Physical properties of labyrinth fluids in human vestibular syste

Meiry, J. L.

Young, L. R.

English

NASA Technical Reports Server

I 
c . 
BIOPHYSICAL EVALUATION OF THU" 
HUMAN VESTIBULAR SYSTEM 
Second Semi-Annual Status Report on 
NASA Grant NGR 22-009-156 
January 1967 
Principal Investigators: Professor J. L. Meiry 
Professor L. R. Young 
Massachusetts Institute of Technology 
Man-Vehicle Control Laboratory 
Center f o r  Space Research 
https://ntrs.nasa.gov/search.jsp?R=19670010654 2020-03-16T18:05:58+00:00Z
MV-67-2 
BIOPHYSICAL FVALUATION OF THE 
HUMAN VESTIBULAR SYSTEM 
ABSTRACT 
The physical properties of the labyrinthine fluids and 
their variation with temperature were measured. A precision 
microviscometer was built and calibrated to measure viscosity 
of endolymph and perilymph. Progress in experiments and 
modeling of the vestibular caloric stimulation process is 
reported. Analytical efforts to establish a fluid dynamic 
model of the semicircular canals are discussed. 
by Principal Investigators: J. L. Meiry 
L. R. Young 
January 1967 
2. 
I. PHYSICAL PROPERTIES OF THE LABYRINTHINE FLUIDS 
4 
In the last half of 1966 the construction and calibra- 
tion of the micro-viscometer described in the First Semi-Annual 
Status Report (MV-66-2, June 1966) was ccmpleted, and the physi- 
cal properties of density (f), coefficient of volume expansion 
($ s), viscosity p), and thermal coefficient of viscosity 
(g), have been measured for both cat and human perilymph, and 
human endolymph. These results and their error bounds are 
presented in table 1. The experimental methods used in the 
measurement of the properties of the labyrinthine fluids are 
described in the following paragraphs. 
Density Measurements 
The measurement of viscosity by the "rolling sphere'' 
viscometer requires imowlege of the dmsitg of the fluid mea- 
sured (see MV-66-2). However, since the tungsten carbide 
sphere used in our micro-viscometer has a density near 13, 
and the labyrinthine fluids have densities near 1, then the 
absolute accuracy of their differences is relatively insensi- 
tive to errors in the density measurement of the fluids. It 
is sufficient for this purpose to measure densities to an 
absolute accuracy of f2$. 
3 .  
c 
U s i n g  a precis ion chemical balance t o  weigh a ca l ibra ted  
micropipette empty, f i l l e d  w i t h  water, and f i l l e d  w i t h  c a t  o r  
human endolymph o r  perilymph, it was found t h a t  the  labyrin-  
t h ine  f l u i d s '  densi ty  i s  indis t inguishable  from water, t o  an 
accuracy of -2%. + 
Thermal Coeff ic ient  of Expansion 
To ca lcu la te  the torque on the endolymph due t o  ca lo r i c  
s t imulat ion it i s  necessary t o  know the change i n  densi ty  of 
endolymph due t o  var ia t ions i n  temperature. For t h i s  purpose 
i t  is  convenient t o  r e c a l l  that :  
where 
V = volume 
9 = densi ty  
T = temperature. 
A V  The coef f ic ien t  of expansion (m) was obtained by measuring 
the change i n  length of a 0.500 inch column of f l u i d  i n  a 
glass capi l la ry .  A microscope equipped w i t h  a micrometer ad- 
jus tab le  t a b l e  having a resolut ion of .05 x loa3 i n .  was used 
f o r  the readout instrument. By measuring the change i n  length 
f o r  a 10°C change i n  temperature and t a k i n g  i n t o  account 
4. 
c 
0 
the expansion of the glass pipette, the coefficient of expan- 
sion was found to be 4.4 x 10-4/0c for cat and human endolymph 
and perilymph. Error analysis bounds the measurement accuracy 
to +5$. 
Coefficient of Thermal Conductivity 
To evaluate analytically the thermal time constant of the 
caloric stimulation model which was presented in the First Semi- 
Annual Status Report (MV-66-2, June 1966), the thermal conduc- 
tivity of endolymph and perilymph must be known. 
A device to measure the thermal conductivity of 1 samples r 
is under construction. It measures the time constant of decay 
of the thermal gradient between two insulated bodies connected 
by a tube of fluid. It is expected that this measurement will 
be completed in the first quarter of 1967. 
Modification of Proposed Viscometer Design 
In practice it was found to be necessary to modify some 
of the original design features of the micro-viscometer. The 
first of two major changes was the inclusion of a closed loop 
temperature controller to maintain the sample within 0.loC of 
the desired value. Secondly, it was found to be necessary to 
include an electrostatic shield in the design of the instru- 
