ANNALS OF EIOMEDICA.L ]ENGINEERING ~, 248--259 (1977)
Ciliary Activity by Laser Light-Scattering Spectroscopy ~ WYLIE I. LEE 2 AND PEDRO VERDUGO
Center for Bioengineering and Department of Biological structure, University of Washington, Seattle, Washington 98195 Received March 4, 1977 The frequency of ciliary beat was measured by laser light-scattering spectroscopy in cultures of ciliated cells of the rabbit oviduct. Measurements performed by this new method agree with those obtained by high speed cinematography. When beating cilia are illuminated by a laser beam, the scattered light shows a frequency modulation due to the oscillatory motion of cilia. The spectral structure of the scattered light depends on the frequency and time-space coherence of ciliary beat. This paper reports the experimental validation of this technique and the theoretical basis for obtaining the frequency and coherence of ciliary beat from the autocorrelation function of the spectrum of light scattered from moving cilia. Fiber optic light transmission could permit the extension of this method to assess ciliary activity in situ for applications in animM experimentation and clinical studies.
INTRODUCTION Cilia are hairlike contractile organelles that are found on some unieellulars and on the free epithelial surface of certain organs in metazoa. In many protozoa, cilia have an important function in locomotion. But in vertebrates, it is mostly related to transport of material. Mammalian ciliary epithelia perform an important function in both the respiratory and reproductory organs. In humans, for example, it is well recognized that an impairment of the inueoeiliary transport in the lung is a critical pathophysiologie element in chronic inflammatory diseases of the respiratory tract. Evidence has been published recently (Halbert, Tam, and Blandau, 1976) that strongly supports the idea that ciliary activity may play a most important role in transporting the egg through the Fallopian tube. However, despite the significance of their function, a simple, accurate, and reliable method to study the physiology of cilia has not been available. The earlier methods used to assess ciliary function were indirect. The ciliary activity was related to the transport of charcoal powder or seeds over eiliated cells (Sharpey, 1835) or to the rotation of spheres or a glass spindle which was suspended over the surface of ciliated cells (Englemann, 1868; 1877; Inehley, 1921). A direct method was first introduced by Martius in 1884, who used the stroboscope to measure the frequency of ciliary beat in the frog's pharynx. A i Supported by USPHS Grant HL 20192-01 and Contract N01 HD 3-2788. 2 Supported by Fellowship HL 05147-18 from USPHS. 248 Copyright ~ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN
0090-6964
CILIARY ACTIVITY BY LIGHT-SCATTERING
249
marked improvement over direct visual observation was made later by adding photography to the stroboscopic method (Lueas, 1931). In 1933, Proetz devised a microscopic apparatus to be used with a motion picture camera. To date, high speed cinematography combined with phase contrast microscopy has proved to be the most accurate method of measuring ciliary activity. However, it is expensive, time consuming, and does not permit on-line data analysis. The photometric monitoring method (Dalhamn and Rylander, 1962), which employs a photomultiplier or photodiode to detect light transilluminated through the eiliated specimens, permits on-line recording of ciliary activity. Unfortunately, this method is not reliable when the beating mode of cilia becomes asynehronie (Naitoh and Kaneko, 1973). In search of a simplier, yet reliable, method which would allow on-line monitoring of ciliary activity, we have developed a new application of laser light-scattering spectroscopy to measure the frequency of ciliary beat. The method is based on the analysis of the spectrum of light scattered from moving targets. When moving objects are illuminated by a laser beam, the spectral structure of scattered light depends on both the type and magnitude of movement of the effective scatterers. In this particular instance, the spectral analysis of the scattered light permits the direct detection of ciliary activity. This new technique allows precise on-line monitoring of the frequency and coherency of ciliary beat, thus providing convenient and quantitative method for characterizing ciliary activity. A short communication on this method, omitting its theoretical basis, was published by the present authors earlier (Lee and Verdugo, 1976). This paper reports the development, validation, and theoretical basis of the application of laser lightscattering spectroscopy to measure ciliary activity. THEOI~ETICAL ANALYSIS
