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MODIFICATION OF 4 MHz N.M.R. WATER PROTON RELAXATION TIMES
IN VERY HIGH DILUTED AQUEOUS SOLUTIONS

NMR Relaxation in Very High Diluted Aqueous Solutions

J.L. DEMANGEAT ¹, P.GRIES ¹, B .POITEVIN ²

¹ Nuclear Medicine Department, General Hospital, Haguenau, France

² French Association for Homeopathy Research, Vendat, France

1 - Introduction
2 - Preliminary Experimental Considerations
3 - Preparation of Potencies and Particular Conditions of the Study
4 - Results
5 - Discussion

1. Introduction

The NMR properties of water in the vicinity of molecules in solution differ from those of water in the pure state. Water molecules interact with the solute via hydrogen bonds and/or electrostatic forces related to their high dipolar momentum. At room temperature, the correlation times t of rotational and translational movements, of the order of 10^-11 to 10^-12 s in pure water may increase to 10^-8 or even 10^-6 in the hydration layer of macromolecules (Packer, 1977; Fung, 1977; Mathur-DeVré, 1979), giving rise to a drastic reduction in T1 and T2 water proton NMR relaxation times from 2-3 s to a few hundred milliseconds. Similarly, lowering the temperature of pure water promotes hydrogen bonding and affects relaxation in the same way as the introduction of a solute, leading to water correlation times as high as 10-5 s in ice (Glasel, 1972). Due to the wide 10-5-10-11 s range in correlation times observed in biological or non biological systems, NMR relaxation in the 1-100 MHz domain is one of the potent techniques capable of demonstrating modifications in the mobility and degree of organization of water molecules in solutions or tissues, although it is not very precise in determining the absolute structure. NMR medical imaging is a clear strong successful application of this principle.

Experimentally, protons of H₂ O possess a magnetic spin (I=1/2) which align along an external magnetic field Bo; in the mechanical description of NMR phenomenon, excitation of the solution by an electromagnetic wave in the radiofrequency field causes absorption of energy by protons and their displacement from initial orientation; maximal absorption occurs when the excitation frequency equals the Larmor free precession of the protons (42.57 MHz/T) in the applied magnetic field Bo (Tesla), achieving thus the Nuclear Magnetic Resonance conditions. After release of the radiofrequency excitation, protons realign along the Bo direction (Relaxation) at a rate which can be described by a time constant observed in the direction of Bo (T1=longitudinal or spin-lattice). A second time constant (T2=transverse or spin-spin) characterizes the disappearance of the NMR signal in the plane perpendicular to Bo. Relaxation is a complex process resulting from the dipolar magnetic interaction between adjacent intra and intermolecular protons, the molecular movements of rotation and translation, the exchange of protons between neighbouring molecules and the presence of paramagnetic substances (Mn⁺⁺, Cu⁺⁺, Fe⁺⁺, Fe⁺⁺⁺, free radicals, molecular O₂...). These mechanisms are moreover strongly influenced by temperature. For an isotropic molecular movement that can be described by a unique correlation time t (this is the case of liquid water where rotation and translation are strongly coupled):

1/T1 = C {2t /(1 + w_o²t²) + 8t /(1 + 4 w_o²t² )} (1)

1/T2 = C {3t + 5t /(1 + w_o²t²) + 2t /(1 + 4 w_o²t²)} (2)

where w_o is the Larmor frequency, i.e. 4 MHz in our study. For movements which are rapid compared to Larmor frequency, T1 and T2 are equal, long and independent of the frequency. When movement is limited, both T1 and T2 decrease, the latter more rapidly, and become frequency dependent: rapid movements influence T1 and T2 but those of low frequency influence primarily T2. T2 can become much lower than T1, since any process influencing T1 necessarily influences T2 while the reverse is not true. So, the T1/T2 ratio is a more sensitive parameter than T1 and T2 separately.

