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Statistical analysis of physiologic signals
María G. Ruiz & Leticia Pérez.
Laboratory of Biophysics, Institute of Physics and Mathematics, University of Michoacan at, Morelia, Mich., México. Cp.58040.
Background
In spite of two hundred years of clinical practice, Homeopathy still lacks of scientific basis.
Its fundamental laws, similia principle and the activity of the denominated ultra-high dilutions are controversial issues that do not fit into the mainstream medicine or current physical –chemistry field as well. Aside its clinical efficacy, the identification of physical – chemistry parameters, as markers of the homeopathic effect, would allow to construct mathematic models [1],which in turn, could provide clues regarding the involved mechanism.
Objective
The general goal is to characterize the homeopathic effect by means of physical chemistry parameters, which should be objective, systematic and repetitive under methodical procedures [2,8]. In this context, as basic mechanisms are involved, the biological effects of ultra – high – dilutions are studied on living beings.
The assessment of the above parameters is not a trivial matter; to make it a practical tool in clinical practice would be an immediate goal. However, the first implication would be to simplify communication with other knowledge fields i.e. physics , chemistry or mathematics, through a common terminology regarding homeopathic effect. In fact, the scope would exceed the homeopathic field as current thermodynamics concepts should be reviewed, and new ones should be coined to deal with a specific kind of solutions without solute.
Method
In a wide context, our general method relies in the fact that living beings emit electric signals; according to their source, they could be of different nature i.e. EEG, EKG, photopletismographic, etc.
It is expected that when a stimulus was applied those physiologic voltages would change, perhaps in a subtle way. Mathematical analysis (lineal and no-lineal) would reveal those slight changes, which must be systematic, repetitive and objectively related to the expected physiologic outcome.
We have focus on electroencephalogram (EEG) [3,6] and electrocardiogram (ECG) [7] study, as their alterations are related to relevant health disturbances.
Particularly, the record and further analysis of these signals through sleeping time would avoid bias due to a possible interference of subject awareness.
EEG Method
EEG generation
The electrical current producing voltage fields as recorded by the EEG at the scalp, originates entirely from the cortex and is due to changes in conductance of the neuronal membranes. It is mainly due to synaptic activity rather than the action potentials. The polarity of the potential recorded at the cortical surface is dependent upon the character, location, duration, and interaction of the synaptic activity. Rhythmic variation in the voltage at the cortical surface is due to synchronization of neuronal elements in the specific projection nuclei of the thalamus through the mechanism of recurrent inhibition. The recurrent inhibitory loop in turn is regulated to some degree by the diffuse projection system of the thalamus with its appropriate behavior correlates [8].
EEG in sleep
Nowadays, sleep condition is characterized through three main brain rhythms: spindles (7-14 Hz), delta waves (0.5-4 Hz) and slow (< 1 Hz) oscillations [8] (all of them have been detected during the sleep/wake cycle of a freely-moving rat [9]), and the evaluation of sleepdisorders through the electroencephalogram (EEG) power spectra recorded during sleep time is a well developed area. Regarding insomnia, the main marker is associated with “sleep homeostasis”, which is the propensity of the sleep regulating system to keep a regular level of sleep. Sleep loss propitiate a balancing counteraction which evolves as an increase in sleep intensity [10]. One of the main markers of the intensity in non-rapid-eye-movement (non-REM) sleep is EEG slow-wave activity, which can be defined as the spectral power density in delta band [11], this definition is kept because the majority of the authors refer to it as stated in spite of the existence of the novel slow rhythm (< 1 Hz). To avoid confusion, in this paper, the term slow wave or slow rhythm will be used to name <1 Hz oscillations; slow wave activity will be identified as the spectral power density in delta band).
Slow frequency (<1 Hz) oscillations in EEG were recently identified in neocortical activity [12]. Relations between slow and delta rhythms become evident through two main interactive mechanisms [13]: the EEG delta waves grouping with a periodicity of 0.3 Hz and the correlation between both rhythms reflecting the increase in cortical and thalamic synchronization. Power ratio between 0.32-0.48Hz ( 0.3Hz) over delta (slow/delta power ratio) can reflect the level of such coordinated activity between thalamic and cortical networks.
EEG record
Three 1.5 mm diameter stainless steel electrodes (resistance < 0.1 ) are implanted in the animals' cranium vault. The electrodes are set on the skull by means of trepanation with a hand-held Foredom drill , securing them with dental resin, so they could be wired to a multichannel amplifier. Before trepanation, each rat is intraperitoneally anaesthetized with 40 mg of pentobarbital sodium per kilogram of body mass. Two of the electrodes are implanted bilaterally in the parietal region, and one in the frontal area for reference (ground). Trepanation points are spotted stereotaxically and correspond to the following stereotaxic coordinates: 3.8 mm posterior to Bregma and 4.5 mm lateral to the side of central line for the bilateral electrodes. Stereotaxic coordinates were determined according to Paxinos and Watson map[14]. After implantation, a 6-day recovery period took place followed by a further day light conditioning one-day period in which the electrodes were connected to a signal amplifier by a cable that allowed the animal freedom of movement. Next day measurements started.