A utocorrelation Function of Light Scattered from Beating Cilia Laser light-scattering has become, in recent years, a useful technique for the study of the hydrodynamics of polymers and biological macromolecules (Dubin et al., 1967; Ford, 1972; Berne and Pecora, 1976). It has also been applied to assess sperm motility (Berg~ et al., 1967) and to study bacterial movements (Nossal and Chen, 1971). The theory of laser light-scattering spectroscopy has been discussed in numerous reviews, most recently by Berne and Pecora (1976). The theoretical basis of this new application of laser light-scattering spectroscopy is presented to show that the frequency of ciliary beat can be evaluated from the spectrum of scattered light. Because the dimensions of cilia are about 0.2 pm in diameter and 10 to 100 ~m in length, which are large in comparison with the wavelength of laser light, the scattering of light from ciliated epithelium may be treated as in the case of scattering from rough surfaces (Beckmann and Spizzichino, 1963; Marathay et al., 1970). A schematic view of the laser light-scattering spectrometer is shown in Fig. I. A collimated laser beam is normally incident on the surface of the eiliated cells and the scattered light is detected at distances larger than the dimensions of the
250
LEE AND VERDUGO
NSITY
Z
BEAM PROFILE
R (r,~5 =o, Z) Z
FIG. 1. Geometry of light scattered fl'om ~he cultured cells of a ciliated epithelium. The incident laser beam, focused normally onto the cultures, is assumed to have a Gaussian intensity profile whose width is a. scattering region and the wavelength (Fraunhofer zone). The scattered electric field at the detector point R --- (r, ~' = 0, z) is (Jakeman, 1974)
Aoe-i'~~ Z ds' e-iklR-r'le-i~(r" t)e-"~l'~'
E~(R, t) =
(1)
where o:0 and h are the frequency and the w~vevector of the light, Ao is a constant which includes the amplitude of the incident light, a is the width of intensity profile of the laser beam, and 4)(r', t) is a r a n d o m l y fluctuating phase variable introduced by the surface of the epithelium. Since both the ciliary beat and the roughness of epithelial surface contribute to r t), we m a y separate ~ into two terms: one comes from periodic beating and the other from the r a n d o m phase of the surface, ~b(r', t) = wr + ~ ( r ' , t), (2) where ~ is the frequency of ciliary beat and ~b~(r', t) = hh describes the phase shift which is associated with the surface function h. The surface function will be given as h = h(r', t) and the mean level of the surface is the plane z = 0 (Beckmann and Spizzichino, 1963). E q u a t i o n (1) can be written in terms of the physical parameters shown in Fig. 2 as E~(R, t) =
Aoe-i('~176 -ikR Z ds'e-~k~' sin ~ cos r162
t)e--r'2/a2
(3)
b y using an approximation IR - V[ ~ [R[ -- r' sin0 cos ~b' in the far field. T h e autocorrelation function of the scattered field is defined as
G(~)(~) = (E*,(R, t + ~)E~(R, t)>, where
E*, is the
(~)
complex conjugate of E~. F r o m Eq. (3) we have
1
2
X e-(r'12+r'2~)l"2(e q~'(''l' t+~')-4,.0:'2, t)]).
(5)
251
CILIARY ACTIVITY BY LIGHT-SCATTERING
T h e angular brackets in Eqs. (4) and (5) indicate t h a t the quantities between the brackets are to be evaluated b y ensemble average. If we assume t h a t the surface function is Gaussian distributed such t h a t 1
~-~v:"'
p (h) = - (2~)~
(6)
and (h) = o,
(7)
t h e n the value of the ensemble average can be expressed as ( B e c k m a n n and Spizzichino, 1963; M a r a t h a y et al., 1970) (e i[r162
= e-k2~[I-C(',~)].