ment to eliminate the effects of the electrostatic force field 
on the rolling sphere. 
c 
5. 
Modification of Sample Handling Techniques 
Samples of human and c a t  labyrinthine f l u i d s  were obtained 
from D r .  Herbert S i lve r s t e in  a t  the Massachusetts m e  and Ear 
Infirmary. These samples were the remainder of samples that  
had been used fo r  chemfcal analysis ,  and although they were 
large enough fo r  use i n  the viscometer, they contained small 
b i t s  of paraff in ,  o r  glass ,  and a l l  were sealed wi th  mineral 
o i l .  It became necessary t o  centr i fuge the  samples t o  separate  
t h e  foreign p a r t i c l e s  and t o  separate  the drople t s  of o i l  from 
the tungsten carbide sphere. 
The mineral o i l  serves both as a s e a l  t o  prevent evapora- 
t i o n  and contamination, and as a b a r r i e r  which prevents the  
sphere from being caught in the surface tension of the  f l u i d ;  
thus the cap which had been spec i f i ca l ly  designed f o r  those 
purposes, f o r  the capi l la ry  tubes, was no longer needed. It 
was also found necessary t o  demagnetize the  tungsten sphere 
a f t e r  i n se r t ion  i n  the sample tube. 
Newtonian Behavior of the  Labyrinthine Fluids  
The v iscos i ty  of human endolymph was measured by the vis-  
cometer using two d i f fe ren t  angles of i nc l ina t ion  of the  plane 
of r o l l i n g  (20' and 35O). 
d i d  not vary appreciably with the angle of  tilt even though the 
terminal veloci ty  of the sphere was near ly  doubled. Similarly,  
It was found t h a t  t he  v i s c o s i t i e s  
6.  
c 
c 
measurements indicate  that when the sealed sample was l e f t  t o  
s e t  without disturbance for  one day, and one week, there  i s  
no measurable change i n  v iscos i ty  within the 2% accuracy l i m i -  
t a t i o n  of the instrument. Thus, it appears that  the f l u i d s  
do not change v iscos i ty  with " s e t t i n g  time" or  increasing 
shear rates, and can therefore  be considered as Newtonian 
Fluids .  To f'urther substant ia te  t h i s  claim, the chemical 
ana lys i s  of endolymph shows a low pro t ien  content whereas the 
non-Newtonian o r  shear thinning" f lu ids ,  such as glycer ine,  
have a high pro t ien  content. 
11 
. 
c 
7. 
11. VERIFICATION OF THE MODEL OF CALORIC STIMULATION 
U t i l i z i n g  t he  thermal lag model f o r  ca lo r i c  st imulation, 
as presented i n  MV-66-2 i t  can be shown that 
P-' 1 
G C ( t )  = A Ti 1 
s ( s  + - ) ( s  + $ ) ( s  + A  ) 
73 1 2 ? 
where 
ec(t) = time h i s to ry  of cupular displacement due t o  
a s t ep  input of ca lo r i c  i r r i g a t i o n  
c 
z = 25 sec. = thermal l a g  coe f f i c i en t  
z 
1 
2 = 10 sec. = l ong  time constant of l a t e r a l  canal 
= .1 sec. = shor t  time constant of l a t e r a l  canal *3 
A = system constant 
Ti = +,empera$ure above normal body temperature. 
After expansion of the above equation and a f t e r  performance 
of the  Inverse Laplace Transformation: 
1 4 / 7 3  T32 e - 
8. . 
If one attempts to fit 8 (t) by a power expansion in powers 
of t of the form: 
Bn n = Bo + Blt + B2 t 2 + . . .  firt %) 
it turns out that 
Bo = B1 = B2 = 0 
B3 = 1 
1 + -  - 1 1 
2 *3 B 4 - 5  + -  7
1 1 1 - - + - + -  
'2 *3 '1 *3 
Because of the presence of the short time constant, the poly- 
nomial requires many terms to approximate caloric responses 
since the polynomial coefficients attempt to fit the initial 
part of the response. Therefore, it is more suitable to 
evaluate Q(t) vs. t numerically. 
Ignoring the presence of the short time constant of the 
canal is a simplification that can readily be justified be- 
cause of the long delay of the thermal lag. 
9. 
Then 
(2) 
\p -' 
7 = 25 sec. 
T = 10 sec,  
1 
2 
c 
K T  f ( t )  
Figure 1 shows the  function f ( t )  as computed from both (1)  and 
(2)  f o r  a u n i t  s tep  input, f o r  the  time i n t e r v a l  0 t o  75 sec- 
onds. There i s  l i t t l e  difference i n  t h e  two computed functions; 
the  maximum difference between them is  within the  thickness of 
t he  l i n e  on the curve. 
It should now be possible t o  show, analogous t o  the 
Muelder product," that  the la tency time t o  t he  onset of cal-  11 
o r i c  nystagmus follows the re la t ionship ,  he rea f t e r  r e fe r r ed  
t o  as the  "Caloric Latency Product:'' 
10 . 
f(zL) Ti = C = constant. 
I n  f igure 2, f (TL)  Ti is plotted f o r  several  values of C. 