Set up
They werehoused individually in wooden cages built on purpose to avoid external disturbances but allowing their observance. Temperature was held constant at 29 0.5 oC, in order to avoid sleep pattern alterations by unforeseen temperature variations[15 ].
Each subject was connected to a 15A54 Grass amplifier module, its controls set as follows: sensitivity 20.0 V/div, display gain 1, band-pass filter 0.3-35 Hz, line filter on. The output was sampled at 8 Hz and online digitized with a National Instruments AT-MIO-64E-3 card and PolyView v 2.0 software. The outcoming numerical register was stored in a computer for mathematical analysis. Sampling frequency was chosen taking into account delta band features as well as the Nyquist theorem.
Mathematical analysis
Before any mathematical operation, the register is visually examined and noisy segments due to eventual disconnection or external artifacts (body movement) are eliminated.In order to eliminate the frequencies outside the selected bands, two sequences of filtering were similarly performed:
a)A band-pass filter with low and high cutoff frequencies, 0.5 and 2.5 Hz respectively.
As EEG delta waves are the essence of deep non-REM sleep, in this research non-REM activity as a marker of sleep intensity was estimated through our own marker defined as spectral power density in 0.5-2.5 Hz band evaluated in the complete filtered 0.5-2.5 Hz noise-free file. As a fact, such domain constitutes non-REM main frequency component. Even more, it exceeds those of waking and rapid-eye-movement (REM) sleep in two and one order of magnitude respectively, so it could be correlated to slow wave non-REM activity. Besides, results obtained from caffeine administration supports the adequacy of this selected marker as indicator of sleep intensity.
b)A low-pass filter with 2.5 Hz cut frequency. The spectral power density in 0.32-0.48 Hz ( 0.3Hz) band was also evaluated; power ratio between 0.3Hz over 0.5-2.5 Hz (delta) band “slow/delta power ratio” was subsequently calculated..
The filtered data are subjected to a Fast Fourier Transformation (FFT) algorithm and the chosen band power is computed for such file according to the periodrogram method.
ECG Method
ECG generation
The rhythmic cardiac impulse originates in pacemaking cells in the sinoatrial (SA) node, located at the junction of the superior vena cava and the right atrium. Primarily through the tree specialized pathways (anterior, meddle, and posterior internodal tracts) between the SA and atrioventricular (AV) nodes. Bechmann’s bundle (interatrial tract) come off the anterior internodal tract leading to the left atrium. The impulse passes from the SA node in an organized manner through specialized conducting tracts in the atria to activate first the right and then the left atrium. Passage of the impulse is delayed at the AV node before it continues into the bundle of His, the right bundle branch, the common left bundle branch, the anterior and posterior divisions of the left bundle branch, and de Purkinje network. The right bundle branch runs along the right side of the interventricular septum to the apex of the right ventricle before it gives off significant branches. The left common bundle crosses to the left side of the septum and splits into the anterior division (which is thin and long and goes under the aortic valve in the outflow tract to the anterolateral papillary muscle) and the posterior division (which is wide and short and goes to the posterior papillary muscle lying in the inflow tract) [16].
Heart Rate Variability (HRV)
Heartbeat rate has been related in recent years to some holistic features of the blood circulation system. Its power spectrum shows fractal behavior at low frequencies and some cardiac pathologies seem to be correlated with an excessive simplification in its spectral composition, like the appearance of one or more dominant frequencies [17].
A significant relationship between autonomic nervous system and cardiovascular mortality, including sudden cardiac death, have been identified through the last two decades [18].
Spectral analysis of RR interval variability provided quantitative markers of sympathetic and vagal (autonomic) control of the sinus node and of sympathetic modulation of vasomotor tone. With this approach, the low-frequency, LF ( = 0.1 Hz) component of RR interval is considered a marker mainly of sympathetic activity , whereas the high-frequency, HF ( 0.25 Hz) component of RR interval variability, associated to respiration, seems to be a marker primarily of vagal activity.
It is possible to detect a pronounced and consistent reduction in the markers of sympathetic activity and an increase in those of vagal activity during the night.
Noninvasive studies confirmed the early morning rise of the markers of sympathetic activity and the circadian pattern of sympathovagal balance.
Results suggest that at about 6:00 am the pattern of neural cardiovascular control begins to undergo a drastic and rapid rearrangement characterized by a rise in sympathetic drive to the heart and blood vessels and a simultaneous reduction of vagal cardiac activity. It has been hypothesized that these fast neural changes facilitate the higher rate of cardiovascular acute events appearing in the morning
These data indicate that the menacing increase in rate of cardiovascular events in the morning hours may mirror the sudden rise of sympathetic activity and the reduction of vagal tone [19].
ECG record
Five electrodes are attached on the chest (right and left clavicles, next to the sternum, fifth left intercostals space, under the axial; fourth right intercostals space, at the edge of the sternum, and lower right thoracic wall, ground); the electrodes are then connected to an ambulatory recorder. This signal is recorded on the tape of the recorder. To digitize the audio signal, the tape is played back, and the output is sampled and digitized through a DAQ. The output of the card is then stored in a computer for further analysis.
