2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
The biological reactions of Paramecium in the different ultrasonic frequencies
exposed
Yi-Cheng Huang
Department of Mechanical Engineering, Cheng Shiu University
E-mail: huang@csu.edu.tw
(NSC 95-2221-E-230-005)
dynamic, Paramecium
Abstract
1. Introduction
The effects of ultrasonic irradiation at different
frequencies, i.e. 0.5, 1, and 2.25 MHz, on the activation
The use of ultrasound in the biological or medical
of the single cell creature biological reaction have been
application has been a subject of research and
investigated. The ability shown by ultrasound in
development for many years. Under appropriate
promoting and/or accelerating many reactions has been
conditions, ultrasound can produce profound biological
shown to be a useful field. In this paper, it is necessary
effects through its action on specific tissues. The
to ascertain an appropriate frequency value of
interactions
ultrasound, capable of driving an obviously biological
mammalian tissues
reaction; thus, the oscillation of the cells in response to
investigation of growth and structural alterations. The
the
using
lower or higher order animals, much interest has arisen
Rayleigh-Plesset’s bubble activation theory and the
in regarding the ultrasound induced biological effects,
numerical analysis. According to the simulation, the
which have demonstrated the potential both to damage
resonant frequency of the Paramecium vacuole is
and/or stimulate tissues. Reporting on the effects of
among 0.54 ~ 1.24 MHz. In the experiments, the
ultrasound on Paramecium, Yang noted that the
resonant (1 MHz), approach the resonant (0.5 MHz) and
maximum relative growth rate was increasing 18% with
non-resonant (2.25 MHz) frequencies of various
1MHz ultrasound exposure under certain conditions [1].
intensities were employed.
Thus, by careful regulation of the acoustic parameters,
ultrasound
radiation
is
simulated
between
ultrasonic
have
frequencies
and
been reported on the
The samples irradiated from different frequencies
the damaged or beneficial results could be available.
of ultrasound are likely to cause the changes of the cell
The acoustic parameters are including the frequency,
proliferation. When the 1 MHz frequencies of lower
intensity, waveform or exposure time and so on. This
intensities of ultrasound was irradiated in the samples,
paper is to seek the correlation between ultrasonic
the cell numbers was higher than that of exposed to the
frequencies exposure and the Paramecium biological
other frequencies. For the non-resonant frequency
reaction, as an indication of fundamental interactions
ultrasound exposure, the increase or decrease of cell
between
proliferation was observed which did not depend upon
suspensions.
the irradiated intensity range in the experiments.
Keywords: ultrasound, biological effects, bubble
the
acoustic
parameters
and
cells
in
The most important approach to the study of
bioeffects of physical agents is the mechanistic one. For
2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
ultrasound, this approach leads to consideration of
non-viable cells into the medium during the first 24
thermal and nonthermal mechanisms. The thermal
hours.
mechanism involves the conversion of ultrasonic energy
The purpose of this study is then to explore the
into heat, and the resulting elevated temperatures cause
relationship between the ultrasonic frequencies and the
the harmful bioeffects. Nonthermal mechanisms depend
activation of the Paramecium cells at its growth
on whether or not the cavitation phenomenon occurs.
condition. The Paramecium, which possesses many
Cavitation can be defined as the interaction between the
features typical of higher-order animal cells, is an
ultrasonic field and the gas filled structure in the
appropriate choice for this study. The vacuole
medium. For convenience, cavitation may include the
organelles of the specific structure of Paramecium are
two types: (1) gas body activation (or stable cavitation)
the subjects to study the resonant effects in ultrasonic
and (2) inertial cavitation (or transient cavitation) [2].
system. Additionally, cells in vitro can be exposed to a
Gas body activation only requires a lower level of
carefully setup of ultrasonic field under conditions
ultrasound intensity to activate a pre-existing gas body.
which minimize thermal effects and enhance the
The gas body may be supported by the cellular
nonthermal mechanisms of action. In this study, the
structures. Inertial cavitation needs a higher ultrasound
physical theory for the oscillation of the bubble mode in
intensity to induce the microbubble.
