Computer-assisted rheological evaluation of microsamples of mucus
Pau lo S6rgio Panse Silveira 2, Gy6rgy Mikl6s B 6 h m 1,2, H y u n Mo Y a n g 2, C h a o L u n g W e n 2,
El iane Tigre Guimar~es 1, Mar ia A n g e l a Cavalhe i ro P a r a d a 1, Malco lm King 4
and Paulo Hilfirio Nasc imen to Saldiva 2,3
1 Laborat6rio de Poluiq~o Atmosf~rica Experimental, 2 Disciplina de Informdtica M~dica, 3 Instituto do Cora~fio, FMUSP, S~o Paulo, Brazil, and 4 Pulmonary Defense Group, University of Alberta, Edmonton, Canada
Dynamic viscoelasticity measurements are required in many studies on biological fluids and they can be performed by determining the corresponding strain when a sinusoidal shear stress is applied to a sample. In several circumstances the amount of fluid that can be obtained for analysis in physiological conditions does not exceed microliters. In this context, the microrheometer technique is a useful approach to determine the dynamic rheological profile of the samples. However, the manual calculation of the desired parameters is tedious and time-consuming. This paper describes a menu-oriented program in order to facilitate its use by non-experts. The comparison between manual and computer-aided calculations demonstrated that the program reduced the time of measurement, and reduced intra- and interobserver variations. The program was developed on an IBM compatible PC in Microsoft C 5.1, and tested in a blind study to check the advantages in terms of time and reproducibility of the system verified by the concordance of two independent observers (interobserver influence) in two different occasions (intraobserver influence).
Rheologic property; Viscoelastic property; Microsample of airway Mucus; Biological fluid; Magnetic microrheometer technique; Computer-assisted rheological evaluation
1. Introduction
The mucociliary apparatus represents the first defense mechanism of the respiratory system against airborne noxious agents [1]. Its action is based on the mechanical coupling between airway mucus and the underlying cilia, which causes an upward flow of airway secretions towards the larynx and the clearance 0f t rapped inhaled parti- cles. The viscoelastic properties of airway mucus interfere significantly with the efficiency of the
Correspondence: Paulo Hil~rio Nascimento Saldiva, MD, PhD, Departamento de Patologia, Faeuldadede Medicina da USP, Av. Dr. Arnaldo 455, CEP 01246 S~o Paulo, SP, Brazil. Fax: (55-11) 280-4381.
energy transfer from the cilia to the mucus. In this context, the determination of mucus mechan- ical properties provides important information about the effects of adverse environments, smok- ing, and drugs on respiratory susceptibility to infections [2-4].
Due to its complex biochemical and polymeric structure, mucus has both viscous and elastic properties, thus behaving as a viscoelastic gel. The proper determination of the rheological properties o f bronchial mucus is not easy, due to the complexity of the experimental procedures and the paucity of the samples that can be ob- tained by regular methods (for example by en- doscopy in human patients). Viscoelastic fluids present frequency-dependent rheologic behavior
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and dynamic measurements provide more com- prehensive information on mucus properties. However, most measurement techniques are not routinely applied to samples from normal sub- jects or small laboratory animals, since the amount of mucus that can be collected in these circum- stances is usually very small (microliters). In this context, most of our knowledge of mucus rheol- ogy is derived from samples collected in diseased patients, with productive mucus expectoration [5-7].
Theoretically, a dynamic viscoelasticity mea- surement can be performed by determining the corresponding strain when a sinusoidal shear stress is applied to the sample at different fre- quencies [8]. The magnetic microrheometer tech- nique, originally developed by Litt and coworkers [9] and adapted by King and Macklem [10], allows dynamic viscoelastic measurements to be per- formed in microliter quantities of mucus. Briefly, this technique is based on the analysis of the motion of a small steel ball inserted into the mucus sample and driven by an oscillating mag- netic force. This force is applied with different frequencies, ranging from 1 to 100 radian, s -1, in order to determine mucus transportability by the simulation of ciliary beating (lower frequencies), and cough (higher frequency).
The purpose of this work is to present a pro- gram aimed to increase reproducibility and to shorten the time of analysis of mucus rheology, based on the magnetic microrheometer method. It also intends to generalize this technique to other biomaterials of interest, that show similar dynamic behavior.
