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Homoeopathic effect on the sleep pattern of rats
British Homoeopathic Journal October 1997, Vol. 86, pp. 201-206
Homoeopathic effect on the sleep pattern of rats GUADALUPE RUIZ, PHD* and JOSI~-LEONEL TORRES, PHD**
Abstract The effect of Nux vomica on the EEGs of rats during sleep was quantified in terms of snitable statistical parameters that showed systematic changes after the homoeopathic stimulus. Our results are consistent with a decrease in the coherence of the brain signal compared to results obtained by using either the solvent on its own or pure water, and can be interpreted in terms of irritation of the animals' central nervous system due to the applied stimulus. This coincides with the effect Nux vomica has on healthy humans and suggests a means of characterizing the homoeopathic effect in physicochemical terms, based on parameters similar to those found appropriate in this study, calculated for physiological data from animal models for specific conditions. It also lends scientific support to ongoing attempts to extend Hahnemann's principles of similitude and potentiation beyond their original context, into the realm of veterinary medicine. KEYWORDS: Nux
vomica; Sleep patterns. parts of the body. Specifically, we record the electroencephalogram (EEG) from rats and look for systematic and reproducible changes derived from the administration of a potentized preparation. The EEG electrodes are implanted directly in the animal's brain, the signal is digitized and subjected to various mathematical treatments that yield diverse parameters of potential interest. The experimental procedure involves giving the animal pure water to drink the first day, and the following day either the homoeopathic medicine or its solvent on its own, and looking for systematic changes in the parameters under consideration. Rats that received solvent only made up our first control group. Another set of animals was given pure water to drink and served as a second control group. Measurements were performed during the sleep period of the animals, as we were searching for changes in the EEG of rats produced by a h o m o e o p a t h i c medicine (Nux vomica) known to alter the sleep pattern in humans.
Introduction The psychological element is relevant both in conventional and in homoeopathic medicine but is difficult to quantify. One manifestation is the placebo effect and clinical trials have traditionally been designed to minimize or eliminate it. In fact, one of the main arguments against homoeopathic treatment is that it can be 'reduced' to a placebo response, and hence discounted as a medical alternative.l, 2 Regardless of questions of the clinical legitimacy of the placebo effect, and of its intrinsic scientific interest, a potentially profitable approach in homoeopathy consists of minimizing it by using animals as models for certain human disorders. Conceptually, this involves extending Hahnemann's homoeopathic principles of similitude and potentiation through dilution and succussion 3 to the much wider context of all animals, or at least a subset of them, including those that h a v e customarily been used in clinical trials?, 5 In more practical terms, it bears on the task of providing a scientific basis for the attempt to extend homoeopathic concepts and methods to veterinary medicine. 6,7 In this work we employ rats in our ongoing effort to characterize the homoeopathic effect in physicochemical terms, 8, 9 based on the analysis of electrical signals from different
Experimental setup and method Three stainless steel electrodes 1.5 m m in diameter were i m p l a n t e d in the brain of healthy Wistar (male) rats between 250 and 350 grams in body mass. The electrodes were set on the surface of the cerebral cortex by means of trepanation, sealing with dental gum so that they they could be connected to a multichannel amplifier. Two of the electrodes were implanted bilaterally in the parietal
*Escuela de Ingenieria Qulmica **Instituto de Ffsica y Matem~iticas, Universidad Michoac~in 201
202 region, and one in the frontal area for reference (ground). Trepanation points were located manually and correspond to the following stereotaxic coordinates 10 from Bregma - 9.16, anterioposterior (AP) - 2.8, lateral (L) 2.8, vertical (V) 0.4, for the bilateral electrodes; for the ground electrode: AP 4.3, L 2.6, V 0.4. Before trepanation each rat was intraperitoneally anaesthetized with 40 mg of pentobarbital sodium per kilogram of body mass, and after a 7-day interval of recovery its electrodes were connected to a signal amplifier with a wire that allowed the animal freedom of movement. After a further 'conditioning' period of one day, measurements started. The experimental setup consisted of two wooden cages with one glass wall to permit observation of the animal. The cages were designed for sound attenuation and allowed their occupantS a cubic moving space of 50cm per side. Each cage housed a rat connected to a G R A S S - 7 D multichannel amplifier as described in the above paragraph. The output from the amplifier was sampled at intervals of interest and digitized with a National Instruments AT-MIO-16XE-50 card, and the resulting numerical record stored in a computer for statistical analysis. The experimental procedure consisted of placing two rats, one to each cage, just after they had completed the preparation stage described above, and connecting them to the amplifier. All measurements were performed during the 8-hour