If NMR is known as a powerful tool to study dynamics of water in biological and non biological systems, what about aqueous high dilutions such as those used in homeopathic practice? The obvious advantage is given by the abundance of water generating quasi-maximal and constant signal/noise ratio in opposite to techniques designed to detect the solute and which become ineffective at high dilution. But at least two main difficulties arise: first relaxation is very slow in quasi-pure water, thus particularly sensitive to temperature and contaminants, especially the paramagnetic ones among them dissolved atmospheric oxygen is the most common. Second, very minor modifications are expected, hardly distinguishable from random experimental fluctuations. So, in this field of high dilutions, a drastic controlled protocol is required for preparation and measurements. In a preliminary part of this work we exhaustively examined several experimental chemicophysical sources of variations and their influence on NMR measurements.

2. Preliminary Experimental Considerations

2.1. NMR MEASUREMENTS

Measurements were carried out on an inframillimetric NMR imaging device especially developed in our laboratory and purposed for the study of the biomechanics of the arterial wall (Gries and Constantinesco, 1987; Constantinesco et al, 1989); it consisted in a 4 MHz Bruker PC104 Minispec connected to a Drusch EAF 16A 0.09406 Tesla resistive magnet with a 5.18 cm air-gap and a central field uniformity of ± 10 ppm. The radiofrequency transmitter-receiver coil was 7.5 mm in diameter and 19 mm in height. Standard Bruker 7.5 mm diameter test tubes were used, the filling level (1.5 ml) and the position in the coil of which were strictly controlled. A temperature of 1 ± 0.2 °C was achieved by circulation of cryostatic proton-free fluid (Fluorinert FC 40) and controlled by thermocouple. According to Glasel (1972) such a stability corresponds to maximal variations in relaxation times of about 12.5 ms. T1 was determined using the inversion-recovery method and a monoexponential fitting of an 8-points experimental curve; error on the computerized fitting was in the range 10-25 ms. Each sample was measured at least 10 to 15 times. T2 was determined by the Carr-Purcell-Meiboom-Gill sequence and monoexponential fitting of a 160-points curve, with a fitting error of 2-15 ms. Each sample was measured 15 to 20 times.

2.2. PRELIMINARY CONTROLS

Since dissolved O₂ in the test samples is a powerful proton relaxant, variability in relaxation times due to uncontrolled PO₂ levels resulting from preparation should be evaluated. All procedures were carried out under a laminar-flow exhaust hood set to laboratory temperature. Before use, all solvents or solutions were equilibrated to temperature under the hood over 30 min. All pipetting/sampling procedures were performed with single-use Eppendorf tips. PO₂ measurements (Corning 158 blood analyzer) were carried out within a maximum of 20 min on samples collected using a 2 ml plastic syringe without a needle, by carefully avoiding any intrusion of air. Detailed procedures for preparation of potencies are given in section 3.

2.2.1. Influence of Barometric Pressure

It is well-known that atmospheric oxygen dissolves proportionnally to partial pressure according to Henryís law. In water samples vortexed during 60 s in contact with air, a linear relationship between dissolved PO₂ and barometric pressure was indeed found (figure 1) but with a higher slope than expected, indicating enhancement of dissolution by the agitation process.

Figure 1. O₂ partial pressure dissolved in pure water samples vortexed during 60 seconds in contact with air at laboratory temperature as a function of barometric pressure at the time of preparation (samples from the same batch). Dotted line: relationship expected from Henry's law in non agitated samples (PO₂ = 0.21Patm).

The relaxant effect of dissolved O₂ on water protons is shown on figure 2, where a decrease of about 40 ms in T2 is induced by a 20 mmHg increase in barometric pressure; such fluctuations in laboratory conditions may be current. The linear relationship observed corroborates the dependence between relaxation rates (1/T) and No, the number of O₂ molecules per milliliter in pure water (Glasel, 1972):

1/T1 = 0.284 + 4.55 . 10^-19 No (3)

1/T2 = 0.455 + 5.25 . 10^-19 No (4)

Figure 2. Relaxation rate 1/T2 of water samples as a function of barometric pressure at the time of preparation (results from 19 experiments). Samples from the same batch were equilibrated in contact with air at laboratory temperature without agitation for 15 min before NMR measurement.

Figure 3. Influence of the vortexing duration in contact with air on atmospheric O₂ dissolution (results of 7 experiments with water, saline or 3CH Sil/Lac samples). PO₂ for each sample corresponds to the asymptote calculated from the 50, 60 and 70 s durations average.

2.2.2. Influence of Vortexing Duration on Atmospheric Oxygen Dissolution

O2 dissolution was proportional to duration up to 10 s; beyond this, dissolution became asymptotic with maximal deviations of 2 to 2.5% of the PO2 value (figure 3).

2.2.3. Influence of the Dilution/Agitation Process on Atmospheric Oxygen Dissolution

Dissolved O₂ was determined in successive centesimal dilutions/agitations over the whole range concerned in the study (figure 4). The dilution/agitation process itself, when performed over a short period of time, was unlikely to produce PO₂ variations exceeding 2.5% either for diluted substances or for solvent.

Figure 4. Influence of the centesimal dilution/agitation process in contact with air on atmospheric O₂ dissolution (constant vortexing duration of 60 s). PO₂ (dil) was standardized in each case to PO₂ , the mean value of the 3 highest dilutions 13CH, 14CH and 15CH.

2.2.4. Implications

According to pharmacopea, potencies used in homeopathy are prepared in the presence of air; moreover it has been argued that they were ineffective when prepared under pure nitrogen (Cazin et al, 1991). So it would not be logical that physicists working on high dilutions solve out the problem by suppressing oxygen, as it is usually done for most NMR studies. In order to ensure a similar if not identical level of dissolved oxygen in samples, 3 conditions must be respected: i) preparation of all samples of a given series within the same day - ii) minimum 20 s vortexing duration at controlled rate for the dilution/agitation process - iii) closing the test tubes for delayed NMR measurements. Despite these precautions, PO₂ fluctuations from about 2 to 2.5% might be observed. For T1 and T2 values from 1.5 to 2 s and according to eqs (3) and (4), such PO₂ fluctuations can produce T1 and T2 variations of 20-25 ms and 5-12 ms respectively. The table 1 summarizes the expected fluctuations despite maximal care in our experimental protocol, which are due to oxygen, temperature and mathematical fitting. Observed standard deviations in solvents are found of that order or slightly greater, as logically expected; the maximal differences between high dilutions and solvents will hardly exceed these values, indicating very minor modifications, attesting thus the need for a drastically controlled protocol.

TABLE 1. Expected and observed experimental variations

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T1 T2

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Expected fluctuations

- Dissolved O2 2.5 % 20 -25 ms 5 - 12 ms

- Temperature 0.2 °C 12.5 ms 12.5 ms

- Monoexponential fitting 10-25 ms 2-15 ms

- Total 42.5 - 62.5 ms 19.5 - 39.5 ms

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Standard deviation

observed in solvents * 57 - 69 ms 30 - 32 ms

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Maximal mean value differences

observed between solutions or 52 ms 49 m

solvents*s

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* From Table 2 data

3. Preparation of Potencies and Particular Conditions of the Study

Two successive experiments are described. In the first one we study Silica/Lactose (Sil/Lac) saline potencies above 3CH (dilution level 106) which were previously demonstrated by Davenas et al. (1987) to be active at very high dilution on mouse peritoneal macrophages when administered in drinking water; the production of paf-acether, a mediator in allergy and inflammation, was significantly increased in the isolated, zymosan-stimulated macrophages of the mice. The effect was found at a dilution level as high as 10¹⁸ (9CH). The involvement of silica as active constituent (lactose being an excipient) was attested from controls receiving saline, lactose or a non-specific substance (Gelsemium) at the same level of dilution. Besides, in homeopathic physiciansí all-day practice the effect of Silicea (Sil/Lac) in recurring infections and chronic suppurations is one of the most regular clinical observations. In the second experiment additional Manganese/Lactose (Mn/Lac) and Histamine (Hist) aqueous dilutions were studied simultaneously as Sil/Lac in saline. Manganese was chosen as a control due to its paramagnetism, in order to evaluate a possible influence on water proton relaxation at high dilution; histamine was chosen because, as for Sil/Lac, biological effects have been reported at high dilution (Sainte-Laudy and Belon, 1993). All samples were prepared by the Laboratoires Homéopathiques de France.

3.1. FIRST EXPERIMENT (WATER - SALINE - SIL/LAC)

Silica dioxyde (insoluble) was first homogenized by three successive triturations with pure lactose than added with 0.9% NaCl saline (0.3 g in 3 ml). This initial solution was successively diluted to 1/100th strength 13 times by addition of 0.3 ml to 30 ml 0.9% NaCl (Aguettant, pH 6.0-6.9), using a pipette the plastic tip of which being discarded after each operation, under controlled agitation of the mixture in a Cenco Vortex rate 5 for 25 seconds. Subsequently only 5 centesimal dilutions were retained (3CH, 6CH, 9CH, 12CH, 15CH) corresponding to 10⁶-10¹²-10¹⁸-10²⁴-10³⁰ dilution levels and containing theoretical silica concentrations of 1.66.10^-5 M to 1.66.10^-29 M and lactose concentrations of 2.92.10^-3 M to 2.92.10^-27 M. As references, 0.9% NaCl and distilled water (Meram, pH 6.5-7.5) were submitted to identical concomitant cycles of dilution/agitation and also called centesimal dilution although the term dilution was inappropriate. All samples of a given series (Sil/Lac, water, saline) were imperatively prepared on the same day. After filtration by 0.22m Millipore, precise 1.5 ml aliquots of these dilutions were directly deposited in the NMR Bruker PC 7.5 test tubes previously cleaned with ether, copiously rinsed with bidistilled water and autoclaved. These tubes were flame-sealed and labeled with a code number for NMR measurements. Seven independent series of all samples were prepared on a monthly basis, using new solvent batches each time.

Figure 5. Correspondance between centesimal designation (CH), dilution level and molar concentrations.

3.2. SECOND EXPERIMENT (WATER - SALINE - SIL/LAC - MN/LAC - HIST)

Among four new independent series of Sil/Lac, saline and water, three series of Manganese/Lactose (Mn/Lac) and Histamine (Hist) dilutions were prepared in the same conditions except that the solvent was water instead of saline and the first potency was 4CH instead of 3CH, in order to minimize a potential effect of the magnetic (Mn) and protonated (Hist) solutes on the NMR signal. As manganese is insoluble, Mn/Lac was prepared from triturations in lactose, as for Sil/Lac. In final retained samples (4CH, 6CH, 9CH, 12CH, 15CH), manganese concentrations ranged from 1.82.10^-7 M to 1.82.10^-29 M and lactose concentrations from 2.92.10^-6 M to 2.92.10^-28 M; histamine ranged from 9.8.10^-8 M to 9.8.10^-30 M.

3.3. SUMMARY OF THE SPECIAL CONTROLLED CONDITIONS OF THE STUDY

. Preparation under laminar-flow exhaust hood

. 25 s vortexing at controlled rate

. Discarding pipette tip for each operation

. One-day preparation for all samples of a given series

. Several independent series using new batches of solvent

. Samples Millipore-filtered and flame-sealed

. Code-labeling for blind NMR measurements

. 0.2"C temperature stability during NMR measurements

. Code only broken at the end of the second experiment

4. Results

4.1. FIRST EXPERIMENT (WATER - SALINE - SIL/LAC)

4.1.1. Saline Versus Water

The relaxation times of pure water at 1°C were found slightly lower than those reported in the literature (Engel and Hertz, 1968; Cope, 1969; Glasel, 1972; James and Gillen, 1972), probably due to a higher level of dissolved O₂ resulting from the dilution/agitation process. Saline differed from water by a lower T2 (1366 ± 30 ms and 1415 ± 32 ms respectively) and a higher T1/T2 ratio (1.127 ± 0.046 and 1.082 ± 0.032 respectively); but there was no significant difference in T1.

TABLE 2 . Relaxation times (ms) measured in Experiment 1.

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Substance Dil. (CH) N T1 T2 T1/T2

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Saline 0-1-3-6-9-12-15 48 1538 ± 69 1366±30 1.127±0.046

Water 0-1-3-6-9-12-15 47 1526 ± 57 1415±32 1.082±0.032

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Saline 3-6-9-12-15 34 1533 ± 67 1371±30 1.121±0.036

Sil/Lac in saline 3-6-9-12-15 34 1570±73 1367±35 1.148 ± 0.053

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Saline 9-12-15 20 1520 ± 67 1375±30 1.109± 0.032

Sil/Lac in saline 9-12-15 21 1572 ± 86 1370 ± 37 1.145 ± 0.061

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Such a result could be expected as it reflects the orientation and reduction in mobility of the dipolar water molecules in the powerful electric field of Na⁺ and Cl^- ions, since T2 is more sensitive than T1 to restriction of movement. It should be noted in support of our results that Engel and Hertz (1968) also reported the absence of decrease, and even a slight increase, in T1 values of inframolar NaCl solutions.

4.1.2. Sil/Lac in Saline Versus Saline

The Sil/Lac solution differed from its saline solvent by higher T1 (1570 ± 73 ms and 1533 ± 67 ms respectively) and higher T1/T2 values (1.148 ± 0.053 and 1.121 ± 0.036 respectively) without significant variation in T2. Moreover, differences did persist when the least diluted samples (3CH and 6CH, possibly containing subponderal amount of solute) were excluded from analysis; in the Sil/Lac dilutions thus remaining under consideration and which were still different from the solvent, there only remained theoretical concentrations lower than 1.66.10^-17 M silica and 2.92.10^-15 M lactose. These changes observed in Sil/Lac dilutions were unexpected and paradoxical: T1 found to be higher than in pure water appeared in favour of water destructuralization while the T1/T2 increase suggested the reverse. T1/T2 progressively increased from water to saline and from saline to Sil/Lac.

4.1.3. Analysis of Variance and Discriminant Analysis

The two factors variance analysis (factor substance and factor dilution - table 3) clearly showed significant differentiation of substances. T1 recognized Sil/Lac from water and saline, T2 recognized water from Sil/Lac and saline whereas T1/T2 differentiated all substances; differences persisted with an almost identical significance level over the 10¹⁸ dilution (9CH). On the contrary no global significant effect was found with potency, although figure 6 suggested a tendency of enhancement of the changes in the most diluted samples (above 9CH).

Discriminant analysis is a multivariate statistical procedure that enables an optimized grouping of individuals who are described by a set of variables. This analysis provides so-called discriminant functions that are linear combinations of the variables:

F_i (X_j) = S_k a_k x_jk

where F_i is the i^th discriminant function of the X_j individual, a_k the k^th coefficient of this function and x_jk the k^th parameter value for the X_j individual. The coefficients of the discriminant function are calculated so that the between group/within group ratio is maximum. The separation between groups can be evaluated by performing the Wilkís test, or more qualitatively by looking at the well-classified percentage. This analysis demonstrated separation of all substances with a half-plane discrimination between water and saline on one hand and between solvent and solution on the other hand (p<0.021, figure 7). When this analysis was performed above the 10¹⁸ dilution level, the discrimination was no more significant (p = 0.16) but the diagram looked nevertheless illustrative of separation with a 57.1 %, 85.7 % and 100 % of well-classified observations in the water, saline and Sil/Lac groups respectively (non represented).