2. Material and Methods
The following is a brief outline of the funda- mental aspects of the magnetic microrheometer; a more detailed explanation of its theory and construction exists but is beyond the scope of this paper [10,11].
2.1. Description of the magnetic rheometer
An electromagnet (a steel toroid with coated wire windings) is mounted on the stage of a projecting microscope. The magnet is connected both to a DC power supply (coil 1 - - to stabilize the steel ball - - see below) and an AC power amplifier (coils 2 and 3), driven by a sine-wave generator (Fig. 1). The mucus sample is mounted in a plexiglass container and placed in a 2.5 mm gap in the front part of the toroid. A 100 /zm
tNalo ot steel bal l
(dlwplaoonont)
7,--" T
~ ~lammeA CbBtmeen O-D~ D)
A () I I.............I Fig. I. Schematic representation of the experimental setup (modified from ref. 11).
steel ball is placed in the sample, and then the ball is submitted to magnetic forces generated by the AC current. The shadow of the ball is pro- jected over two photocells and a differential cir- cuit registers the magnetically induced move- ment, giving an electrical output proportional to the displacement of the moving ball. The AC current and the output of the photocells are sent to a digital storage oscilloscope.
The present system combines the original idea of the dynamic analysis of viscous-elastic mea- surements by means of a magnetic microrheome- ter with an IBM compatible personal computer connected to the oscilloscope through a GPIB connection (General Purpose Interface Bus). We intend to demonstrate that this configuration per- mits agility in performing the calculation and increases the reproducibility among different re- searchers and between two calculations made by the same researcher.
2.2. Theory
The moving steel ball inserted in the sample of mucus acts as a rheological probe, since its mo-
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ti0n in the medium, due to the sinus0idally oscil- lating magnetic field, is opposed mainly by vis- cous and elastic forces. If the sinusoidal AC sig- nal (channel 1 of the oscilloscope) is plotted against the signal of the photocells, which corre- sponds to the displacement of the ball inside the mucus (channel 2 of the oscilloscope), an ellipse (Lissajous figure) is observed. The magnitude of the phase lag of the displacement of the ball (shear stress) in relation to the applied force (strain) is indicative of the relative contribution of the viscous and elastic components to the overall impedance (Fig. 2). Also, it is possible to decom- pose the displacement of the ball into two com- ponent vectors, one in phase with the applied force and the other lagging it by 90 ° , both exhibit- ing the same period. These correspond respec- tively to the "pure" elastic and "pure" viscous elements of mucus. The results can be expressed in terms of Elastic Modulus (G', dyn- cm -z) and viscosity (r/', mPa.s -1) , or, alternatively, as G* (vectorial sum of elasticity and viscosity, dyn. cm -2) and tan 3 (the ratio between viscosity and elasticity) [11].
il . . . . . . . . . . : • ~ i I . " I . . . . . . . . . . . . . . . ~ '
v a "
Fig. 2. Theory: (a) two sinusoidal waves showing phase lag; (b) plotting one sinusoid against the other the oscilloscope generates a Lissajous figure; the ellipse reflects the vectorial sum of the elastic and viscous elements of the mucus; (c) vectorial decomposition of the displacement of the ball into two component vectors: G', the "pure" elastic and , ' , the "pure" viscous element, lagged by
90 ° behind G '.
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three frequencies that simulate the range from ciliary beating (1 and 10 radian. S - 1 ) to cough (100 radian • s- 1).
2. 3. Experimental problems
Although this technique is simple in concept there are some relevant experimental difficulties that are not easy to overcome:
(1) the measurement time must be as short as possible, in order to minimize the effects of sam- ple deterioration caused by heat irradiation of the microscope light source. (2) the signal-to-noise ratio of the photocell out- put is usually extremely low especially at higher sinusoidaFfrequencies and with purulent or rigid sputum. (3) the determination of the phase lag between shear stress and strain is a time-consuming man- ual calculation and is influenced by subjective factors (corrections of baseline changes and vi- sual recognition of ellipse arms) particularly at higher frequencies.