sleep period of the animals (between 9 a.m. and 5 p.m.) under ideal conditions, when recording was not interrupted due to problems with the cap connecting the craneal electrodes to the external wire (a major source of trouble and concern throughout the experiment). The rats were not systematically observed throughout the data recording sessions, to keep external stimuli to a minimum. During preliminary recording sessions the various sleep patterns in the EEG were identified with the help of a simultaneous electromyogram (EMG), obtained with the stainless steel electrodes implanted on the bilateral antigravitatory neck muscles of the animal, and connected to the amplifier through the same cap as the craneal electrodes (Figure 1). The test proceeded as follows: First day. After completing their 24-hour conditioning period, during which the rats
British HomoeopathicJournal were given pure water to drink from a feeding bottle placed in the cage, the first recording session started for both of them. The computer record from this day constituted our reference signal. At the end of this session (around 5 p.m.) one of the rats was given 20 drops (1 ml) of N u x v o m i c a obtained from Grupo Homeopatico Medicor, at 30c concentration, dissolved in 450 ml of pure water in the feeding bottle; the other animal was given the same amount of the homoeopathic solvent (87% alcohol) in its drinking water. The person in charge of this task was unaware of the nature of the substance being given to each rat, and care was taken to ensure that she would not be able to identity it by smell or taste. Second day. A second data gathering session started at the same time as the previous day. At the end of the session the animals were released to be used in other experiments and the process was repeated with a new pair. The mathematical analysis of results was performed by a person unaware of the specific source of the data under consideration. This completed our blind procedure for the experiment. Control group. Our original intention was to use as control the group of rats that had received only the solvent, due to limitations in the number of channels available in our
T I M E UNITS
FIGURE1. A typical digitized record from the EEG of a sleeping rat (upper plot). Periods of greater (lesser) physical activity correspond to narrower (wider) traces in the plot, as shown by a simultaneous electromyogram (EMG: lower plot) from the bilateral antigravitatory neck muscles of the animal. Vertical scales in arbitrary units. This record has 30,000 points and corresponds to about 15 hours of observation, with a sampling frequency of 5 Hz.
203
Volume 86, October 1997
amplifier. This allowed only 2 animals to be handled at a time. A total of 9 such pairs were studied this way. Subsequent analysis of data proved this procedure to be untenable, as the control group showed a distinct variation in the same parameters as those from rats undergoing homoeopathic stimulation. This forced us to define a new control with a group of 6 rats prepared as before, that were given only pure water to drink and had 2 data recording sessions in the way described above.
Mathematical analysis We sampled our signal from the amplifier at a frequency of 5 Hz, as we wanted to record f e a t u r e s f r o m the slow sleep stages (or NREM sleep, characterized by a synchronized signal with frequency between 0.5 and 2 Hz, and amplitude greater than 751aV.11The sampling theorem from statistics then forced us to use a frequency at least twice 2 Hz). A full 8-hour long record became a time series with about 140,000 voltage readings, and clearly s h o w e d the usual sleep patterns observed in EEGs (cf. Figure 1). We then applied a low-pass filter with cutoff frequency 1 Hz, 12 chosen by trial and error so a large fraction of high frequency noise would be eliminated, but without wiping out relevant low-frequency features of the data. For technical reasons (to keep computational time within reasonable limits) each record was divided into sectors with 30,000 readings each (corresponding to about 1.5 hours of continuous detection), which were then separately analysed in identical fashion. The total number of usable data sets from a given animal was limited by the observation time allowed by the cap where the cranial electrodes were connected to the external wire: when this cap fell off a new pair of rats had to be selected to continue the experiment. The correlation deviation of one of the rats from its reference value turned out to be so much greater than all the others that it was treated as a statistical outlier and the associated data were discarded. The purpose of our mathematical analysis was to extract from the data suitable parameters that would show systematic and reproducible changes when the medicine was administered, and use them to characterize the homoeopathic effect in physicochemical terms. 8, 9 To this end we tried various quantities calculated from the
fourier transform (the mathematical expression of the signal as a sum of contributions from its component frequencies), like the power spectrum and diverse correlations, and some non-linear ones including correlation d i m e n s i o n , 13 L y a p u n o v exponents, entropies, ~4 and the Lempel-Ziv measure of complexity. 15