response to the ultrasound radiation is adapted from
Cell suspensions have been used in many studies
Rayleigh-Plesset’s bubble activation theory [7] and is
of the mechanisms of ultrasound on the cells and their
compared to the numerical analysis results. This theory
components [3-4]. The cell suspension systems offer
can calculate the resonant frequency of the bubbles in
many advantages, including considerable control of
the liquid medium. However, the stable cavitation does
environmental, biological and exposure parameters.
not exist in most cell structure. It still raises a question:
Coakley and Hampton [5] used the 1 MHz ultrasound to
Is it possible that the bubble-like structure can be
irradiate the suspension of amoeba. It possesses many
activated in the resonant frequency of ultrasonic fields?
features typical of higher-order animal cells. The
To find out the evidence is the main objective in this
samples were irradiated the ultrasound at 515 W/cm2 for
paper. Though the target organelle: the contractile
10 minutes. The cavitations produced by ultrasound
vacuoles of the Paramecium do not match the
were found the correlation between the number of
assumptions
cavitations occurring and the decrease in cell numbers.
completely (the contractile vacuoles are not filled with
Kaufman and Miller [6] used the continuous ultrasound
air totally). It can provide an initial direction to study
of 1 MHz and the axial intensity of 2.5 W/cm2 to expose
the resonant biological effects of the ultrasound in the
the suspensions of Chinese hamster V-79 cells for 1
particular organelles of the cell structure. Studies of this
minute. They found that the attached cells were little
kind are likely to provide new insights in the resonant
increased in the cell growth rate for 24 hours after
effects of the cells. Based on the dimensions of the
sonication. Then the cell numbers will return to normal
vacuoles, the theoretical resonant frequencies of the
growth approximately 36 hours after sonication. The
vacuoles can be calculated. According to the theoretical
cell growth would slow down due to an approximate
solution, the exposure frequency of the ultrasound can
balance between proliferation of viable cells and loss of
divide into two parts; that is, resonant and non-resonant
of
the
Rayleigh-Plesset’s
theory
2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
frequencies. There are three different ultrasonic
the effects of ultrasonic irradiation at different
transducers were employed in the experiment, which
frequencies and intensities on the activation of bubbles
were operated at central frequencies of 0.5, 1, and 2.25
are the important factors to induce a change of inside
MHz, respectively.
the cells. The basic dynamical problem of the activation
Throughout the above-mentioned review, effects
of bubbles is to determine the fluid medium system,
of ultrasound on creatures have been reported for the
together with the motion of bubble wall (the bubbles’
most part. Not only the exposure frequency of
field), when under the influence of an acoustic pressure
ultrasound, but the intensity is an important factor to
(the acoustic field) [7].
induce the bioeffects. It must be realized that by careful
The liquid medium is only one phase present and
regulation of the ultrasonic intensity, the inhibitive or
the liquid can be characterized by physical parameters,
beneficial bioeffects could be available. In the
such as temperature (T), viscosity (η), density (ρ) and
experiments, each of the ultrasonic transducers was
surface tension (σ), etc. The acoustic field comprised
operated at several intensities varied from 0 to 0.5
of acoustic waves traveling through the liquid medium,
mW/cm2 (SPTP). The cell proliferation analysis was
and it can be characterized by the frequency f = ω/2π
used as a model to discuss the biological effect of
and by the pressure P = PAsinωt where PA is the peak
ultrasound. The growth conditions for each of the
acoustic pressure amplitude value. The bubbles’ field
populations
constitutes the population of gas filled cavities. A
examined
are
described
predictions
obtained by the resonant theory.
physical description of such cavities can be achieved by
taking into account their volume, and the parameters of
2. Theory
their fluid content; i.e., the pressure, density and the
The low amplitude oscillations of bubbles were
politropic ratio γ of the gas.
able to characterization by linear resonance theory of
The acoustic wave traveling through the medium
simplified model system. The model describes the low
will induce the bubbles that will pulsate with a radial
amplitude pulsation of free spherical bubbles as
motion of their walls. The bubble’s wall motion can be
discussed by Coakley and Nyborg [8]. Since the bubble
described by the Rayleigh-Plesset equation:
activation is typically studied under low power
oscillation conditions, the relatively simple linear theory
is adequate for analyzing most experimental results.