TABLE 3. Analysis of variance in Experiment 1.

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Dil.(CH) T1 T2 T1/T2

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Factor Substance 3-6-9-12-15 p=0.0008 p<0.0001 p<0.0001

- differentiable Sil/Lac"`Water Saline"`Water Sil/Lac"`Water"`Saline

Sil/Lac "` Saline Sil/Lac "` Water

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Factor CH 3-6-9-12-15 ns ns ns

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Factor Substance 9-12-15 p=0.0013 p=0.0008 p<0.0001

- differentiable Sil/Lac "`Water Saline "`Water Sil/Lac "`Water

Sil/Lac "` Saline Sil/Lac "` Water Sil/Lac "`Saline

________________________________________________________________________________________

Factor CH 9-12-15 ns ns ns

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Multifactorial analysis of variance with interaction - ns: p>0.01.

Differentiable substance determined by Newman-Keuls a posteriori test - ns: p>0.01.

4.2. SECOND EXPERIMENT (WATER - SALINE - SIL/LAC - MN/LAC - HIST)

4.2.1. Sil/Lac in Saline Versus Saline

No significant differences were found between Sil/Lac and saline in experiment 2 comprising fewer series (table 4); T1 values were quite identical and T2 exhibited a slight decrease in Sil/Lac contrary to experiment 1. Nevertheless, a higher T1/T2 ratio was again observed in Sil/Lac with respect to saline which maintained above 9CH. Moreover discriminant analysis succeeded in demonstrating separation of Sil/Lac from saline and from water according to a similar pattern as in the first experiment with 100% of well-classified observations (figure 7). Above the 9CH dilution level, the substances remained separated on the diagram with a 100% amount of well-classified observations (figure 8).

TABLE 4 . Relaxation times (ms) measured in Experiment 2.

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Substance Dil. (CH) N T1 T2 T1/T2

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Saline 3-6-9-12-15 19 1587±75 1575±45 1.008±0.050

Sil/Lac in saline 3-6-9-12-15 20 1581±78 1550±57 1.021±0.040

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Saline 9-12-15 12 1595±68 1576±39 1.013±0.049

Sil/Lac in saline 9-12-15 12 1581±80 1544±54 1.024±0.036

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Water 3-6-9-12-15 15 1591±75 1555±58 1.023±0.022

Hist in water 4-6-9-12-15 15 1623±36 1557±44 1.043±0.020

Mn/Lac in water 4-6-9-12-15 14 1613±26 1560±53 1.035±0.029

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Water 9-12-15 9 1589±78 1561±54 1.017±0.022

Hist in water 9-12-15 9 1629±39 1548±44 1.052±0.014

Mn/Lac in water 9-12-15 9 1616±23 1570±58 1.029±0.034

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Overall data concerning four series of Sil/Lac and three series of Mn/Lac and Hist.

4.2.2. Mn/Lac and Hist Versus Water

T1 was increased in Mn/Lac and Hist compared to water (1613 ± 26 ms and 1623 ± 36 ms respectively; water = 1591 ± 75 ms) as well as T1/T2 (1.035 ± 0.029 and 1.043 ± 0.020 respectively; water = 1.023 ± 0.022). In the analysis of variance the differences were significant at the 1% level for T1 in Hist (table 5) and maintained (p = 0.0285) above the 10¹⁸ dilution level where histamine concentration was lower than 9.8.10^-18M. Besides, discriminant analysis succeeded in separating at the same time water, Hist and Mn/Lac with a 100% amount of well-classified observations (figure 7) despite a non significant Wilkís test, possibly due to the small number of samples. Above the 9CH dilution level, the different substances remained well-separated on the diagram (figure 8). Curiously, the analysis of variance showed a tendency of T1/T2 to differentiate the substances (p=0.062) above 9CH only.

TABLE 5. Multifactorial analysis of variance in Experiment 2.

