures
τ1
Difference
τ2
Difference
[s] [%] [s] [%]
Volume average 2.34 / 728.20 /
Cortex 2.18 –7 516.73 –41
Corona Radiata 2.26 –3 1199.16 39
Internal structures 3.34 30 889.52 18
Corpus Callosum 2.57 9 1453.31 50
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

803
A comparison ofbrain retraction mechanisms using finite element analysis andtheeffects of…
Figure11 clearly shows that region-specific parameters
are required for simulations of brain surgery, especially in
the region of the corpus callosum. However, interestingly,
while we found differences between the 1R and the 4R
model in terms of the peak stress values, little difference
is shown in their stress relaxation behaviour in Fig.10—
albeit the significantly different time constants. In order to
explore the effects of heterogeneous viscoelastic properties
in more detail, we performed simulations of the fully seg-
mented brain with regionally heterogeneous hyperelastic
0 500 1000 1500 2000
0
25
50
75
100
Spatula Circle Ellipse
Avg von Mises Stress
[% of max]
Avg von Mises Stress
[% of max]
Time [s] Time [s]Time [s]
Superior
Lateral
4R model
1R model
Superior
Lateral
4R model
1R model
0 500 1000 1500 2000
0
25
50
75
100
0 500 1000 1500 2000
0
25
50
75
100
0 500 1000 1500 2000
0
25
50
75
100
0 500 1000 1500 2000
0
25
50
75
100
0 500 1000 1500 2000
0
25
50
75
100
Fig. 10 Normalized average simulated von Mises stress over time in
the four segmented regions of the brain for each of the three retrac-
tion mechanisms comparing two different models: A fully homogene-
ous model (1R) and the region-dependent model (4R). Each retrac-
tion was performed at two locations, one from the top and one lateral
0
5
10
15
20
25
30
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
0
20
40
60
80
100
0
10
20
30
40
50
60
Maximum von Mises
Stress [Pa]
Maximum von Mises
Stress [Pa]
Spatula Circle Ellipse Spatula Circle Ellipse
Spatula Circle Ellipse Spatula Circle Ellipse
4R model
1R model
4R model
1R model
Fig. 11 Maximum averaged simulated von Mises stress in the regions
of the internal structures and corpus callosum of the brain for each of
the three retraction mechanisms comparing two different models: A
fully homogeneous model (1R) and the region-dependent model (4R).
Each retraction was performed at two locations, one from the top and
one lateral
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

804 E.Griffiths et al.
properties but homogeneous viscoelastic properties (4Req-
1Rvisco) undergoing a circular tube retraction. These were
then compared to both the fully heterogeneous (4R) model
and the fully homogeneous (1R) model. The maximum aver-
age von Mises stress and average von Mises stress over time
are shown in Fig.12.
In this figure, the effects of the higher time constants of
the homogeneous model can be seen. A more pronounced
stress relaxation behaviour (compared to Fig.10) can be
seen in the internal brain structures. The corpus callosum
the 4Req-1Rvisco model also undergoes a greater stress
relaxation. It is thus not appropriate to model the viscoelas-
tic behaviour of these regions as a homogeneous material.
For the internal brain structures, the 4Req-1Rvisco model
shows a lower maximum stress value than the 1R model, but
it is still greater than the 4R models. A similar trend is seen
for the corpus callosum. This indicates that both the equilib-
rium response and the viscoelastic response of the material
affect the peak von Mises stress predicted by the simulations.
Comparing Figs.11 and 10 with12, we observe that it is
important to incorporate heterogeneous material parameters for
both the hyperelastic and viscoelastic behaviour of the brain.
While regions close to the site of loading show similar hypere-
lastic and viscoelastic responses independent of the model used,
in regions far away, the average stress response differs greatly.
4 Conclusions andrecommendations
FE analysis presents a unique opportunity to model neuro-
surgical procedures under controlled conditions, whereby
equipment can be tested and probed easily and efficiently.