(8)
T h e variance a s describes the roughness of the surface and large a s corresponds to large roughness. C(s, .r) is the normalized autocorrelation function of h(r', t) t h a t gives the coherency between the r a n d o m values assumed b y h at two points separated b y a distance s = #1 -- r'2 + vr, where v is the relative velocity of these two points. We do not know the function C(s, "r), owing to the lack of complete knowledge of the ciliary motion. However, we m a y assume ( M a r a t h a y et al., 1970). C(s, r) --~ 1 - (s/}) ~, if/c2a2 ) ) 1, (9) where } is the correlation length. Points t h a t are s e p a r a t e d b y a distance larger t h a n } will be statistically independent. Therefore, Eq. (9) is meaningful only for s < } and r < TI, where rl is some correlation t i m e and has a m a g n i t u d e of the order of ~/v. W i t h o u t knowledge of a n y specific function a b o u t time dependence of C(s, r), we m a y a p p r o x i m a t e the expression in Eq. (9) as
C(s, r) ~ 1
~
p
(D
(lO)
e
/
f'_~_ .dffg~"-'
Z=0
FIG. 2. Surface of ciliated ceils is described by ~ function h(r', t) which is Guussian distributed with zero mean. k is a wave vector which represents the direction of the incident beam, r' is the distance of a point on the surface measured from the center of the beam.
LEE AND VERDUGO
252
with p(0) = 0. We can now write Eq. (5) as
G(1)(T) --- ~r2a21Aol%i(~~
-k~"(~)
uduJo(kU sin 0) x exp
-
+
--. / u 2
,
(11)
where J0 is the zero-order Bessel function, and u = r'~ - r'2. After the integration we have ~2--si-n~0- I . ~ l A01 ~ (12) G(~)(r) = 2 d4k2~2[ + a2 ~2 j Therefore, the amplitude of the autocorrelation function of the scattered electric field decreases exponentially as the scattering angle 0 increases. The function itself also decays in time; however, whether it will decay exponentially or decay as a Gaussian depends on the n a t u r e of the function p ( r / r s ) . If one observes in a time much shorter than the coherence time Ts then the r a n d o m motion of the surface appears as a free motion, where s ~ - (st) 2 ~md p ( r ) ~ (r/Ts) 2. The normalized autocorrelation function becomes g(1) (r) -
G(1)(r) G(1) (0)
- ei(~o+~o)~e-k2~2"2/~2z.
(13)
On the other hand, if one observes at a time longer t h a n the coherent time, the motion of the surface will appear as a diffusional motion, where s 2 --~ r, and p(r/r~.) ~ r/vs. We have g(1) = ei(~0+~o)re k2~2~/~s. (14) In either case, the roughness of the epithelial surface z 2 affects the decay time. In summary, we propose t h a t the light scattered by a ciliated epithelium can be treated as the scattering from a rough surface. We submit t h a t the m o v e m e n t of this surface can be approximately described as a superposition of two motions: first the periodic oscillations of the cilia with an average frequency ~ ; and second a random motion due to the metaehronal coordination of the clusters of cilia which m a y be characterized b y the coherence length } and coherence time vz. Consequently, the autocorrelation function of light scattered by cilia shows a frequency modulation due to the ciliary beat and a decay relaxation related to the time-space coherency or metachronal coordination of the ciliated epithelium. DESCRIPTION OF PROCEDURES
(a) Heterodyne Detection of the Frequency of Ciliary Beat The block diagram of the laser scattering spectrometer used in this experiment is shown in Fig. 3. The optical part of the spectrometer, which includes laser, mirrors, Rose chamber holder, lenses, aperture, and photomultiplier tube, are all
CILIARY ACTIVITY BY LIGHT-SCATTERING
L
ROSE CHAMBERII
253
I
M"ERATURd [ \ [
-%
CONTROL I
_jo2:22 sL,o .... OM,pCOVER
CORRELATION ANALYZER
ROSE CHAMBER
t
FIG. 3. Schematicdiagram of the laser spectrometer. The optical heterodyne mixingis achieved by collectingthe light scattered from cultured cells and the light scattered elastically at the glass slip (inset shows the components of the Rose chamber). carefully positioned and rigidly bolted on the surface of a vibration-isolated optical table (Modern Optics Model MSTT 12E). The laser beam of a He-Ne laser (Spectral Physics Model 125A) is attenuated and focused on the eiliated cells contained in a Rose chamber (see insert in Fig. 3). A neutral density filter with a 5-10% transmission is used to avoid saturation in the photodetector and/or overheating of the specimens. The beam size at the region of scattering is approximately (_
Ciliary Activity by Laser Light-Scattering Spectroscopy ~ WYLIE I. LEE 2 AND PEDRO VERDUGO
Center for Bioengineering and Department of Biological structure, University of Washington, Seattle, Washington 98195 Received March 4, 1977 The frequency of ciliary beat was measured by laser light-scattering spectroscopy in cultures of ciliated cells of the rabbit oviduct. Measurements performed by this new method agree with those obtained by high speed cinematography. When beating cilia are illuminated by a laser beam, the scattered light shows a frequency modulation due to the oscillatory motion of cilia. The spectral structure of the scattered light depends on the frequency and time-space coherence of ciliary beat. This paper reports the experimental validation of this technique and the theoretical basis for obtaining the frequency and coherence of ciliary beat from the autocorrelation function of the spectrum of light scattered from moving cilia. Fiber optic light transmission could permit the extension of this method to assess ciliary activity in situ for applications in animM experimentation and clinical studies.