 
RR
3 2 1
2 R 0 3 2 4R
R  [( P0 
)( ) 

 P ]
2

R0 R
R
R
(1)
Where R0 is the bubbles’ radius at equilibrium, P 0
A reasonable definition of bubble dynamics is: the
is the gas pressure above the surface of the liquid and
induction and maintenance of oscillation by the
the P∞ is the pressure in the liquid far from the bubble.
interaction of an ultrasonic field with stabilized volumes
By using the suitable approximations, for example,
in a liquid. The oscillations are often associated more
substituting R = R0 + r, where r/R0 > 1, expanding in
with the structure than with the pulsation of the bubbles.
powers of 1/R0 and retaining only the first-order terms,
This relationship needs to study carefully what effects
Equation (1) can reduce to the more concise form:
would appear in the surroundings of the activated
bubbles,
including
the
quantitative
comparisons
between theory and experimental results. In this study,
r   r2 r 
PA
R0
sin  t
.
Where the resonant frequency
(2)
r,
under the
2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
undamped linear oscillations, is given by:
( r ) 2 
raised the following question: Whether the ultrasound
1
2
2
[3 ( P0 
)
]
2
R0
R0
R0 .
induce the resonant effects in the cavitation-like
(3)
structure. The objective of this paper is to investigate
The eigen-frequency of this equation is similar to
the
biological
effects
of
growth
conditions
of
that referring to a linear oscillation system under an
Paramecium in a cavitation-like cell structure induced
impressed sinusoidal pressure. If one considers the
by the ultrasound. For the theoretical results, as this
viscous forces of the bubble surface, the resonant
phenomenon can be considered as a form of biological
frequency becomes
catalysis, it can be used to accelerate the cell division
 2

2
( r ) 2   r   
2
 R0
2



 .
and induce a activation reaction, and to ensure assuring
maximum efficiency. This work was to demonstrate the
(4)
If a bubble of equilibrium radius R0 is submitted
relationship between the theoretical vacuole oscillation
to an acoustic field, its wall will pulsate steadily with
system and the activation reaction of Paramecium cell
the same frequency of the driving field. As this
growth.
frequency approaches the eigen-frequency ω
γ
,
resonant effects would occur. In this research, the
physical
parameters
are
measured
such
as
the
temperature T = 20.0 ℃, the politropic ratio γ = 1.4,
the surface tension σ = 1.63~2.57 × 104 dyn/cm, the
density of the liquid ρ= 0.99821g/cm3 , the hydrostatic
pressure P0 = 760 torr, and the viscosity factor η=
1.002 × 10-2 g/cm•s. By using the values of above
parameters, the resonant frequency of Paramecium can
be obtained. The resonant frequency may be calculated
and falls into the range of 0.54 ~ 1.24 MHz for the
Figure 1. The numerical analysis of the Paramecium
cells by using the ANSYS software.
vacuole radius R0 of the Paramecium in the range of
3~7 μm. The contractile vacuoles of Paramecium are
composed of pools of distinct membranes which are
associated sequentially in space. Compared to the the
theoretical results, the numerical analysis is used the
ANSYS software to calculate the resonant frequencies.
The model of the contractile vacuoles are illustrated in
the Figure 1. The resonant frequency can be calculated
and falls into the range of 0.24 ~ 1.45 MHz. Unlike the
spherical bubble mode, the contractile vacuole is filled
with fluid more than air. However, the contractile
vacuoles are the observed and stable structure inside the
cell, it can be treated as a cavitation-like model. It also
3. Methods
Cell culture and proliferation
The cell types used in the experiments were
Paramecium samples. The cells were grown in
suspension using distilled water supplemented with
essential medium. They were cultured in the incubator
at 28 ± 0.1℃ and were harvested for approximately 7
days before they could be collected for experimental use.