In this study, we have used FE analysis to provide insights
into how three different retraction mechanisms affect the
brain. We compared traditional spatulas to tubular retractors
and found higher predicted stresses in the brain when using
traditional spatulas in several different locations. We also
showed how changes in the location of insertion can greatly
0 500 1000 1500 2000
0
25
50
75
100
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
Maximum von Mises
Stress [Pa]
Superior Lateral
Superior
Lateral
Locations Locations
0
10
20
30
40
50
60
4R model
1R model
4Req-1Rvisco model
Time [s] Time [s]
Avg von Mises Stress
[% of max]
Superior
Lateral
4R model
1R model
4Req-1Rvisco model
0 500 1000 1500 2000
0
25
50
75
100
a)
b)
Fig. 12 a Normalized average and b maximum average simulated von
Mises stress in the internal structures and corpus callosum for a cir-
cular retraction mechanism comparing three different models: A fully
homogeneous model (1R), a heterogeneous hyperelastic but homoge-
neous viscoelastic model (4Req-1Rvisco) and the fully heterogene-
ous model (4R). Each retraction was performed at two locations, one
from the top and one lateral
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

805
A comparison ofbrain retraction mechanisms using finite element analysis andtheeffects of…
affect the predicted stress results. By using FE analysis, dif-
ferent locations of access could thus be probed to find those
that minimize the expected stresses throughout the brain.
While we had to make certain assumptions to model this
neurological procedure, we strongly believe that our analyses
have provided valuable insights into how different retraction
mechanisms affect the surrounding brain tissue.
This study supports the clinical observations that tubu-
lar retractors may cause less secondary brain damage than
traditional spatulas. Our simulations show that, at the same
location, the tubular retractors predict a lower maximum
von Mises stress in the internal structures of the brain and
in corpus callosum. As there are large variations inherent in
these types of surgeries, one cannot, however, assume that
the tubular retractor is always the safer option. For exam-
ple, when retraction location was varied, certain locations
showed a lower predicted maximum stress using spatulas
compared to using tubular retractors at other locations. This
shows an important interplay between these two parameters
that should be considered before surgery. By using FE analy-
sis these parameters (and other variations such as cutting
depth and patient-specific brain anatomy) are easier and
safer to investigate.
We have also investigated the importance of using
region-specific hyperelastic and viscoelastic material prop-
erties and revealed interesting results for the modelling of
three-dimensional brains during surgery. Our study high-
lights that both region-dependent hyper- and viscoelastic
parameters should be used as they greatly affect the pre-
dicted stress in the internal structures of the brain and the
corpus callosum.
In conclusion, our study highlights the relevance of
simulating neurosurgical procedures and the importance
of region-specific parameters for clinically relevant predic-
tions. Our analysis presents a preliminary example of how
FE simulations could be used to find the safest and most
suitable route to perform retraction based on models that are
patient-specific, both anatomically and mechanically.
Appendix A: Mesh convergence study
We have conducted a convergence study for various ele-
ment sizes at the mesh refinement site. The four meshes
of decreasing element size and corresponding results are
shown in Fig.13.
Figure14 shows a clear path towards mesh convergence
in the regions of the corona radiata and the grey matter.
Due to a restriction to hexahedral elements in deal.II and
the complex nature of the brain model, we are unable to
refine the mesh any further. However, by extrapolation of the
curves, we predict convergence to be achieved with only one
more step. As we do not compare the maximum predicted
von Mises stress for the corona radiata and the grey matter
when comparing the mechanisms in Fig.6 or for the location
comparisons in Fig.9, we believe this final mesh to be suf-
ficient. For these figures, we limited ourselves to the corpus
callosum and internal structures, which show a convergence
in the mesh convergence study.
Using the element size of this final converged mesh, we
refined the initial meshes of the other two retraction mecha-
nisms with similarly sized elements.
Fig. 13 Four meshes at the cir-
cular retraction site of decreas-
ing element size to be used to
conduct the mesh convergence
study
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

806 E.Griffiths et al.
Author contributions SB conceptualized the study, acquired funding,
and supervised the study. EG performed all simulations and wrote the
initial manuscript. All authors reviewed and edited the manuscript.
Funding Open Access funding enabled and organized by Projekt
DEAL. We gratefully acknowledge the financial support by the
Deutsche Forschungsgemeinschaft (DFG, German Research Founda-
tion) through the grant BU 3728/1-1.