INTRODUCTION Cilia are hairlike contractile organelles that are found on some unieellulars and on the free epithelial surface of certain organs in metazoa. In many protozoa, cilia have an important function in locomotion. But in vertebrates, it is mostly related to transport of material. Mammalian ciliary epithelia perform an important function in both the respiratory and reproductory organs. In humans, for example, it is well recognized that an impairment of the inueoeiliary transport in the lung is a critical pathophysiologie element in chronic inflammatory diseases of the respiratory tract. Evidence has been published recently (Halbert, Tam, and Blandau, 1976) that strongly supports the idea that ciliary activity may play a most important role in transporting the egg through the Fallopian tube. However, despite the significance of their function, a simple, accurate, and reliable method to study the physiology of cilia has not been available. The earlier methods used to assess ciliary function were indirect. The ciliary activity was related to the transport of charcoal powder or seeds over eiliated cells (Sharpey, 1835) or to the rotation of spheres or a glass spindle which was suspended over the surface of ciliated cells (Englemann, 1868; 1877; Inehley, 1921). A direct method was first introduced by Martius in 1884, who used the stroboscope to measure the frequency of ciliary beat in the frog's pharynx. A i Supported by USPHS Grant HL 20192-01 and Contract N01 HD 3-2788. 2 Supported by Fellowship HL 05147-18 from USPHS. 248 Copyright ~ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN
0090-6964
CILIARY ACTIVITY BY LIGHT-SCATTERING
249
marked improvement over direct visual observation was made later by adding photography to the stroboscopic method (Lueas, 1931). In 1933, Proetz devised a microscopic apparatus to be used with a motion picture camera. To date, high speed cinematography combined with phase contrast microscopy has proved to be the most accurate method of measuring ciliary activity. However, it is expensive, time consuming, and does not permit on-line data analysis. The photometric monitoring method (Dalhamn and Rylander, 1962), which employs a photomultiplier or photodiode to detect light transilluminated through the eiliated specimens, permits on-line recording of ciliary activity. Unfortunately, this method is not reliable when the beating mode of cilia becomes asynehronie (Naitoh and Kaneko, 1973). In search of a simplier, yet reliable, method which would allow on-line monitoring of ciliary activity, we have developed a new application of laser light-scattering spectroscopy to measure the frequency of ciliary beat. The method is based on the analysis of the spectrum of light scattered from moving targets. When moving objects are illuminated by a laser beam, the spectral structure of scattered light depends on both the type and magnitude of movement of the effective scatterers. In this particular instance, the spectral analysis of the scattered light permits the direct detection of ciliary activity. This new technique allows precise on-line monitoring of the frequency and coherency of ciliary beat, thus providing convenient and quantitative method for characterizing ciliary activity. A short communication on this method, omitting its theoretical basis, was published by the present authors earlier (Lee and Verdugo, 1976). This paper reports the development, validation, and theoretical basis of the application of laser lightscattering spectroscopy to measure ciliary activity. THEOI~ETICAL ANALYSIS