Results and discussion We found a systematic behaviour of the type we were looking for in 3 of the parameters considered: Pearson correlation, correlation time and the fraction of signal energy contained in its lowest frequencies (cf. Figures 2-4). All of them showed changes that allowed a consistent interpretation in homoeopathic terms. Our results imply a decrease in the degree of coherence of brain signals from rats due to the intake of a homoeopathic medicine (Nux vomica) that according to the materia medica 16 would irritate the central nervous system of healthy human subjects. We quantified such a decrease in terms of several parameters extracted from the signal: Pearson correlation (or self-correlation), correlation time and energy content at low frequencies. Their behaviour reflects an enhanced variability of the EEG after the homoeopathic stimulus is applied, consistent with a greater frequency of transitions among the different types of sleep, 11 which in turn reflects a more unstable sleep pattern due to irritation of the central nervous system by the medicament. The increase in EEG coherence due to the solvent alone came as a surprise and the available data did not provide a satisfactory explanation. One would expect random variation of parameters, with a null average if the solvent is not to interfere with the action of the potentiated medicament. One possibility is that the alcohol slightly intoxicated the animal and made its sleep pattern more stable, but this would be hard to reconcile with the reduction in coherence due to the potentiated m e d i c a m e n t , w h i c h c o n t a i n s the s a m e a m o u n t o f alcohol per v o l u m e , without i n v o k i n g a d o u b l y - s t r o n g action by the homoeopathic agent, capable in this case of countering an opposite tendency from the s o l v e n t alone. It c o u l d also be that the increase reflects an ongoing healing process after the t r a u m a o f t r e p a n a t i o n . In the
British Homoeopathic Journal
204 a b s e n c e o f a d e q u a t e e v i d e n c e to c h o o s e a m o n g these and other alternatives, w e cons i d e r this an o p e n p r o b l e m t h a t c e r t a i n l y merits further attention. The unexpected effect of the solvent (increasing E E G coherence) forced us to d e f m e a new control group, with animals that received only pure water throughout the experiment. T o this end w e prepared 6 rats in the
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FIGURE 3. Correlation time for the same data as in Figure 2. Medicine and solvent intake correspond to continuous and broken lines, respectively. The separation of average correlation times from solvent and medicine, with one above and one below the horizontal line at null deviation, is again highly significant, with p = 0.001. la
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FIGURE 2. Pearson correlation of EEGs from rats taking homoeopathic N u x vomica (continuous line), and from rats taking only the solvent of this medicine (alcohol: broken line). Each point corresponds to 30,000 consecutive filtered data values, or about 1.5 hours of observation (see text), and represents the per cent deviation of the Pearson correlation from its reference value, defined for pure water intake during the first day. Paired points correspond to data taken simultaneously from two different rats, one ingesting Nux vomica and the other solvent alone, mixed with drinking water. (One exception to this rule: the last pair of points come from measurements taken 5 days apart due to technical difficulties, under conditions as similar to each other as possible). Horizontal ordering of paired points is chronological and numbers indicate different pairs of animals; letters next to a number label consecutive 30,000-point data sets from the same pair of animals. Error bars represent the standard error of the m e a n (standard deviation)/~/n, with n the number of points in the plot), and are drawn just once for the sake of clarity. The average values from the upper and lower graphs are as follows: 5.67 + 1.66 (solvent), and - 6.82 _+ 2.98 (medicament). The separation of these two average values, one above and one b e l o w zero, is highly s i g n i f i c a n t (p v a l u e = 0.0007, with a one-sided distribution.17)
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FIGURE 4. Energy fraction in lowest frequencies for the same data as in Figure 2. This fraction was calculated in the following way: the fourier power spectrum was obtained for each set of 30,000 points; it contained 15,000 energy values corres p o n d i n g to the s a m e n u m b e r of d i f f e r e n t frequencies. The first 1,000 of them were then added together and the result divided by the sum of all 15,000 values and multiplied by 100. Graph convention is the same as in Figure 1, and the separation of average energy fraction values from medicine and from solvent is again highly significant, with p = 0.009. The signal's energy content at low frequencies measures the relative weight of its long-period oscillations, which in turn reflect its degree of coherence: a large content of longp e r i o d o s c i l l a t i o n s g e n e r a l l y i m p l i e s a long correlation time and a high self-correlation.
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a conceptual f o u n d a t i o n for homoeopathic veterinary therapies. 6, 7 To substantiate this claim we must perform similar m e a s u r e m e n t s in other a n i m a l s commonly used in medical studies and several other homoeopathic medicines with a definite effect on the human central nervous system, the b l o o d circulation and other sources of detectable electrical voltages. W o r k along these lines is currently in progress.