To t h i s  end, a sequence of experiments i s  current ly  
being conducted t o  measure the latency time t o  the onset of 
ocular nystagmus f o r  calor ic  i r r iga t ion  a t  various temperatures. 
. 
11. 
111. FLUID DYNAMIC ANALYSIS OF THE CUPULA-ENDOLYMPH SYSTEM 
t 
J 
The primary expenditure of effort on the problem of fluid 
dynamic analysis of the semicircular canal system has been 
toward the solution of the Navier-Stokes equations in closed 
form under the assumptions of laminar flow of a Newtonian 
Fluid in an inflexible tube when subjected to angular accelera- 
tions. From the results of our measurements of the labyrin- 
thine fluids it is clear that the assumptions of a Newtonian 
Fluid undergoing laminar flow are indeed valid. 
of the assumption of a "rigid" tube is questioned by some 
researchers, however, Since the measured densities of endo- 
lymph and perilymph are very nearly identical, the canal system 
must be very nearly neutrally buoyant and thus not appreciably 
distended by the application of linear or angular accelera- 
tions. 
The validity 
Although the Navier-Stokes equations are simple in form, 
they are difficult to apply in practice. 
analysis it is expedient to use a conformal mapping technique 
to expand the closed circular tube into an infinitely long 
straight tube of radius r and to solve the Navier-Stokes equa- 
tions in cylindrical coordinates, rather than in spherical 
coordinates. The transformation can later be inverted if 
necessary. 
For preliminary 
To further justify such a temporary simplification, 
12. 
c 
t h e  r a t i o  of rad i i  o f  the  torus  of the semicircular canal i s  
20 t o  1 and thus the " t h i n  ring" approximations a r e  very 
appl icable  (see f igure  3 ) .  
The equation t o  be solved i n  cy l ind r i ca l  coordinates can 
be reduced t o  the form 
where 
#A = viscos i ty  
fu = kinematic v iscos i ty  a ( t )  = angular acce lera t ion  
a,(t)  = a ( t ) R  
R = long rad ius  o f  torus  v ( r , t ) =  veloci ty  of f l u i d  
r = rad ius  of to rus  duct P ( t , t ) =  pressure i n  f l u i d  
t = time -4 = length along duct 
subJect t o  the boundary condition 
If the  cupular damping term i s  ignored, then the  so lu t ion  of 
(3)  f o r  a z ( t )  = -4c i s  ( c  i s  a constant)  
13. 
1 
Since cupular displacement is  proport ional  t o  the i n t e g r a l  of 
the flow through the tube it i s  convenient t o  evaluate  the 
average of v ( r , t )  over the crossect ion of the tube. Then: 
where hi 's  are the  solut ions of the  'zero '  order  Bessel 
function, Jo(hia) = 0. 
Further  consideration of (3) by inclusion of the cupular 
damping term leads t o  the r e s u l t s  that  the dynamic behavior 
of the semicircular  canals can i n  f a c t  be described by a 
t r a n s f e r  funct ion i n  the form: 
Ai 
U ( s )  = 1 s 2 + 2Ii wi s + wi 2 
i=1 
Note tha t  t h i s  ana ly t ica l  model i s  of the form measured ex- 
perimentally. The evaluation of the constants Ai, f i J  and 
i s  being worked on a t  t h e  present  time. T h i s  i s  d i f f i c u l t  wi 
because of problems i n  calculat ing the cupular def lec t ion  
I1 spr ing  constant.  It 
Analysis of "Flexible  Canals'' 
Nystagmus i n  the presence of counter-rotating motion 
poses the question of whether o r  not the semicircular  canals, 
because of t h e i r  f l e x i b i l i t y ,  are subject  t o  exc i t a t ion  by 
14. 
I 
counter-rotating motion. It is shown by the simple counter- 
rotation of a glass filled with liquid that a circulation 
(y) in the fluid can be induced by counter-rotation. 
can be shown qualitatively to be the result of' the free 
surface of the fluid, and that it is a result of the initial 
transient of  the motion (the start of the counter-rotation 
motion) . 
This 
The semicircular canals are being analyzed to determine 
whether their flexibility can allow a circulation in the 
presence of counter-rotating motion. It is anticipated that 
this work will be completed in the first half of  1967. 
. 
a 
15 
IV. ROTATING CHAIR SIMULATOR 
A ro t a t ing  cha i r  simulator has been designed and i s  
cur ren t ly  being constructed t o  be used i n  various experiments 
inves t iga t ing  the human vest ibular  system. The chair  port ion 
w i l l  be an e n t i r e l y  enclosed module i n  which the subject  w i l l  
s i t  upright seeing no outs ide reference,  h i s  head supported 
by a head r e s t ,  and h i s  mouth f ixed t o  a b i t e  board H e  w i l l  