2.4. Computational methods
The intention was to build a menu-oriented program in order to facilitate its use by non-ex- perts. The program was developed on an- IBM compatible PC, in the C language (Microsoft C 5.1 compiler) for a conventional 2-channel digital storage oscilloscope (Tektronix model 2221), with 4096 bytes of memory for both channels. We linked our developed functions with the relocat- able C object modules from GPIB board, sup- plied by the manufacturer (SEP Eletr6nica Ltda, Brazil), to transfer data between the oscilloscope and the computer.
The structure of the program is based on two independent modules, that can be accessed by the main menu: Capture and Calculation.
The Capture module is designed to collect the ellipse from the oscilloscope and the information from the user about the experimental conditions, storing both on the PC's hard disk. Before com- mitting to disk, the program can decompose the ellipse into its X and Y sinusoidal individual
components and plot them on the computer screen. The user can critically evaluate the signals and subsequently decide to save them or nOt. The variable experimental conditions (mucus volume, diameter of the steel ball, calibration of the pho- tocells, etc.) are defined at the moment of cap- ture of the first ellipse, whereas the operational conditions of the oscilloscope (gains of each channel and time-base of measurements) are au- tomatically stored. Non-variable parameters - -
-- • . . . . . . . SINUISOIO PLOTTED ~ ~ OVER THE NOISY SIGNAL
Fig. 3. Captured S;gilals: (a) Aspects of the computer screen dump used on manual calculation (see below), reproducing the oscilloscope display of Lissajous figure; captured signals with a gross artifact (arrows); (b) action of the Cut routine; (c) filtering of the channel 2 (photocell output); (d) calculation routine showing adjustment ~0f the ideal sinusoid in the chan-
nel 2.
the magnetic constant of the steel toroid, micro- scope magnification factor and the length of the photocells - - are stored with each experimental data, and can be easily changed whenever (al- though rarely) necessary, by a specific item in the menu.
The Calculation module is an off-line proces- sor for the stored data. The program lists the sinusoidal frequencies at which the experiments were performed, allowing the user to call specifi- cally one frequency. The sinusoidal shear stress and strain signals are displayed again, and the user can choose among Filter, Cut a n d / o r Calcu- lation routines. The filter routine is useful for noisy signals (specially those provided by the pho- tocells) and uses a 5-point promediation and in- terpolation algorithm. Filtering can be done as many times as desired by the user. The filtered signal is displayed in order to be compared with the original one, and the user decides whether the filtering was advantageous or not (Fig. 3c). The cut routine permits the selection of specific segments of the sinusoidal signals. This proce- dure is necessary when gross experimental arti- facts are present in order to improve on the calculation precision (fig. 3a, b). Calculation al- lows the visual amplification of the signal and the definition of the peaks and amplitude of the sinusoidal waves. This module works interactively with the user and plots ideal signals over the original one allowing the user to verify the ade- quate coincidence between the two signals. When the user authorizes the calculation of the rheo- logic variables, the result can be printed and /o r stored in a data base (fig. 3d).
2.5. Procedure to test reproducibility of the computational aid
We used 10 sets of ellipses, randomly sorted into 4 groups. Each set of data consisted of 3 ellipses performed at 1, 10 and 100 radian, s-1. Two groups of ellipses were given to two re- searchers (ETG and MACP) and independent manual and computer aided calculations were carried out. Manual calculations were achieved by computer screen dumps to a dot.matrix printer, the computer screen reproducing the oscilloscope
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display (fig. 3a). Computer-aided calculation em- ployed the program described above.
The person who initially divided the 10 sets of ellipses was unaware of the origin of the samples of mucus. The two researchers who performed the calculations were unaware of the order within the 4 groups. After the calculation it was discov- ered that there were 7 sets of ellipses from nor- mal rat mucus from an air pollution experiment (control group) and 3 from human patients with cystic fibrosis.
In four sets of ten measurements in each fre- quency we tested intra and interobserver agree- ments. In order to estimate the agreement, arith- metic media was calculated of the first observa- tion of observer 1 with the first observation of observer 2 and so on, to evaluate the intraob- server agreement and the arithmetic media of the two observations from observer 1 and the two observations from observer 2, in order to com- pute the interobserver difference. So we em- ployed two approaches: Chi square: the pairs of data sets (x and y corre- sponding to the first and second data sets from the observers or observations) were considered as two data sampling from the same universe (ie, the supplied ellipses). In this case the chi-square test,
2 named here as ,'](sample, can be performed by the following formula [12]:
2 ~ ( xi-yi)2 Xsample= i=l (Xi-t-Yi)
evaluating if there was any statistical difference between the two data sets. Linear regression: this analysis was done by the same pairs of data sets, used for the chi-square study.