A utocorrelation Function of Light Scattered from Beating Cilia Laser light-scattering has become, in recent years, a useful technique for the study of the hydrodynamics of polymers and biological macromolecules (Dubin et al., 1967; Ford, 1972; Berne and Pecora, 1976). It has also been applied to assess sperm motility (Berg~ et al., 1967) and to study bacterial movements (Nossal and Chen, 1971). The theory of laser light-scattering spectroscopy has been discussed in numerous reviews, most recently by Berne and Pecora (1976). The theoretical basis of this new application of laser light-scattering spectroscopy is presented to show that the frequency of ciliary beat can be evaluated from the spectrum of scattered light. Because the dimensions of cilia are about 0.2 pm in diameter and 10 to 100 ~m in length, which are large in comparison with the wavelength of laser light, the scattering of light from ciliated epithelium may be treated as in the case of scattering from rough surfaces (Beckmann and Spizzichino, 1963; Marathay et al., 1970). A schematic view of the laser light-scattering spectrometer is shown in Fig. I. A collimated laser beam is normally incident on the surface of the eiliated cells and the scattered light is detected at distances larger than the dimensions of the
250
LEE AND VERDUGO
NSITY
Z
BEAM PROFILE
R (r,~5 =o, Z) Z
FIG. 1. Geometry of light scattered fl'om ~he cultured cells of a ciliated epithelium. The incident laser beam, focused normally onto the cultures, is assumed to have a Gaussian intensity profile whose width is a. scattering region and the wavelength (Fraunhofer zone). The scattered electric field at the detector point R --- (r, ~' = 0, z) is (Jakeman, 1974)
Aoe-i'~~ Z ds' e-iklR-r'le-i~(r" t)e-"~l'~'
E~(R, t) =
(1)
where o:0 and h are the frequency and the w~vevector of the light, Ao is a constant which includes the amplitude of the incident light, a is the width of intensity profile of the laser beam, and 4)(r', t) is a r a n d o m l y fluctuating phase variable introduced by the surface of the epithelium. Since both the ciliary beat and the roughness of epithelial surface contribute to r t), we m a y separate ~ into two terms: one comes from periodic beating and the other from the r a n d o m phase of the surface, ~b(r', t) = wr + ~ ( r ' , t), (2) where ~ is the frequency of ciliary beat and ~b~(r', t) = hh describes the phase shift which is associated with the surface function h. The surface function will be given as h = h(r', t) and the mean level of the surface is the plane z = 0 (Beckmann and Spizzichino, 1963). E q u a t i o n (1) can be written in terms of the physical parameters shown in Fig. 2 as E~(R, t) =
Aoe-i('~176 -ikR Z ds'e-~k~' sin ~ cos r162
t)e--r'2/a2
(3)
b y using an approximation IR - V[ ~ [R[ -- r' sin0 cos ~b' in the far field. T h e autocorrelation function of the scattered field is defined as
G(~)(~) = (E*,(R, t + ~)E~(R, t)>, where
E*, is the
(~)
complex conjugate of E~. F r o m Eq. (3) we have
1
2
X e-(r'12+r'2~)l"2(e q~'(''l' t+~')-4,.0:'2, t)]).
(5)
251
CILIARY ACTIVITY BY LIGHT-SCATTERING
T h e angular brackets in Eqs. (4) and (5) indicate t h a t the quantities between the brackets are to be evaluated b y ensemble average. If we assume t h a t the surface function is Gaussian distributed such t h a t 1
~-~v:"'
p (h) = - (2~)~
(6)
and (h) = o,
(7)
t h e n the value of the ensemble average can be expressed as ( B e c k m a n n and Spizzichino, 1963; M a r a t h a y et al., 1970) (e i[r162
= e-k2~[I-C(',~)].