Declarations
Conflict of interest The authors declare that they have no known com-
peting interests.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article's Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article's Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
References
Adachi K, Inoue Y, Kanki H, etal. (2007) Finite element mode-
ling of brain tissue retraction for neurosurgical simulation. In:
Volume 2: biomedical and biotechnology engineering. ASMEDC,
IMECE2007. 10.1115/imece2007-41772
Andrews RJ, Bringas JR (1993) A review of brain retraction and rec-
ommendations for minimizing intraoperative brain injury. Neu-
rosurgery 33(6):1052–1064. https:// doi. org/ 10. 1227/ 00006 123-
19931 2000- 00014
Awasthi A, Gautam U, Bhaskar S etal (2020) Biomechanical model-
ling and computer aided simulation of deep brain retraction in
neurosurgery. Comput Methods Programs Biomed 197:105688.
https:// doi. org/ 10. 1016/j. cmpb. 2020. 105688
Bander ED, Jones SH, Kovanlikaya I etal (2016) Utility of tubular
retractors to minimize surgical brain injury in the removal of
deep intraparenchymal lesions: a quantitative analysis of FLAIR
hyperintensity and apparent diffusion coefficient maps. J Neuro-
surg 124(4):1053–1060. https:// doi. org/ 10. 3171/ 2015.4. jns14 2576
Bander ED, Jones SH, Pisapia D etal (2018) Tubular brain tumor
biopsy improves diagnostic yield for subcortical lesions.
J Neuro-Oncol 141(1):121–129. https:// doi. org/ 10. 1007/
s11060- 018- 03014-w
Budday S, Nay R, de Rooij R etal (2015) Mechanical properties of
gray and white matter brain tissue by indentation. J Mech Behav
Biomed Mater 46:318–330. https:// doi. org/ 10. 1016/j. jmbbm.
2015. 02. 024
Budday S, Sommer G, Birkl C etal (2017) Mechanical characterization
of human brain tissue. Acta Biomater 48:319–340. https:// doi. org/
10. 1016/j. actbio. 2016. 10. 036
Budday S, Sommer G, Haybaeck J etal (2017) Rheological characteri-
zation of human brain tissue. Acta Biomater 60:315–329. https://
doi. org/ 10. 1016/j. actbio. 2017. 06. 024
Budday S, Sommer G, Holzapfel G etal (2017) Viscoelastic parameter
identification of human brain tissue. J Mech Behav Biomed Mater
74:463–476
Fig. 14 The maximum von Mises stress predicted using the different meshes introduced in Fig.13 in each region of the segmented brain model
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

807
A comparison ofbrain retraction mechanisms using finite element analysis andtheeffects of…
Budday S, Ovaert TC, Holzapfel GA etal (2019) Fifty shades of brain:
a review on the mechanical testing and modeling of brain tissue.
Arch Comput Methods Eng 27(4):1187–1230. https:// doi. org/ 10.
1007/ s11831- 019- 09352-w
Cohen-Gadol AA (2013) Minitubular transcortical microsurgical
approach for gross total resection of third ventricular colloid cysts:
technique and assessment. World Neurosurg 79(1):207.e7-207.
e10. https:// doi. org/ 10. 1016/j. wneu. 2011. 03. 045
Echeverry N, Mansour S, MacKinnon G etal (2020) Intracranial tubu-
lar retractor systems: a comparison and review of the literature of
the BrainPath, vycor, and METRx tubular retractors in the man-
agement of deep brain lesions. World Neurosurg 143:134–146.
https:// doi. org/ 10. 1016/j. wneu. 2020. 07. 131
Eichberg DG, Di L, Shah AH etal (2020) Minimally invasive resec-
tion of intracranial lesions using tubular retractors: a large, multi-
surgeon, multi-institutional series. J Neuro-Oncol 149(1):35–44.
https:// doi. org/ 10. 1007/ s11060- 020- 03500-0
Evins AI (2017) Minimally invasive tubular retraction and transtubu-
lar approaches in neurosurgery. https:// doi. org/ 10. 6093/ UNINA/
FEDOA/ 11507
Franceschini G, Bigoni D, Regitnig P etal (2006) Brain tissue deforms
similarly to filled elastomers and follows consolidation theory. J
Mech Phys Solids 54(12):2592–2620. https:// doi. org/ 10. 1016/j.