2 We can evaluate the named Xfitting, using:
n ( a x i + b _ x i ) 2 2
Xfitting- E i=l Xi
where x is the abscissa, a is the tangent of the slope angle, b is the intercept in the ordinate, and n is the total number of points (equals 10 in this paper). The term ax i + b corresponds to the fitted straight line.
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The 2 )(fitting shows the agreement between lin- ear regression and the identity line y = x, that is the expected relation between the measurements
in the absence of errors. It is slightly different from the 2 Xsample because here we know the ex- pected x value [13].
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f Fig. 4. Comparison between the manual and computer calculations methods. The points were obtained by arithmetic media between the two measurements of each observer (interobserver graphics) and by the media between the first observation of the two observers against the second ones (intraobserver graphics). The full line is the linear regression obtained and the dotted line
represents the ideal curve of perfect concordance:
3. Results and Discussion
Computer-based storage of data and off-line calculations significantly improved the experi- mental conditions in the three critical aspects previously listed (see experimental problems).
The storage of ellipses at each frequency from
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the oscilloscope was previously done by means of photographs or graphic plotters. This procedure represents a critical amount of time when obtain- ing the ellipses, a delay that can modify the quality of the mucus sample submitted to the microscope light. This problem was minimized with the computer-based storage of data. The
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program gets the ellipse in a few seconds through GP1B, leaving the oscilloscope free to start the capture of a new ellipse at another frequency during the recording on the hard disk.
The problem caused by the low signal/noise ratio is significantly avoided by the use of filter and cut routines• The first routine permits the smoothing of the stored signal, and the second allows the user to exclude gross experimental artifacts and improves the precision due to the expansion of the not-cut signal on the screen. Also, if there is a drift in the baseline during the capture, the resultant ellipse is broadened, and this causes great difficulty in determining visually the median value. With the cut routine we can isolate many short segments of the sinusoidal signals and perform the calculation anyway. Usu- ally we perform three calculations, one at the beginning, one in the middle and one at the end part of the captured signal and the differences among these results is small•
The manual and computer calculations were performed twice by each researcher, allowing comparison between calculations of the same re- searcher (intraobserver subjectivity influence) and between both different researchers (interobserver influence)•
In some instances we can observe a relative overestimation of the manual over the computer method. There is no way to verify the "real" value because all the earlier measurements were obtained by manual calculation• However, the computer method results are more reproducible• We believe it is possible to determine the normal values using the computer method within nar- rower range of acceptable results•
Plotting the results obtained by one observer against those of the other using linear regression, we can show that there is a close concordance with the expected value in the computer aided method, both in intraobserver and interobserver graphics• (Fig. 4). The major experimental prob- lem occurs at high frequency, where the noise / signal relation is bigger than in the lower ones. In this case, the computer aided method in compari- son with the manual method permitted to obtain more reproducible results than by the manual method•
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It should be noted that observer 1 overesti- mated tan 6 when compared with observer 2, using the manual calculation method. This dis- crepancy was particularly pronounced at the highest frequency, as indicated by the sharp devi- ations from the ideal slope in the manual panels of Fig. 4. On the other hand, the two observers obtained very similar results when using the com- puter-assisted method, and the slopes of the lines in the computer panels of Fig. 4 do not appear to deviate from the line of identity.
Comparing the experimental points with an ideal curve of perfect concordance we observed that there was no significant discordance between the two observers/observations using the manual method (table 1). However, observing Table 1,
2 Xsample showed better results than the computer one in the calculation of tan 6 at two lower frequencies: 1 rad ian . s -~ and 10 radian" s -1. This contradiction can be explained by the limita- tions of the 2 Xsample approach, which indicates only whether there is any concordance between
2 two data sets. Observing Xfit t ing, the computer-as- sisted method shows an excellent concordance with the identity line in ellipses performed at 10 radian s-~ The 2 • " }(sample exhibited a bad result in the case of the computer method because of one outlayer point. The Xfitting2 didn't show better con- cordance only at 1 radian, s-~ where the visual recognition to the manual method was easy. The correspondent graphic shows that the second ob- servation was overestimated. Possibly in the two cases there are apparent contradictions caused by experimental errors allied to favorable conditions of the manual method.