The cell suspensions were diluted by the addition of
growth medium to yield cell densities of 0.15 × 103
cells/ml. From this moment, the samples would transfer
2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
to the exposure chamber with 5 ml volumes. The
visible positioning system, with the beam directed
exposure chamber consisted of a cylindrical shape hole
horizontally from one end of the tank toward an
at the center. A 2 mm thick plastic plate sealed the front
absorptive material which covered the far end. The
and the back of the chamber. Following the transfer of
Neoprene, used as a wave absorber was placed in the
the samples to the exposure chamber, the suspensions
tank opposite the transducer to minimize reflections.
were then used directly in the experiments. In the
Three different narrow band transducers (Panametrics)
exposure duration, the variation of the temperature in
were employed for this study, which were operated at
the chamber was detected and maintained at the range
frequencies of 0.5, 1, and 2.25 MHz.
of ±0.1℃; therefore, the thermal mechanisms would
The light microscope fitted with a digital video
not appear in the experiments. After exposure, the cells
camera was compatible of taking the static state and the
were maintained in the same chamber to prevent the
movement picture. The acoustic fields were measured
environment change of the cell culture.
with a bilaminar polyvinylidene fluoride (PVDF)
A light microscope fitted with a graticule eyepiece
hydrophone (Miniature PVDF Ultrasonic Hydrophone
was used to measure the cell numbers. Relative growth
Probe MH28-10). The intensity at the position of the
number is defined as the ratio of the cell numbers of
sample chamber was obtained by measuring in a plane
irradiated samples to the numbers of control samples.
perpendicular to the axis of the beam. The sample
Counts of the numbers of control samples and the
chamber was placed near the transition zone away from
numbers of irradiated samples were made before and
the near field region of the beam. The function
after the ultrasonic exposure. Sampling mode was
generator was a HP 33120A unit, produced by Hewlett
among the ten randomly selected regions of each
Packard. This apparatus can be set to work with
chamber. Each region was obtained a volume of
arbitrary waveform.
approximately 5 μl. The sampling rate is defined as the
In the experiments, the exposure intensities are
ratio of the sampling volume of the cell suspension to
important for understanding the bioeffects of ultrasound.
the total volume of the cell suspension in the chamber.
Figure 3 shows the flow chart of the experimental
In the experiment, the sampling rate was about 0.016.
procedure. The waveform in this experimental series
To find out the conditions of cell proliferation of each
was set to the tone pulse mode, pulsing 1:1. The pulse
period in the chamber, the chamber was set to culture in
repetition frequency of each pulse was 25 kHz.
incubator at the temperature 28 ± 0.1℃, the humidity
Treatments were of 5 minutes exposure duration and
was about 70 %.
were given one time. After irradiation for one hour, the
Instrumentation
number of the Paramecium cells in the treated and
The sonications were carried out in a water-filled
control samples were counted. In addition, the
tank. An exposure system comprised of ultrasound
controlled and treated cells would be re-incubated up to
transducer operating in alternating pulses was devised,
12 hr. The next counting procedure was at 12 hr (the
and is illustrated in Figure 2. In Figure 2, the exposure
double time of the Paramecium was about 11.22 hr)
chamber was constructed from thin wall plastic
after exposed. In the experiments, the different
containers. The ultrasound transducers and the loaded
intensities of ultrasound were used to expose the
sample chambers were mounted and positioned on a
samples and the change of the relative growth number
2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
was observed. The observation of the experiments can
illustrated in Figures 4 ~ 6. The cell number is defined
define the relationship between the cell proliferation and
as the ratio of the cell numbers of the treated samples to
the irradiated frequency. For a given frequency,
that of the control samples. All the results are reported
exposures of the Paramecium were made over a range
as the arithmetic mean + standard deviation of the mean.
of intensities spanning 0 to 0.5 mW/cm2. The power
The uncertainty for each point is shown by the vertical
amplifier (Amplifier Research 25A250A) was used to
bars in all figures. To further observe the long-term
generate the transducer output intensities of 0.1, 2, 4, 6
effect of ultrasound, the cell numbers were counted in 1
and 8 levels. Nevertheless, the cell counting method was
and 12 hours after exposure.
checked by comparing pairs of counts from the three
containers
operated
at
the
same
procedures.
camera
The
samples
after
irradiated
at
different
frequencies or exposure intensities in the culture
containers are shown as a relative cell number and
illustrated in Figures 4 ~ 6. All the results are reported
PVDF
hydrophone
PC
as the arithmetic mean + standard deviation of the mean.