jmps. 2006. 05. 004
Fukuhara A, Tsujita T, Sase K etal. (2014a) Optimization of retrac-
tion in neurosurgery to avoid damage caused by deformation of
brain tissues. In: 2014 IEEE international conference on robotics
and biomimetics (ROBIO 2014). IEEE. https:// doi. org/ 10. 1109/
robio. 2014. 70903 94
Fukuhara A, Tsujita T, Sase K etal (2014) Proposition and evaluation
of a collision detection method for real time surgery simulation of
opening a brain fissure. ROBOMECH J. https:// doi. org/ 10. 1186/
s40648- 014- 0006-7
Gassie K, Wijesekera O, Chaichana KL (2018) Minimally invasive
tubular retractor-assisted biopsy and resection of subcortical intra-
axial gliomas and other neoplasms. J Neurosurg Sci. https:// doi.
org/ 10. 23736/ s0390- 5616. 18. 04466-1
Govindjee S, Reese S (1997) A presentation and comparison of two
large deformation viscoelasticity models. J Eng Mater Technol
119(3):251–255. https:// doi. org/ 10. 1115/1. 28122 52
Griffiths E, Hinrichsen J, Reiter N etal (2023) On the importance
of using region-dependent material parameters for full-scale
human brain simulations. Eur J Mech A/Solids 99:104910.
https:// doi. org/ 10. 1016/j. eurom echsol. 2023. 104910
Hansen KV, Brix L, Pedersen CF etal (2004) Modelling of interac-
tion between a spatula and a human brain. Med Image Anal
8(1):23–33. https:// doi. org/ 10. 1016/j. media. 2003. 07. 001
Hendricks B, Cohen-Gadol A (2016) Principles of intraventricu-
lar surgery. In: Neurosurgical Atlas. Neurosurgical Atlas, Inc.,
https:// doi. org/ 10. 18791/ nsatl as. v4. ch05.1
Hinrichsen J, Reiter N, Bräuer L etal (2023) Inverse identification
of region-specific hyperelastic material parameters for human
brain tissue. Biomech Model Mechanobiol 22(5):1729–1749.
https:// doi. org/ 10. 1007/ s10237- 023- 01739-w
Iyer R, Chaichana K (2018) Minimally invasive resection of deep-
seated high-grade gliomas using tubular retractors and exo-
scopic visualization. J Neurol Surg Part A Cent Eur Neurosurg
79(04):330–336. https:// doi. org/ 10. 1055/s- 0038- 16417 38
Jackson C, Gallia G, Chaichana K (2017) Minimally invasive biop-
sies of deep-seated brain lesions using tubular retractors under
exoscopic visualization. J Neurol Surg Part A Cent Eur Neuro-
surg 78(06):588–594. https:// doi. org/ 10. 1055/s- 0037- 16026 98
Jamshidi AO, Priddy B, Beer-Furlan A etal (2018) Infradentate
approach to the fourth ventricle. Oper Neurosurg 16(2):167–
178. https:// doi. org/ 10. 1093/ ons/ opy175
Jamshidi AO, Beer-Furlan A, Hardesty DA etal (2020) Management
of large intraventricular meningiomas with minimally invasive
port technique: a three-case series. Neurosurg Rev 44(4):2369–
2377. https:// doi. org/ 10. 1007/ s10143- 020- 01409-w
Kaessmair S, Distler T, Schaller E etal (2021) Identification of
mechanical models and parameters for alginate-based hydrogels
as proxy materials for brain tissue. PAMM. https:// doi. org/ 10.
1002/ pamm. 20200 0338
Kassam AB, Labib MA, Bafaquh M etal (2015) Part i: the challenge
of functional preservation: an integrated systems approach using
diffusion-weighted, image-guided, exoscopic-assisted, transul-
cal radial corridors. Innov Neurosurg. https:// doi. org/ 10. 1515/
ins- 2014- 0011
Kelly PJ, Goerss SJ, Kall BA (1988) The stereotaxic retractor in com-
puter-assisted stereotaxic microsurgery. J Neurosurg 69(2):301–
306. https:// doi. org/ 10. 3171/ jns. 1988. 69.2. 0301
Kyriacou SK, Mohamed A, Miller K etal (2002) Brain mechanics
for neurosurgery: modeling issues. Biomech Model Mechano-
biol 1(2):151–164. https:// doi. org/ 10. 1007/ s10237- 002- 0013-0
Lamprich BK, Miga MI (2003) Analysis of model-updated mr
images to correct for brain deformation due to tissue retrac-
tion. In: Galloway RLJr. (ed) SPIE Proceedings. SPIE. https://
doi. org/ 10. 1117/ 12. 480217
Li P, Wang W, Zhang C etal (2016) Invivo investigation of the
effectiveness of a hyper-viscoelastic model in simulating brain
retraction. Sci Rep. https:// doi. org/ 10. 1038/ srep2 8654
Mansour S, Echeverry N, Shapiro S etal (2020) The use of Brain-
Path tubular retractors in the management of deep brain lesions:
a review of current studies. World Neurosurg 134:155–163.