(8)
T h e variance a s describes the roughness of the surface and large a s corresponds to large roughness. C(s, .r) is the normalized autocorrelation function of h(r', t) t h a t gives the coherency between the r a n d o m values assumed b y h at two points separated b y a distance s = #1 -- r'2 + vr, where v is the relative velocity of these two points. We do not know the function C(s, "r), owing to the lack of complete knowledge of the ciliary motion. However, we m a y assume ( M a r a t h a y et al., 1970). C(s, r) --~ 1 - (s/}) ~, if/c2a2 ) ) 1, (9) where } is the correlation length. Points t h a t are s e p a r a t e d b y a distance larger t h a n } will be statistically independent. Therefore, Eq. (9) is meaningful only for s < } and r < TI, where rl is some correlation t i m e and has a m a g n i t u d e of the order of ~/v. W i t h o u t knowledge of a n y specific function a b o u t time dependence of C(s, r), we m a y a p p r o x i m a t e the expression in Eq. (9) as
C(s, r) ~ 1
~
p
(D
(lO)
e
/
f'_~_ .dffg~"-'
Z=0
FIG. 2. Surface of ciliated ceils is described by ~ function h(r', t) which is Guussian distributed with zero mean. k is a wave vector which represents the direction of the incident beam, r' is the distance of a point on the surface measured from the center of the beam.
LEE AND VERDUGO
252
with p(0) = 0. We can now write Eq. (5) as
G(1)(T) --- ~r2a21Aol%i(~~
-k~"(~)
uduJo(kU sin 0) x exp
-
+
--. / u 2
,
(11)
where J0 is the zero-order Bessel function, and u = r'~ - r'2. After the integration we have ~2--si-n~0- I . ~ l A01 ~ (12) G(~)(r) = 2 d4k2~2[ + a2 ~2 j Therefore, the amplitude of the autocorrelation function of the scattered electric field decreases exponentially as the scattering angle 0 increases. The function itself also decays in time; however, whether it will decay exponentially or decay as a Gaussian depends on the n a t u r e of the function p ( r / r s ) . If one observes in a time much shorter than the coherence time Ts then the r a n d o m motion of the surface appears as a free motion, where s ~ - (st) 2 ~md p ( r ) ~ (r/Ts) 2. The normalized autocorrelation function becomes g(1) (r) -
G(1)(r) G(1) (0)
- ei(~o+~o)~e-k2~2"2/~2z.
(13)
On the other hand, if one observes at a time longer t h a n the coherent time, the motion of the surface will appear as a diffusional motion, where s 2 --~ r, and p(r/r~.) ~ r/vs. We have g(1) = ei(~0+~o)re k2~2~/~s. (14) In either case, the roughness of the epithelial surface z 2 affects the decay time. In summary, we propose t h a t the light scattered by a ciliated epithelium can be treated as the scattering from a rough surface. We submit t h a t the m o v e m e n t of this surface can be approximately described as a superposition of two motions: first the periodic oscillations of the cilia with an average frequency ~ ; and second a random motion due to the metaehronal coordination of the clusters of cilia which m a y be characterized b y the coherence length } and coherence time vz. Consequently, the autocorrelation function of light scattered by cilia shows a frequency modulation due to the ciliary beat and a decay relaxation related to the time-space coherency or metachronal coordination of the ciliated epithelium. DESCRIPTION OF PROCEDURES
(a) Heterodyne Detection of the Frequency of Ciliary Beat The block diagram of the laser scattering spectrometer used in this experiment is shown in Fig. 3. The optical part of the spectrometer, which includes laser, mirrors, Rose chamber holder, lenses, aperture, and photomultiplier tube, are all
CILIARY ACTIVITY BY LIGHT-SCATTERING
L
ROSE CHAMBERII
253
I
M"ERATURd [ \ [
-%
CONTROL I
_jo2:22 sL,o .... OM,pCOVER
CORRELATION ANALYZER
ROSE CHAMBER
t
FIG. 3. Schematicdiagram of the laser spectrometer. The optical heterodyne mixingis achieved by collectingthe light scattered from cultured cells and the light scattered elastically at the glass slip (inset shows the components of the Rose chamber). carefully positioned and rigidly bolted on the surface of a vibration-isolated optical table (Modern Optics Model MSTT 12E). The laser beam of a He-Ne laser (Spectral Physics Model 125A) is attenuated and focused on the eiliated cells contained in a Rose chamber (see insert in Fig. 3). A neutral density filter with a 5-10% transmission is used to avoid saturation in the photodetector and/or overheating of the specimens. The beam size at the region of scattering is approximately (_