The uncertainty for each point is shown by the vertical
Cell
Samples
microscope
bars in all figures. To further observe the long-term
ultrasonic
transducer
effect of ultrasound, the cell numbers were counted in 1
and 12 hours after exposure.
water tank
absorptive material
Figure 4 shows the cell number of the
Paramecium cells after irradiated at 0.5 MHz frequency
oscilloscope
function generator
power amplifier
of ultrasound. It should be noted that the range of
Figure 2. Schematic diagram of the isonation and
resonant frequency was from 0.54 to 1.24 MHz (the
measurement apparatus used.
theoretical result is about 0.24 ~ 1.45 MHz); therefore,
chosen
exposure
intensity
controlled
samples
the irradiation frequency of 0.5 MHz was approached to
the resonant range. For the case of one hour after
treated
samples
exposure, it was observed that as the intensity increased,
sham
exposure
the harmful or beneficial effects were not apparently
5 minutes
exposure
1 hr incubate
1 hr incubate
occurred. As can be seen in the figure, the cell numbers
appear to change slowly after 1 hour ultrasonic exposed.
count the cells
The exposed cell numbers is lower than the control cells
12 hr incubate
count the cells
in the period. It seems that irradiating at 0.5 MHz
Figure 3. The flow chart of the experiment used to study
frequency and increasing the intensities to 0.5 mW/cm2
the ultrasonic biological effects.
would not reveal any greater variation in the cell
proliferation. The inhibition effects are slightly better
4. Results and discussion
The
samples
after
irradiated
at
than that of the increase effects. The other result in this
different
figure is the cell numbers measured for approximately
frequencies or exposure intensities in the culture
12 hr after exposure. As noted in the figure, the cell
containers are shown as a relative cell number and
numbers for 12 hr after exposure was better than the
2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
control cells (except the level 0.1 and 2, the difference
frequency. Twelve hours later after exposure, the trend
at the other levels are almost double than the control
of the cell proliferation was not reveal at all exposure
cells). It is obviously that the cell creature has the
level. In view of the above fact, it is clear that the
capability to maintain the cell density to a certain degree
Paramecium cells were not sensitive to ultrasound
in the suspension. If the cell numbers were influenced
exposure at non-resonant frequencies.
by external factor, the cell growth would return to
exposure frequency 0.5 MHz
normal growth situation approximately 12 hr after
Kaufman and Miller’s works [6].
The cell suspensions irradiated by 1 MHz
ultrasound with different intensity levels are shown in
cell numbers(*1000)
10
sonication. The same results are reported in the
8
6
1hr after exposure
4
12hr after exposure
2
0
control
Figure 5. This frequency is in the range of theoretical
0.1
2
4
6
8
power amplifer output level
resonant frequency. It can be seen that the relative cell
numbers appear apparently variation. The maximum cell
Figure 4. Paramecium cell numbers as a function of the
number is at level 8 of the power amplifier output. It
exposure intensity, by presenting the data for the
means that the treated cells were increased almost four
frequency of 0.5 MHz. Error bars represent the standard
times than the controlled cells. It seems possible that the
errors of the means.
resonant effects might occur in the living cells. If the
exposure frequency 1MHz
exposure intensity of the resonant frequency was fall in
10
and increase the proliferation. It should be noted that the
results of 12 hr after exposure from Figure 5 was
different to that of the results shown in Figure 4. The
cell numbers between the results of 12 hr are smaller
than that of the results of 1 hr. It is possible that the
cell numbers(*1000)
this intensity range, the cell division would rise rapidly
8
6
1hr after exposure
4
12hr after exposure
2
0
control
0.1
2
4
6
8
power amplifier output level
proliferation of Paramecium cell was apparently
increased after 1 hr in the experiment. The density of
Figure 5. Paramecium cell numbers as a function of the
cell suspension was increased rapidly. Thus, the cell
exposure intensity, by presenting the data for the
growth would slow down due to an approximate balance
frequency of 1 MHz.
between proliferation of viable cells and loss of
non-viable cells during the first 12 hours.
The cell numbers of exposed to 2.25 MHz
ultrasonic frequency are presented in Figure 6. It was
observed that the cell numbers at all exposure levels are
lower than control cells; however, the difference was
not apparently. It means that the inhibitive effects of
ultrasonic irradiation were not apparently at higher
2010 International Symposium on Mechatronic and Biomedical Engineering & Applications
2010 年機電&醫學工程與應用國際研討會
Cheng Shiu University, Kaohsiung, Taiwan
正修科技大學 臺灣、高雄 2010/11/09
gratefully acknowledged.
exposure frequency 2.25MHz
cell numbers(*1000)
10
References
8
[1] S.K. Yang and Y.C. Huang, Biological Effect of
6
1hr after exposure
12hr after exposure
4
Paramecium
in
Diffused
Ultrasonic
Fields,
Ultrasonics 39 (2002) 525-531.
2
[2] M.W. Miller, D.L. Miller and A.A. Brayman, A
0
control
0.1
2
4
6
8
Review of in Vitro Bioeffects of Inertial Ultrasonic
power amplifer output level
Cavitation
from
a
Mechanistic
Perspective,
Figure 6. Paramecium cell numbers as a function of the
Ultrasound in Med. & Biol 22(9) (1996) 1131-1154
exposure intensity, by presenting the data for the
[3] Miller D.L., Bao S. and Morris J. E., Sonoporation
frequency of 2.25 MHz.
of Cultured Cells in the Rotation Tube Exposure
System, Ultrasound in Med. & Biol. 25(1) (1999)
143-149
5. Conclusion
[4] Böhm H., Anthony P., Davey M.R., Briarty L.G.,
In this study, it is assumed that the growth
Power J.B., Lowe K.C., Benes E. and Gröschl M.,
conditions for any frequency represents a stable
Viability of Plant Cell Suspensions Exposed to
activation, thus the cell growth would be enhanced or
inhibited apparently at the resonant frequency range. If
the irradiated frequencies were not in the resonant range,
the cell growth would be less active. Comparing the
theoretical mode and the experimental results, the data
is generally similar to the theoretically expected form.
The maximum cell growth numbers correspond to the
expected resonant frequencies of the vacuole, and the
cell number appeared no significant difference outside
the resonant range. The theory for the oscillation of the
cell organelles is therefore a useful guide in predicting
the
most
efficiency
sonication
frequencies,
and
Homogeneous
Ultrasonic
Fields
of
Different
Energy Density and Wave Type, Ultrasonics 38(1-8)
(2000) 629-632
[5] Coakley W.T. and Hampton D., Quantitative
relationships between ultrasonic cavitation and
effects upon Amoebae at 1MHz, J. Acoust. Soc. Am.
50 (1971) 1546-1553
[6] Kaufman G.E. and Miller M.W., Growth retardation
in Chinese Hamster V-79 cells exposed to 1 MHz
ultrasound, Ultrasound in Med. & Biol. 4 (1978)
139-144
presumably for other unicellular creature. It appeared
[7] Cum G., Galli G., Gallo R., and Spadaro A., Role of
the possibility to elucidate the complex etiology of the
frequency in the ultrasonic activation of chemical
effects of ultrasound on Paramecium.
reactions, Ultrasonics 30 (1992) 267-270
[8] Coakley W.T., Nyborg W.L., Cavitation: Dynamics
of Gas Bubbles; Application. Ultrasound: Its
Acknowledgement
The financial support by the National Science
Council, Republic of China, through Grant NSC
95-2221-E-230-005 of the Cheng Shiu University is
Applications in Medicine and Biology, Fry F.J.
Editor, Elsevier, New York (1978) 77-159