An implanted TA11CA – F40 (DSI ) transmitter (according instructions) emits a radio signal, which in turn is first converted to analog and by means a DAQ.
Mathematical analysis
If it is necessary, the signal is filtered as first step.
QRS complexes are located in time. A series S1 = { T1 , T2 , …..} is obtained from each file , where Tj is the time of occurrence of the jth beat (or more precisely, of the Speak in its QRS complex).
From the series of data S1, a series S2 of time intervals between consecutive beats is further obtained, S2 = {T1 , T2 , …..}, where Tj = Tj +1 , Tj ,and from S2 the series that measures heartbeat variability, defined as S3 = { V1 , V2 , ….., with Vj = Tj +1 , Tj.
FFT algorithm is applied to series S3, LF and HF peaks are further identified in a spectral density vs. frequency diagram.
RESULTS
The research results are shown and fully discussed in ref 1-7, and resumed as followed.
1 Potentization of homeopathic medicines by successive dilutions and succussion at each step is interpreted in terms of stochastic resonance, a non-linear response of certain systems when perturbed by noise and a weak periodic signal, which increasingly enhanced at the output as the magnitude of the noise grows towards an optimal value for maximum signal amplification. The possible relevance of stochastic resonance in other physiological phenomena like the kindling effect, where epileptic convulsions are induced in rats and other animals by periodic stimulation of the brain with weak electric signals, is also considered.
2 Electrical signals from a photoelectric plethysmograph are used to test peripheral blood circulation as a source of a homeopathically relevant parameter that will vary in a reproducible and systematic way following exhibition of specific medicines in homoeopathic doses. Mathematical treatment of the signals gives a Fourier power spectrum with an approximately linear profile (in a long-log plot) at the lowest frequencies. The gradient of this line seems to meet the above requirements of reproducible and systematic variation under a homeopathic stimulus, and this is our basis to propose an analogous treatment for other electrical signals from the body especially those from the heart and brain.
3 The effect of Nux vomica on the EEGs of rats during sleep was quantified in terms of suitable statistical parameters that showed systematic changes after the homeopathic 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 homeopathic effect in physicochemical terms, based on parameters similar to those found appropriate in this study, calculated for physiological date 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.
4 To investigate the effect of the homeopathic medicine Coffea cruda on sleep patterns, it was orally administered to rats at the beginning of their waking period EEG from the parietal region was recorded during their next sleep cycle. Applying an FFT algorithm, spectral in the δ band 0.5-2.5 Hz, was chosen as a marker parameter, evaluated for control and verum groups using a double-blind protocol. Power in the verum group was statistically higher than baseline value. It was not statistically different in the control group. The results indicate that an enhancement in EEG slow delta activity is associated with Coffea cruda.
5 The effect of Coffea cruda 30 and 200c and caffeine on the sleep pattern of rats were investigated. Treatments were administered orally at the beginning of the sleeping period. EEG from the parietal region was recorded. Delta (0.5-2.5 Hz) and slow (‹ 1Hz) waves are two of the major oscillation types that characterize neocortical electrical activity. The spectral power in these bands and the power ratio between 0.32-0.48 Hz and the delta band (slow/delta power ratio) for control and treatment groups were analyzed blind. Power in the delta band was significantly higher than baseline for Coffea 30c and caffeine (15.5 mg/kg). An increase in the slow/delta power ratio between control and treatment was detected for Coffea cruda 30 and 200c. Coffea 30c and caffeine have similar effects on sleep pattern, enhancing delta power; Coffeacruda 200c appears to affect only the synchronization.
6Coffea crudabiological effect was investigated in two conditions:
1) Coffea cruda effect on caffeine pre-administered subjects (Pre),
2) Coffeacruda effect plus post-caffeine administration (Post).
In both cases experimental subjects were male Wistar rats. Caffeine was pre or post Coffea cruda administered, i.p. to sets Pre and Post respectively at the beginning of the rats sleeping period. Coffea cruda 30c (0.1 ml) was post or pre orally provided; simultaneously, in both sets, a control group was tested. To investigate their effecton sleep pattern, the EEG was recorded on parietal region during the same sleep cycle and the aftereffect was evaluated by means of three EEG parameters: the spectral power in both, delta (0.5-2.5 Hz) and slow 0.32-0.48Hz (0.3Hz) bands as well as the power ratio between slow (0.3Hz) over delta band (slow/delta power ratio). These markers were analyzed vs. time for control and homeopathic stimulated groups under a double blind protocol. In Pre set, a similar logarithmic pattern was identified for both, control and verum groups up to the 4th hour. From the 5th hour on, power in delta band (as percentage) was statistically higher in verum group; whereas, both spectral power in slow band and power ratio for Coffea cruda 30c group were smaller than those parameters for control group from the 6th hour on. In Post set, two verum sub-groups were identified: