1. Introduction
The distensibility (or flexibility) of brain tissue is an important
factor in the brain’s response to trauma and various conditions
such as hydrocephalus.5 However, measuring brain distensibility is
challenging because the brain is not directly palpable (except
through the fontanelle in newborns), and it is difficult to obtain
direct measurements of pressures within the brain such as:3
• the pressure of cerebrospinal fluid (CSF)
• arterial blood pressure
• venous blood pressure
With this in mind, a novel equation to quantify brain distensibility
was developed:
Distensibility =
∆𝑉
𝑉0∆𝑃
[1]
Where V0 is the baseline brain volume (ml), DP is the change in
blood pressure from diastole to sytole (mmHg), and DV is the
change in brain volume (ml) in response to DP. V0 can be measured
directly from anatomic MRI, DV can be estimated by measuring the
CSF displaced by the expanding brain, and DP can be measured
using an automated blood pressure cuff. Equation 1 assumes:
1. The skull is fully closed and rigid.
2. The volume of displaced CSF is equivalent to the volume
of the expanding brain.
3. The production of CSF is negligible over the course of a
heartbeat.
4. The blood pressure measurements made at the arm are
proportional to the blood pressure in the brain.1
Abstract
The brain’s distensibility (or flexibility) has rarely been
measured, although it is an important factor in the brain’s
mechanical response to trauma, hydrocephalus, and certain
physiological conditions. Assuming the skull is rigid (i.e. the skull
plates have fused and the fontanelle has closed), and the
production of cerebrospinal fluid (CSF) is negligible over the course
of a heartbeat, the volume of cerebrospinal fluid displaced by brain
expansion at systole is equivalent to the change in volume of the
brain tissue from diastole to systole. We hypothesize that brain
distensibility can be quantified using the following equation:
Distensibility = DV/(V0DP)
where DV is the change in brain volume in response to increased
pressure from the brain at systole, V0 is the baseline volume of the
brain at diastole, and DP is the change in blood pressure over the
cardiac cycle.
Distensibilty was measured in a healthy 59 year old male
volunteer. 3D MRI anatomical images of the brain were acquired
using a cardiac-gated pulse sequence. 2D phase-contrast MRI
velocity data of cerebrospinal fluid through an axial slice at the C2
vertebra in the neck were then acquired. Post-processing software
was used to find V0 and the flux of CSF at the area around the
spinal cavity. The flux was then integrated to find the average
downward CSF volume at systole (DV). DP was measured on the
subject’s left arm with an automated BP cuff. The subject’s brain
distensibility was calculated to be 7.53*10-6 mmHg-1.
This new approach to non-invasively quantifying brain
distensibility may have significant utility for studying brain trauma,
hydrocephalus, and physiologic changes in the brain associated
with normal development and aging.
Methods
Distensibility measurements were made in the brain of a
healthy 59 year old male volunteer using MR imaging. 10 Baseline
brain volume measurements, V0, were made using 3D T1-weighted
imaging with a TR of 25.0 ms, TE of 4.6 ms, 1x1x1 mm3 voxel size,
and 240x240x160 mm3 FOV. The change in brain volume was
estimated with 10 quantitative flow measurements of CSF at the
base of the skull using a phase-contrast flow sequence (see
below). Systolic and diastolic blood pressure was measured using
an automated GETM Dinamap Pro 300v2 BP Monitor.
Phase contrast velocity measurements with MRI
Phase contrast MRI measures the phase shift induced by
the movement of transverse spin magnetization in the presence of
a symmetric bipolar magnetic gradient field pulse. It has been
widely used in MR Angiography.1
A depiction of the effect a bipolar magnetic gradient can
have on moving and stationary spins is shown below in Figure 1.
.
Controlling the amplitude, duration, and spacing of the
bipolar gradients determines the sensitivity of imaging to slow or
fast flow because the motion-induced phase shift of an ensemble of
spins is proportional to velocity1:
 𝑚𝑜𝑡𝑖𝑜𝑛 = 𝑉𝑇𝐴𝑔 [2]
where,  is the gyromagnetic ratio, V is spin’s velocity parallel to the
direction of the applied gradient, T is the time between the centers
of the lobes of the gradient pulse, and Ag is the area of one lobe of
the bipolar pulse1. Flow velocity and volume can be determined
from phase-contrast MRI using the following steps:
• The mean velocity of pixels in an image is calculated (cm/s)
• A cross-sectional region of interest (ROI) is drawn (cm2)
• Velocity of pixels is multiplied by the ROI to compute flow (ml/s)
• Flow rate can be integrated over time to compute volume (ml)
Experiments
A flow phantom was constructed
in an 1.5T Phillips MRI magnet to
quantify fluid flow in a rigid pipe
using 2D Phase-Contrast
Imaging. The flow quantified by
the MR was compared to the flow
calculated using a conventional
graduated cylinder and
stopwatch. A diagram of the set-
up is shown in Figure 2.
The subject was placed in a 1.5T Philips Magnet with a head
and neck coil. 2D Phase-Contrast Imaging was used to measure
velocity of CSF around the spinal cavity through an axial slice at
the mid C2 vertebra (Figures 3a and 3b). 3D anatomical T1-
weighted images of the brain were also gathered to find V0 using a
cardiac-gated pulse sequence (Figure 5). Blood pressure was
measured 6 times in the left arm using the automated BP monitor.
References
Conclusion
In this study, a novel equation was derived to quantify brain
distensibility. From the parameters found in experimentation,
Equation 1 was used to calculate the subject’s brain distensibility
as 7.53*10-6 mmHg-1. For comparison, in past studies a 35 year
old male’s arterial distensibility was calculated to be 2.27*10-3
mmHg-1 1. The uncertainty in the calculated brain distensibility
could be attributed to:
• fluctuations in blood pressure that influences brain
expansion
• Non-identical ROIs produced in all 10 acquired images to
quantify CSF flow.
If these errors are addressed, Equation 1 could have
significant use in identifying a relationship or proportionality
between brain distensibility and intracranial pressure (ICP). This
relationship could then be applicable in studies that evaluate the
brain’s response to changes in intracranial pressure.
For instance, the use of the Valsalva maneuver has been
proven to increase aspects of ICP6. One could hypothesize that
while performing a Valsalva maneuver, the brain, under increased
ICP, has a higher distensibility to expand and release more CSF
fluid. If brain distensibility is proportional to ICP, the extent to which
intracranial pressure is affected could be computed rather than
attempting to measure components of intracranial pressure directly
(which usually involves invasive procedures).
Other ICP studies that could incorporate brain distensibility
measurements include stroke, hypertension, hydrocephalus, and
trauma. For instance, recent trauma studies on the effects of
cervical collars claim the constriction on the neck causes an
increase in the cross-sectional area of the internal jugular vein and
thus increases ICP6. Calculated changes in brain distensibility with
the use of a neck collar could support or refute these claims.
Evaluating brain distensibility can also quantify mechanical
changes in the brain associated with age, development, and
physiological disorders. Partnered with fMRI studies, Equation 1
could be used to evaluate how brain distensibility is related to
cognitive development, and how psychological disorders are
related to mechanical changes in the brain.
In addition, an up-and-coming method of imaging uses
Magnetic Resonance Elastography (MRE) to directly measure the
mechanical properties of tissue by applying shear waves to
tissues5. If MRE was used to measure the difference in brain
elasticity under different physiological conditions, the results could
be validated from the difference in distensibility measurements
calculated using Equation 1.
Estimating brain distensibility with quantitative magnetic resonance CSF flow measurements
Annamarie T Helpling2 , Christopher M Ireland1, 2 , J. Matthew Lanier2
, Charles L Dumoulin2
1 Department of Biomedical Engineering, University of Cincinnati, Cincinnati, Ohio, United States
2 Imaging Research Center, Cincinnati Children’s Hospital Medical Center, Cincinnati, Ohio, United States
1.Dumoulin, C. L., D. J. Doorly, and C. G. Caro. "Quantitative Measurement of
Velocity at Multiple Positions Using Comb Excitation and Fourier Velocity
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(1993): 44-52. Web. 8 July 2015.
2. Elster, Allen D., MD. "Phase Contrast MRA." Questions and Answers in MRI.
AD Elster, Elster LLC, 2014. Web. 16 July 2015.