An additional benefit of this new method is that computer processing is time saving. In our laboratory the manual measurements and calcu- lations usually take a minimum of 30 minutes to 1 hour. Computer processing decreased this time to a few minutes, even when the users were unfamil- iar with the use of the program.
In conclusion, this paper presents a program specifically developed for research in mucus rhe- ology that increases the reproducibility and gain of time during the experiments and calculations. Its characteristics encourage its use in large stud- ies or research groups and clinical studies, con-
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cern ing the eva lua t ion of the effects of air pol lu- t ion on h u m a n hea l th o r d rug trials.
P e r h a p s a s imilar a p p r o a c h can be used for o t h e r k inds of b io logica l f luids tha t can only be o b t a i n e d in small vo lumes or in cr i t ical exper i - men ta l condi t ions w h e r e a shor t t ime exposure of the ma te r i a l u n d e r the m e a s u r e m e n t e q u i p m e n t is necessary. In many s i tuat ions , r a p i d biological events benef i t by the coope ra t i on be tween a digi- tal osc i l loscope and a c o m p u t e r a l lowing the sub- s t i tu t ion o f expensive po lygraph e q u i p m e n t and cri t ical eva lua t ion of the o b t a i n e d signal by the resea rcher .
N.B. T h e p r o g r a m is avai lable on reques t f rom the co r r e spond ing authors .
References
[1] M. King, Mucus, mucociliary clearance and coughing, in: Respiratory Function in Disease ed. D.V. Bates, (Chapter 3, 3rd Ed., Saunders, Philadelphia, 1989).
[2] P.C. Braga, L. Allegra, eds. Drugs in Bronchial Mucology (Raven Press, New York, 1989).
[3] M. King, A. Wight, G.T. De Sanctis, et al., Mucus hypersecretion and viscoelasticity changes in cigarette- smoking dogs, Exp. Lung. Res. 15 (1989) 375-389.
[4] P.H.N. Saldiva, M. King, V.L.C. Delmonte, et al., Respi-
ration alterations due to urban air pollution: an experi- mental study in rats, Environ. Res. 57 (1991) 19-33.
[5] E. PucheUe, F. Girard and J.M. Zahm, Rh6ologie des s6cr&ions bronchiques et transport muco-ciliare, Bull. Eur. Physiopathol. Respir. 12 (1976) 771-779.
[6] M.J. Dulfano and K.B. Adler, Physical properties of sputum. VII. Rheologic properties and mucociliary trans- port, Am. Rev. Respir. Dis. 112 (1975) 341-347.
[7] M.T. Lopez-Vidriero and L. Reid, Chemical markers of mucous and serum glycoproteins and their relation to viscosity in mucoid and purulent sputum from various hypersecretory diseases, Am. Rev. Respir. Dis. 117 (1978) 465-477.
[8] P.C. Braga, L. Allegra and M. King, Mathematical analy- sis of dynamic measures, in: Methods in bronchial mucol- ogy, eds. P.C. Braga and L. Allegra, pp. 85-89 (Raven Press, New York, 1988).
[9] R.J. Lutz, M. Litt and L.W. Chkrin, Physical-chemical factors in mucus rheology, in: Rheology of biological systems, eds. H.L. Gabelnick and M. Litt, pp. 119-157 (Thomas, Springfield, IL, 1973).
[10] M. King and P.T. Macklem, The rheological properties of microliter quantities of normal mucus, J. Appl. Physiol. 42 (1977) 797-802.
[11] M. King, Magnetic microrheometer, in: Methods in bronchial mucology, eds. P.C. Braga and L. AUegra, pp. 73-83 (Raven Press, New York, 1988).
[12] W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, in: Numerical Recipes: the art of scientific computing, pp. 470-471 (Cambridge University Press, 1989).
[13] L.D. Taylor, in: Probability and Mathematical Statistics, pp. 259 (Harper and Row Press, 1974).