https:// doi. org/ 10. 1016/j. wneu. 2019. 08. 218
Mao H, Zhang L, Jiang B etal (2013) Development of a finite ele-
ment human head model partially validated with thirty five
experimental cases. J Biomech Eng 135(11):111002
Marenco-Hillembrand L, Alvarado-Estrada K, Chaichana KL (2018)
Contemporary surgical management of deep-seated metastatic
brain tumors using minimally invasive approaches. Front Oncol.
https:// doi. org/ 10. 3389/ fonc. 2018. 00558
Marenco-Hillembrand L, Prevatt C, Suarez-Meade P etal (2020)
Minimally invasive surgical outcomes for deep-seated brain
lesions treated with different tubular retraction systems: A sys-
tematic review and meta-analysis. World Neurosurg 143:537-
545.e3. https:// doi. org/ 10. 1016/j. wneu. 2020. 07. 115
Miga MI, Roberts DW, Kennedy FE etal (2001) Modeling of retraction
and resection for intraoperative updating of images. Neurosurgery
49(1):75–85
Mihai LA, Chin L, Janmey PA etal (2015) A comparison of hyper-
elastic constitutive models applicable to brain and fat tissues. J
R Soc Interface 12(110):20150486. https:// doi. org/ 10. 1098/ rsif.
2015. 0486
Miller K, Chinzei K (2002) Mechanical properties of brain tissue in
tension. J Biomech 35(4):483–490. https:// doi. org/ 10. 1016/ s0021-
9290(01) 00234-2
Miller LE, Urban JE, Stitzel JD (2016) Development and valida-
tion of an atlas-based finite element brain model. Biomech
Model Mechanobiol 15(5):1201–1214. https:// doi. org/ 10. 1007/
s10237- 015- 0754-1
O’Connor KP, Strickland AE, Bohnstedt BN (2019) A contralateral
transventricular approach for microsurgical clip ligation of a
ruptured intrathalamic aneurysm. J Clin Neurosci 68:329–332.
https:// doi. org/ 10. 1016/j. jocn. 2019. 07. 028
Ogden RW (1972) Large deformation isotropic elasticity: on the cor-
relation of theory and experiment for compressible rubberlike
solids. Proc R Soc Lond A Math Phys Sci 328(1575):567–583.
https:// doi. org/ 10. 1098/ rspa. 1972. 0096
Okasha M, Ineson G, Pesic-Smith J etal (2020) Transcortical approach
to deep-seated intraventricular and intra-axial tumors using a
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

808 E.Griffiths et al.
tubular retractor system: a technical note and review of the litera-
ture. J Neurol Surg Part A Cent Eur Neurosurg 82(03):270–277.
https:// doi. org/ 10. 1055/s- 0040- 17190 25
Platenik L, Miga M, Roberts D etal (2002) Invivo quantification of
retraction deformation modeling for updated image-guidance dur-
ing neurosurgery. IEEE Trans Biomed Eng 49(8):823–835. https://
doi. org/ 10. 1109/ tbme. 2002. 800760
Raza SM, Recinos PF, Avendano J etal (2011) Minimally invasive
trans-portal resection of deep intracranial lesions. Min-Minim
Invasive Neurosurg 54(01):5–11. https:// doi. org/ 10. 1055/s- 0031-
12737 34
Recinos PF, Raza SM, Jallo GI etal (2011) Use of a minimally inva-
sive tubular retraction system for deep-seated tumors in pediatric
patients. J Neurosurg Pediatr 7(5):516–521. https:// doi. org/ 10.