3. Hill, Dr. Lisa, and Dr. Carl Gwinnut. "Cerebral Blood Flow and Intracranial Pressure."
Cerebral Blood Flow and Intracranial Pressure (n.d.): n. pag. Web. 8 July 2015.
4. J. V. Manjón, P. Coupé. volBrain: An online MRI brain volumetry system,
Organization for Human Brain Mapping 15, 2015.
5. Kruse, Scott A., Gregory H. Rose, Kevin J. Glaser, Armando Manduca,
Joel P. Felmlee, Clifford R. Jack Jr., and Richard L. Ehman. "Magnetic
Resonance Elastography of the Brain." NeuroImage 39 (2008): 231-37.
National Center for Biotechnology Information, U.S. National Library of
Medicine. Web. 8 July 2015.
6. Prabhakar, H., P. Bithal, A. Suri, G. Rath, and H. Dash. "Intracranial Pressure
Changes During Valsalva Manoeuvre in Patients Undergoing a Neuroendoscopic
Procedure." Min - Minimally Invasive Neurosurgery
Minim Invasive Neurosurg 50.2 (2007): 98-101. Web. 24 July 2015.
7. Stone, Michael B., Catherine M. Tubridy, and Robert Curran. "The Effect of Rigid
Cervical Collars on Internal Jugular Vein Dimensions."
Academic Emergency Medicine 17.1 (2010): 100-02. Web. 22 July 2015.
Figure 2: Flow Phantom Set-up
Figure 3a and 3b: Magnitude image and flow mapping Figure 5: Sagittal view of brain
Figure 1: Effect of
bipolar magnetic
gradients on net
phase shift of
moving spins2
Results
Figure 5 shows the pixel phase (proportional to the velocity
of the moving spins) in the cross section of the pipe phantom. The
flow had a parabolic velocity profile across the 9.8 mm diameter of
the pipe consistent with laminar fluid.
Over an RR interval of 1024.74
ms, post processing software
calculated:
• Average flux rate: 25.80 ±0.03
ml/s through an ROI of 0.67
cm2
For comparison, volumetric
results yielded:
• Average flowrate: 26.32 ml/s
• Difference in Results: 1.98%
The subject’s average blood pressure was measured to be
112/75. The images quantifying the displacement of CSF during
the cardiac cycle of the subject were split into 2 ROIs to quantify
the flow, as shown below in Figure 6. The ROI of CSF flow was
3.09±0.29 cm2. The flux of the fluid (ml/s) over time of the RR
interval (928.35±15.74 ms) was plotted for both ROI in Figure 7
below.
The measured motion of the spinal cord during each interval
of time (inner ROI) was subtracted from the motion of CSF + cord
(outer ROI) for each time interval to determine CSF flow. DV of the
brain was calculated by computing the volume of CSF flowing
downward during systole (from 420-750 ms in Figure 7). The
Average systole CSF flow from the 10 images was 0.35±0.06 ml.
volBrain™ segmentation software was used to approximate
the average baseline volume of the brain4. The range in brain
volumes calculated from the 10 images was 9.46 ml. The
segmentation for the 3rd image acquired is shown in Figure 8.
• Average baseline brain volume (V0) calculated: 1263.61±3.15 ml
• Change in brain volume during systole (DV): 0.35±0.06 ml
• Subject’s change in blood pressure (DP): 36.83±2.73 mmHg
The subject’s brain distensibility during systole was solved
using Equation 1 and the average input variables calculated:
∆𝑉(𝑚𝑙)
𝑉0(𝑚𝑙)∆𝑃(𝑚𝑚𝐻𝑔)
=
0. 35𝑚𝑙
1263.61 𝑚𝑙 ∗ 36.83 𝑚𝑚𝐻𝑔
= 7.53 ∗ 10−6
1
𝑚𝑚𝐻𝑔
Figure 8: (L to R) Intracranial extraction, tissue classification, macrostructures, subcortical structures
Figure 6: ROI of spinal cord (red) and
CSF flow (green)
Figure 7: Graph of flux (ml/s) over time for spinal
cord (red) and CSF (green)