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FIGURE 5. Effect of pure water. 6 rats were given pure water to drink during 2 days, and their EEGs recorded and filtered in the same way as before. Each point corresponds to a set of 30,000 voltage values, and represents the per cent variation of a specific parameter (Pearson correlation, correlation time or energy fraction at lowest frequencies), with respect to its reference point, defined as its magnitude calculated from the initial data (first day). Convention for numbers and letters next to them is the same as in Figure 2. Standard error bars for correlation time and Pearson correlation were not drawn, as they were about the same size as the symbols used for individual points. The average effect of pure water can be considered null, as the opposite possibility (its average being significantly different from zero) implies p values greater than 0.05: p = 0.338 (Pearson correlation), p = 0.26 (correlation time), p = 0.06 (energy fraction at low frequencies).
same way as before, but gave them pure water to d r i n k d u r i n g the 2-day i n t e r v a l of data recording. Our results are plotted in Figure 5, which shows a random effect on self-correlation, c o r r e l a t i o n t i m e and l o w - f r e q u e n c y energy content of the signal. Our results suggest a method to characterize the homoeopathic effect, using animal models for c e r t a i n d i s e a s e s , a n d p a r a m e t e r s like those that showed systematic changes in this s t u d y . S u c h a m e t h o d w o u l d p e r m i t the design of research procedures to minimize the subjective element in various kinds of homoeopathic research. They also contribute to the task of furnishing a scientific basis for extensions of H a h n e m a n n ' s principles (similitude and potentiation through dilution and succusion) to animals, 4, 5 a necessary step to build
Acknowledgement We thank QFB Leticia Perez Ordaz for help and advice on electrode and rat manipulationtechniques. References 1 Reilly DT, Taylor MA, McSharry C, Aitchison T. Is homoeopathy a placebo response? Lancet 1986; 18 October: 881. 2 Resch G, Gutman V. Scientific Foundations o f Homoeopathy. Germany: Barthel und Barthel 1987. 3 Hahnemann S. Organon o f Medicine. Blame, Washington: Cooper Publishing 1996. English translation of the 6th edition of the original work. 4 Davenas E, Poitevin B, Benveniste J. Effect on mouse peritoneal macrophages of orally administered very high dilutions of silica. European J Pharmacol 1987; 135: 313. 5 Fisher P, House I, Belon P, Turner P. The influence of the homeopathic remedy Plumbum metallicum on the excretion kinetics of lead in rats. Hum Toxicol 1987; 6: 321. 6 Searcy R, Reyes O, Guajardo G. Control of subclinical bovine mastiffs. Br Hom J 1995; 84: 67. 7 Guajardo G, Searcy R, Soto J. Growth promoting effect of sulphur 201c in swine herds. B r Horn J 1996; 85: 15. 8 Torres J-L, Ruiz G. Stochastic resonance and the homoeopathic effect. Br Hom J 1996; 85: 134. 9 Ruiz G, Torres J-L. A possible characterization of the homoeopathic effect. Br Hom J 1997; 86: 4. 10 Paxinos G, Watson C. The rat brain in stereotaxic coordinates. 2nd edition. New York: Academic Press 1986. 11 Rechtschaffen A, Kales A, eds. A manual o f standardized terminology, techniques and score s y s t e m f o r sleep stages o f h u m a n s u b j e c t s .
Bethesda, Maryland: US Department of Health, Education and Welfare 1968. 12Cheng C. A c t i v e f i l t e r design. New Jersey: Hayden Book Co. 1982. 13 Grassberger P, Procaccia I. Characterization of
206 strange attractors. Phys Rev Lett 1983; 50: 346. 14Berge P, Pomeau Y, Vidal C. Order within chaos. New York: John Wiley and Sons 1984. 15 Kaspar F, Schuster HG. Easily calculable measure for the complexity of spatiotemporal patterns, Phys Rev A 1987; 36: 842.
Address for correspondence Ma. Guadalupe Ruiz V. Lluvia # 120 Prados del Campestre 58297 Morelia Michoac~_n Mexico
British HomoeopathicJournal 16Vijnovsky V. Tratado de Materia Medica Homeoptica. Buenos Aires: Macagno, Landa & Cia 1981. 17 Bethea RM, Duran BS, Boullion TL. Statistical Methods for Engineers and Scientists. New York: Marcel Dekker 1985.
Homoeopathic effect on the sleep pattern of rats GUADALUPE RUIZ, PHD* and JOSI~-LEONEL TORRES, PHD**
Abstract The effect of Nux vomica on the EEGs of rats during sleep was quantified in terms of snitable statistical parameters that showed systematic changes after the homoeopathic stimulus. Our results are consistent with a decrease in the coherence of the brain signal compared to results obtained by using either the solvent on its own or pure water, and can be interpreted in terms of irritation of the animals' central nervous system due to the applied stimulus. This coincides with the effect Nux vomica has on healthy humans and suggests a means of characterizing the homoeopathic effect in physicochemical terms, based on parameters similar to those found appropriate in this study, calculated for physiological data from animal models for specific conditions. It also lends scientific support to ongoing attempts to extend Hahnemann's principles of similitude and potentiation beyond their original context, into the realm of veterinary medicine. KEYWORDS: Nux
vomica; Sleep patterns. parts of the body. Specifically, we record the electroencephalogram (EEG) from rats and look for systematic and reproducible changes derived from the administration of a potentized preparation. The EEG electrodes are implanted directly in the animal's brain, the signal is digitized and subjected to various mathematical treatments that yield diverse parameters of potential interest. The experimental procedure involves giving the animal pure water to drink the first day, and the following day either the homoeopathic medicine or its solvent on its own, and looking for systematic changes in the parameters under consideration. Rats that received solvent only made up our first control group. Another set of animals was given pure water to drink and served as a second control group. Measurements were performed during the sleep period of the animals, as we were searching for changes in the EEG of rats produced by a h o m o e o p a t h i c medicine (Nux vomica) known to alter the sleep pattern in humans.
Introduction The psychological element is relevant both in conventional and in homoeopathic medicine but is difficult to quantify. One manifestation is the placebo effect and clinical trials have traditionally been designed to minimize or eliminate it. In fact, one of the main arguments against homoeopathic treatment is that it can be 'reduced' to a placebo response, and hence discounted as a medical alternative.l, 2 Regardless of questions of the clinical legitimacy of the placebo effect, and of its intrinsic scientific interest, a potentially profitable approach in homoeopathy consists of minimizing it by using animals as models for certain human disorders. Conceptually, this involves extending Hahnemann's homoeopathic principles of similitude and potentiation through dilution and succussion 3 to the much wider context of all animals, or at least a subset of them, including those that h a v e customarily been used in clinical trials?, 5 In more practical terms, it bears on the task of providing a scientific basis for the attempt to extend homoeopathic concepts and methods to veterinary medicine. 6,7 In this work we employ rats in our ongoing effort to characterize the homoeopathic effect in physicochemical terms, 8, 9 based on the analysis of electrical signals from different
Experimental setup and method Three stainless steel electrodes 1.5 m m in diameter were i m p l a n t e d in the brain of healthy Wistar (male) rats between 250 and 350 grams in body mass. The electrodes were set on the surface of the cerebral cortex by means of trepanation, sealing with dental gum so that they they could be connected to a multichannel amplifier. Two of the electrodes were implanted bilaterally in the parietal
*Escuela de Ingenieria Qulmica **Instituto de Ffsica y Matem~iticas, Universidad Michoac~in 201
202 region, and one in the frontal area for reference (ground). Trepanation points were located manually and correspond to the following stereotaxic coordinates 10 from Bregma - 9.16, anterioposterior (AP) - 2.8, lateral (L) 2.8, vertical (V) 0.4, for the bilateral electrodes; for the ground electrode: AP 4.3, L 2.6, V 0.4. Before trepanation each rat was intraperitoneally anaesthetized with 40 mg of pentobarbital sodium per kilogram of body mass, and after a 7-day interval of recovery its electrodes were connected to a signal amplifier with a wire that allowed the animal freedom of movement. After a further 'conditioning' period of one day, measurements started. The experimental setup consisted of two wooden cages with one glass wall to permit observation of the animal. The cages were designed for sound attenuation and allowed their occupantS a cubic moving space of 50cm per side. Each cage housed a rat connected to a G R A S S - 7 D multichannel amplifier as described in the above paragraph. The output from the amplifier was sampled at intervals of interest and digitized with a National Instruments AT-MIO-16XE-50 card, and the resulting numerical record stored in a computer for statistical analysis. The experimental procedure consisted of placing two rats, one to each cage, just after they had completed the preparation stage described above, and connecting them to the amplifier. All measurements were performed during the 8-hour sleep period of the animals (between 9 a.m. and 5 p.m.) under ideal conditions, when recording was not interrupted due to problems with the cap connecting the craneal electrodes to the external wire (a major source of trouble and concern throughout the experiment). The rats were not systematically observed throughout the data recording sessions, to keep external stimuli to a minimum. During preliminary recording sessions the various sleep patterns in the EEG were identified with the help of a simultaneous electromyogram (EMG), obtained with the stainless steel electrodes implanted on the bilateral antigravitatory neck muscles of the animal, and connected to the amplifier through the same cap as the craneal electrodes (Figure 1). The test proceeded as follows: First day. After completing their 24-hour conditioning period, during which the rats
British HomoeopathicJournal were given pure water to drink from a feeding bottle placed in the cage, the first recording session started for both of them. The computer record from this day constituted our reference signal. At the end of this session (around 5 p.m.) one of the rats was given 20 drops (1 ml) of N u x v o m i c a obtained from Grupo Homeopatico Medicor, at 30c concentration, dissolved in 450 ml of pure water in the feeding bottle; the other animal was given the same amount of the homoeopathic solvent (87% alcohol) in its drinking water. The person in charge of this task was unaware of the nature of the substance being given to each rat, and care was taken to ensure that she would not be able to identity it by smell or taste. Second day. A second data gathering session started at the same time as the previous day. At the end of the session the animals were released to be used in other experiments and the process was repeated with a new pair. The mathematical analysis of results was performed by a person unaware of the specific source of the data under consideration. This completed our blind procedure for the experiment. Control group. Our original intention was to use as control the group of rats that had received only the solvent, due to limitations in the number of channels available in our
T I M E UNITS
FIGURE1. A typical digitized record from the EEG of a sleeping rat (upper plot). Periods of greater (lesser) physical activity correspond to narrower (wider) traces in the plot, as shown by a simultaneous electromyogram (EMG: lower plot) from the bilateral antigravitatory neck muscles of the animal. Vertical scales in arbitrary units. This record has 30,000 points and corresponds to about 15 hours of observation, with a sampling frequency of 5 Hz.
203
Volume 86, October 1997
amplifier. This allowed only 2 animals to be handled at a time. A total of 9 such pairs were studied this way. Subsequent analysis of data proved this procedure to be untenable, as the control group showed a distinct variation in the same parameters as those from rats undergoing homoeopathic stimulation. This forced us to define a new control with a group of 6 rats prepared as before, that were given only pure water to drink and had 2 data recording sessions in the way described above.
Mathematical analysis We sampled our signal from the amplifier at a frequency of 5 Hz, as we wanted to record f e a t u r e s f r o m the slow sleep stages (or NREM sleep, characterized by a synchronized signal with frequency between 0.5 and 2 Hz, and amplitude greater than 751aV.11The sampling theorem from statistics then forced us to use a frequency at least twice 2 Hz). A full 8-hour long record became a time series with about 140,000 voltage readings, and clearly s h o w e d the usual sleep patterns observed in EEGs (cf. Figure 1). We then applied a low-pass filter with cutoff frequency 1 Hz, 12 chosen by trial and error so a large fraction of high frequency noise would be eliminated, but without wiping out relevant low-frequency features of the data. For technical reasons (to keep computational time within reasonable limits) each record was divided into sectors with 30,000 readings each (corresponding to about 1.5 hours of continuous detection), which were then separately analysed in identical fashion. The total number of usable data sets from a given animal was limited by the observation time allowed by the cap where the cranial electrodes were connected to the external wire: when this cap fell off a new pair of rats had to be selected to continue the experiment. The correlation deviation of one of the rats from its reference value turned out to be so much greater than all the others that it was treated as a statistical outlier and the associated data were discarded. The purpose of our mathematical analysis was to extract from the data suitable parameters that would show systematic and reproducible changes when the medicine was administered, and use them to characterize the homoeopathic effect in physicochemical terms. 8, 9 To this end we tried various quantities calculated from the
fourier transform (the mathematical expression of the signal as a sum of contributions from its component frequencies), like the power spectrum and diverse correlations, and some non-linear ones including correlation d i m e n s i o n , 13 L y a p u n o v exponents, entropies, ~4 and the Lempel-Ziv measure of complexity. 15
Results and discussion We found a systematic behaviour of the type we were looking for in 3 of the parameters considered: Pearson correlation, correlation time and the fraction of signal energy contained in its lowest frequencies (cf. Figures 2-4). All of them showed changes that allowed a consistent interpretation in homoeopathic terms. Our results imply a decrease in the degree of coherence of brain signals from rats due to the intake of a homoeopathic medicine (Nux vomica) that according to the materia medica 16 would irritate the central nervous system of healthy human subjects. We quantified such a decrease in terms of several parameters extracted from the signal: Pearson correlation (or self-correlation), correlation time and energy content at low frequencies. Their behaviour reflects an enhanced variability of the EEG after the homoeopathic stimulus is applied, consistent with a greater frequency of transitions among the different types of sleep, 11 which in turn reflects a more unstable sleep pattern due to irritation of the central nervous system by the medicament. The increase in EEG coherence due to the solvent alone came as a surprise and the available data did not provide a satisfactory explanation. One would expect random variation of parameters, with a null average if the solvent is not to interfere with the action of the potentiated medicament. One possibility is that the alcohol slightly intoxicated the animal and made its sleep pattern more stable, but this would be hard to reconcile with the reduction in coherence due to the potentiated m e d i c a m e n t , w h i c h c o n t a i n s the s a m e a m o u n t o f alcohol per v o l u m e , without i n v o k i n g a d o u b l y - s t r o n g action by the homoeopathic agent, capable in this case of countering an opposite tendency from the s o l v e n t alone. It c o u l d also be that the increase reflects an ongoing healing process after the t r a u m a o f t r e p a n a t i o n . In the
British Homoeopathic Journal
204 a b s e n c e o f a d e q u a t e e v i d e n c e to c h o o s e a m o n g these and other alternatives, w e cons i d e r this an o p e n p r o b l e m t h a t c e r t a i n l y merits further attention. The unexpected effect of the solvent (increasing E E G coherence) forced us to d e f m e a new control group, with animals that received only pure water throughout the experiment. T o this end w e prepared 6 rats in the
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FIGURE 3. Correlation time for the same data as in Figure 2. Medicine and solvent intake correspond to continuous and broken lines, respectively. The separation of average correlation times from solvent and medicine, with one above and one below the horizontal line at null deviation, is again highly significant, with p = 0.001. la
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FIGURE 2. Pearson correlation of EEGs from rats taking homoeopathic N u x vomica (continuous line), and from rats taking only the solvent of this medicine (alcohol: broken line). Each point corresponds to 30,000 consecutive filtered data values, or about 1.5 hours of observation (see text), and represents the per cent deviation of the Pearson correlation from its reference value, defined for pure water intake during the first day. Paired points correspond to data taken simultaneously from two different rats, one ingesting Nux vomica and the other solvent alone, mixed with drinking water. (One exception to this rule: the last pair of points come from measurements taken 5 days apart due to technical difficulties, under conditions as similar to each other as possible). Horizontal ordering of paired points is chronological and numbers indicate different pairs of animals; letters next to a number label consecutive 30,000-point data sets from the same pair of animals. Error bars represent the standard error of the m e a n (standard deviation)/~/n, with n the number of points in the plot), and are drawn just once for the sake of clarity. The average values from the upper and lower graphs are as follows: 5.67 + 1.66 (solvent), and - 6.82 _+ 2.98 (medicament). The separation of these two average values, one above and one b e l o w zero, is highly s i g n i f i c a n t (p v a l u e = 0.0007, with a one-sided distribution.17)
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FIGURE 4. Energy fraction in lowest frequencies for the same data as in Figure 2. This fraction was calculated in the following way: the fourier power spectrum was obtained for each set of 30,000 points; it contained 15,000 energy values corres p o n d i n g to the s a m e n u m b e r of d i f f e r e n t frequencies. The first 1,000 of them were then added together and the result divided by the sum of all 15,000 values and multiplied by 100. Graph convention is the same as in Figure 1, and the separation of average energy fraction values from medicine and from solvent is again highly significant, with p = 0.009. The signal's energy content at low frequencies measures the relative weight of its long-period oscillations, which in turn reflect its degree of coherence: a large content of longp e r i o d o s c i l l a t i o n s g e n e r a l l y i m p l i e s a long correlation time and a high self-correlation.
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Volume 86, October 1997 140
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a conceptual f o u n d a t i o n for homoeopathic veterinary therapies. 6, 7 To substantiate this claim we must perform similar m e a s u r e m e n t s in other a n i m a l s commonly used in medical studies and several other homoeopathic medicines with a definite effect on the human central nervous system, the b l o o d circulation and other sources of detectable electrical voltages. W o r k along these lines is currently in progress.