be wearing photoreceptor goggles t o  monitor eye nystagmus o r  
he w i l l  manipulate a joyst ick o r  both. His head w i l l  be posi-  
t ioned above the axis of rotat ion.  
The chair  w i l l  be powered by two 7-l/2 f t - lb .  torque 
motors connected d i r e c t l y  t o  the shaft of the chair .  They 
w i l l  be dr iven by an amplifi2r i n  such a manner as t o  develop 
a maximum of 15 ft- lbs.  of torque. T h i s  amount of ava i lab le  
torque w i l l  allow t'ne chaii? t o  be driven w i t h  a s inusoidal  
acce lera t ion  whose peak ranges from 10 degrees/sec2 t o  100 
degrees/sec2 a t  any frequency i n  the  range .01 cps t o  1 cps. 
During closed loop operation, a simple pos i t ion  feedback 
w i l l  be used employing a 15 turn,  20 K potentiometer. The 
potentiometer has been geared so  t ha t  a maximum of  42 revolu- 
t i o n s  of the  cha i r  is  possible  i n  a closed loop operation. I n  
open loop, the number i s  unlimited, and the  chair  can be opera- 
ted  a t  constant veloci ty  o r  accelerat ion.  The r o t a t i n g  chair  
simulator i s  expected t o  be completed dur ing  the f irst  par t  
of 1967. 
16 . 
V. PUBLICATIONS 
. 
The following two papers were presented at the Third 
Symposium on the Role of the Vestibular Organs in Space Ex- 
ploration held in Pensacola, Florida, January 23-27, 1967: 
Physical Properties of the Labyrinthine Fluids 
and Quantification of the Phenomenon 
of Caloric Stimulation 
Robert W. Steer, Jr. Laurence R. Young 
Yao T. Li Jacob L. Meiry 
Abstract 
The physical properties of endolymph and perilymph 
(viscosity, density, thermal coefficient of viscoslty, and 
coefficient of thermal expansion) which are pertinent to the 
quantification of the dynamic behavior of the human vestibu- 
lar sensors have been evaluated. Descriptions and error 
analyses of the instruments used for the measurements are 
presented. 
The phenomenon of caloric stimulation of the semicir- 
cular canals is described quantitatively, and a dynamic model 
is presented. To verify the proposed model, the human's re- 
sponse to caloric stirnulation is compared to his response to 
angular acceleration stimulation. 
17. 
A REVISED DYNAMIC OTOLITH MODEL 
Laurence R. Young and Jacob L. Meiry 
Abstract 
The basic dynamic otolith model of Meiry was based on 
observed relations between perceived direction of linear motion 
and input acceleration. Although this model correctly predic- 
ted phase of perceived velocity for lateral oscillation and 
time to detect motion under constant acceleration, it failed 
to account for at least two observations: 
i ) Behavioral and electrophysiological data indicate 
a sustained steady otolith output to sustained tilt angle. 
The model's perceived acceleration or tilt output decayed to 
zero with a time constant of 10 seconds. 
il) Dynamic counterrolling data agree with the model 
at higher frequencies. The experimental counterrolling at 
zero frequency, however, Indicates a static component of 
otolith output with no phase l a g  referred to acceleration; 
whereas the model had no static output and approached 90 
degrees of lead at zero frequency. 
At the suggestion of Dr. H. Von Gierke, a static com- 
ponent was included in the otolith model. The revised linear 
model, which allows steady state response to acceleration, 
is shown in Fig. 1. 
This revised linear model will act approximately as a 
velocity transducer over the mid-frequency range (O.lg<u, (1.5 
rad/sec.). 
perceived tilt or lateral acceleration has a static sensi- 
tivity of 0.4. 
The transfer function from specific force to 
0 
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0 
u < 89 
0 
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64 
k m  
1-10 
0 0  
c u m  
0 u 
. 
f 
1 
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2 
I I 
3 4 
TEMPERATURE 
Figure 1 
Calculated normalized cupular response ( f ( t ) )  as a function of time 
J 
4 
PREDICTED LATENCY TIME 
c 
. 
I I I I I I I I I I 
h 0 n c) CI c 9 e ? ? 
L. - c 
Y r 
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n 
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k 
E-l 
k 
0 
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rl 
PI 
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d 
* 
Figure 3 
Simplified Rigid Model of 
Semicircular Canal 


Biophysical evaluation of the human vestibular system Semiannual status report, 1 Jul. - 31 Dec. 1966

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