3171/ 2011.2. peds1 0515
Reiter N, Roy B, Paulsen F etal (2021) Insights into the microstructural
origin of brain viscoelasticity. J Elast 145(1–2):99–116. https://
doi. org/ 10. 1007/ s10659- 021- 09814-y
Sase K, Fukuhara A, Tsujita T etal (2015) GPU-accelerated surgery
simulation for opening a brain fissure. ROBOMECH J. https:// doi.
org/ 10. 1186/ s40648- 015- 0040-0
Schneiders R (1998) Quadrilateral and hexahedral element meshes. In:
Handbook of grid generation. CRC Press. https:// doi. org/ 10. 1201/
97814 20050 349. ch21
Shapiro SZ, Sabacinski KA, Mansour SA etal (2020) Use of vycor
tubular retractors in the management of deep brain lesions: a
review of current studies. World Neurosurg 133:283–290. https://
doi. org/ 10. 1016/j. wneu. 2019. 08. 217
Shoakazemi A, Evins AI, Burrell JC etal (2015) A 3d endoscopic tran-
stubular transcallosal approach to the third ventricle. J Neurosurg
122(3):564–573. https:// doi. org/ 10. 3171/ 2014. 11. jns14 341
Sidoroff F (1974) Nonlinear viscoelastic model with intermediate con-
figuration. J Mec 13(4):679–713
Viano DC, Casson IR, Pellman EJ etal (2005) Concussion in profes-
sional football: brain responses by finite element analysis: part 9.
Neurosurgery 57(5):891–916
Zagzoog N, Reddy KK (2020) Modern brain retractors and surgical
brain injury: a review. World Neurosurg 142:93–103. https:// doi.
org/ 10. 1016/j. wneu. 2020. 06. 153
Zhong J, Dujovny M, Perlin AR etal (2003) Brain retraction injury.
Neurol Res 25(8):831–838. https:// doi. org/ 10. 1179/ 01616 41037
71953 925
Publisher's Note Springer Nature remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

1.
2.
3.
4.
5.
6.
Terms and Conditions
Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH (“Springer Nature”).
Springer Nature supports a reasonable amount of sharing of research papers by authors, subscribers and authorised users (“Users”), for small-
scale personal, non-commercial use provided that all copyright, trade and service marks and other proprietary notices are maintained. By
accessing, sharing, receiving or otherwise using the Springer Nature journal content you agree to these terms of use (“Terms”). For these
purposes, Springer Nature considers academic use (by researchers and students) to be non-commercial.
These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal
subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription
(to the extent of the conflict or ambiguity only). For Creative Commons-licensed articles, the terms of the Creative Commons license used will
apply.
We collect and use personal data to provide access to the Springer Nature journal content. We may also use these personal data internally within
ResearchGate and Springer Nature and as agreed share it, in an anonymised way, for purposes of tracking, analysis and reporting. We will not
otherwise disclose your personal data outside the ResearchGate or the Springer Nature group of companies unless we have your permission as
detailed in the Privacy Policy.
While Users may use the Springer Nature journal content for small scale, personal non-commercial use, it is important to note that Users may
not:
use such content for the purpose of providing other users with access on a regular or large scale basis or as a means to circumvent access
control;
use such content where to do so would be considered a criminal or statutory offence in any jurisdiction, or gives rise to civil liability, or is
otherwise unlawful;
falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association unless explicitly agreed to by Springer Nature in
writing;
use bots or other automated methods to access the content or redirect messages
override any security feature or exclusionary protocol; or
share the content in order to create substitute for Springer Nature products or services or a systematic database of Springer Nature journal
content.
In line with the restriction against commercial use, Springer Nature does not permit the creation of a product or service that creates revenue,
royalties, rent or income from our content or its inclusion as part of a paid for service or for other commercial gain. Springer Nature journal
content cannot be used for inter-library loans and librarians may not upload Springer Nature journal content on a large scale into their, or any
other, institutional repository.
These terms of use are reviewed regularly and may be amended at any time. Springer Nature is not obligated to publish any information or
content on this website and may remove it or features or functionality at our sole discretion, at any time with or without notice. Springer Nature
may revoke this licence to you at any time and remove access to any copies of the Springer Nature journal content which have been saved.
To the fullest extent permitted by law, Springer Nature makes no warranties, representations or guarantees to Users, either express or implied
with respect to the Springer nature journal content and all parties disclaim and waive any implied warranties or warranties imposed by law,
including merchantability or fitness for any particular purpose.
Please note that these rights do not automatically extend to content, data or other material published by Springer Nature that may be licensed
from third parties.
If you would like to use or distribute our Springer Nature journal content to a wider audience or on a regular basis or in any other manner not
expressly permitted by these Terms, please contact Springer Nature at
onlineservice@springernature.com