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FIGURE 5. Effect of pure water. 6 rats were given pure water to drink during 2 days, and their EEGs recorded and filtered in the same way as before. Each point corresponds to a set of 30,000 voltage values, and represents the per cent variation of a specific parameter (Pearson correlation, correlation time or energy fraction at lowest frequencies), with respect to its reference point, defined as its magnitude calculated from the initial data (first day). Convention for numbers and letters next to them is the same as in Figure 2. Standard error bars for correlation time and Pearson correlation were not drawn, as they were about the same size as the symbols used for individual points. The average effect of pure water can be considered null, as the opposite possibility (its average being significantly different from zero) implies p values greater than 0.05: p = 0.338 (Pearson correlation), p = 0.26 (correlation time), p = 0.06 (energy fraction at low frequencies).
same way as before, but gave them pure water to d r i n k d u r i n g the 2-day i n t e r v a l of data recording. Our results are plotted in Figure 5, which shows a random effect on self-correlation, c o r r e l a t i o n t i m e and l o w - f r e q u e n c y energy content of the signal. Our results suggest a method to characterize the homoeopathic effect, using animal models for c e r t a i n d i s e a s e s , a n d p a r a m e t e r s like those that showed systematic changes in this s t u d y . S u c h a m e t h o d w o u l d p e r m i t the design of research procedures to minimize the subjective element in various kinds of homoeopathic research. They also contribute to the task of furnishing a scientific basis for extensions of H a h n e m a n n ' s principles (similitude and potentiation through dilution and succusion) to animals, 4, 5 a necessary step to build
Acknowledgement We thank QFB Leticia Perez Ordaz for help and advice on electrode and rat manipulationtechniques. References 1 Reilly DT, Taylor MA, McSharry C, Aitchison T. Is homoeopathy a placebo response? Lancet 1986; 18 October: 881. 2 Resch G, Gutman V. Scientific Foundations o f Homoeopathy. Germany: Barthel und Barthel 1987. 3 Hahnemann S. Organon o f Medicine. Blame, Washington: Cooper Publishing 1996. English translation of the 6th edition of the original work. 4 Davenas E, Poitevin B, Benveniste J. Effect on mouse peritoneal macrophages of orally administered very high dilutions of silica. European J Pharmacol 1987; 135: 313. 5 Fisher P, House I, Belon P, Turner P. The influence of the homeopathic remedy Plumbum metallicum on the excretion kinetics of lead in rats. Hum Toxicol 1987; 6: 321. 6 Searcy R, Reyes O, Guajardo G. Control of subclinical bovine mastiffs. Br Hom J 1995; 84: 67. 7 Guajardo G, Searcy R, Soto J. Growth promoting effect of sulphur 201c in swine herds. B r Horn J 1996; 85: 15. 8 Torres J-L, Ruiz G. Stochastic resonance and the homoeopathic effect. Br Hom J 1996; 85: 134. 9 Ruiz G, Torres J-L. A possible characterization of the homoeopathic effect. Br Hom J 1997; 86: 4. 10 Paxinos G, Watson C. The rat brain in stereotaxic coordinates. 2nd edition. New York: Academic Press 1986. 11 Rechtschaffen A, Kales A, eds. A manual o f standardized terminology, techniques and score s y s t e m f o r sleep stages o f h u m a n s u b j e c t s .
Bethesda, Maryland: US Department of Health, Education and Welfare 1968. 12Cheng C. A c t i v e f i l t e r design. New Jersey: Hayden Book Co. 1982. 13 Grassberger P, Procaccia I. Characterization of
206 strange attractors. Phys Rev Lett 1983; 50: 346. 14Berge P, Pomeau Y, Vidal C. Order within chaos. New York: John Wiley and Sons 1984. 15 Kaspar F, Schuster HG. Easily calculable measure for the complexity of spatiotemporal patterns, Phys Rev A 1987; 36: 842.
Address for correspondence Ma. Guadalupe Ruiz V. Lluvia # 120 Prados del Campestre 58297 Morelia Michoac~_n Mexico
British HomoeopathicJournal 16Vijnovsky V. Tratado de Materia Medica Homeoptica. Buenos Aires: Macagno, Landa & Cia 1981. 17 Bethea RM, Duran BS, Boullion TL. Statistical Methods for Engineers and Scientists. New York: Marcel Dekker 1985.