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Dil.(CH) T1 T2 T1/T2

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Factor Substance 3-4-6-9-12-15 p=0.0086 p=0.056 ns

- differentiable Hist "` Water

Saline"`Water

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Factor CH 3-4-6-9-12-15 ns ns ns

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Factor Substance 9-12-15 p=0.0285 p=0.060 p=0.062

- differentiable none

_______________________________________________________________________________

Factor CH 9-12-15 ns ns ns

_______________________________________________________________________________

Performed only on the three complete series containing Sil/Lac, Mn/Lac and Hist. - ns: p>0.05.

Differentiable substance determined by Newman-Keuls a posteriori test - ns: p>0.05.

4.3. SYNTHESIS OF BOTH EXPERIMENTS

The figure 6 presents another expression of the results enabling comparison of water and saline solutions at the same time. It appears a common feature that T1 and T1/T2 were increased in all cases in high dilutions, whatever the solvent and whatever the level of dilution. Above 9CH there was a tendency of enhancement of the differences in both T1 and T1/T2, but not established statistically. For T1 values in experiment 2 only, a discrepancy was observed, but non significant. Considering discriminant analysis it is worth noting that separation of Sil/Lac, water and saline was found as a similar graphic pattern in both experiments and that the five species Sil/Lac, Mn/Lac, Hist, saline and water could hardly be separated in a so limited number of series and measurements (figure 7). From figure 7 it was possible to distinguish three areas assigned to water (A), aqueous solutions (B) and saline solutions (C) respectively, corresponding to three increasing degrees of complexity. To our amazement, the paramagnetic solute (Mn/Lac) exhibited the smallest changes in relaxation times.

Figure 6. T1 and T1/T2 ratio in solution versus solvent (water or saline) for all concentrations and for very high diluted solutes only (above 9CH).

Figure 7. Discriminant analysis. X and Y axes represent 1st and 2nd discriminant functions and p, the probability from the Wilkís test. Upper diagram: Experiment 1. Lower diagram: Experiment 2. A: pure water, B: solutes in water, C: solutes in saline.

Figure 8. Discriminant analysis in Experiment 2 limited to dilutions above 9CH. In both diagrams the Wilkís test was not significant but all substances were well-classified (100%).

5. Discussion

This study demonstrated changes in 4 MHz NMR proton relaxation times in very high diluted aqueous solutions compared to solvent. Results of experiment 1 have been partially published and discussed previously (Demangeat et al, 1992; 1993); they have nevertheless been reported here and re-examined statistically together with a second set of new results (Experiment 2). Increases in T1 and T1/T2 ratio were observed in Sil/Lac saline solutions compared to pure saline for Sil/Lac at concentrations lower than 2.92.10^-3 M lactose and 1.66.10^-5 M silica. These changes were still present when the lactose and silica concentrations were lowered below 2.92.10^-15 M and 1.66.10^-17 M respectively; above a 10¹⁸ dilution level changes looked even more pronounced, but non significantly. High dilutions of Mn/Lac and Hist in water did confirm the increase in T1 and T1/T2 with respect to pure water, non significantly for Mn/Lac but significantly for Hist. Above the 10¹⁸ dilution level where differences were still present but with a lower degree of significance, there only remained theoretical concentrations of less than 9.8.10^-18 M histamine. Of course the changes observed were minute and in the range of experimental fluctutions; but higher changes in such very high dilutions were a priori not expected. Therefore a rigorously controlled protocol was imperatively needed as well as multiplicity of independent series, multiplicity of substances and use of powerful statistical tests; so, where the classical Student's test or analysis of variance failed to prove differences, discriminant analysis succeeded in separating substances. Such unexpected and paradoxical results necessitate critical analysis of the experimental protocol, looking for possible biases.

Magnetism of Solutes. (i) Sil/Lac. The silica molecule ²⁸Si¹⁶O₂ (spin number I=0) does not yield an NMR signal. The ²⁹Si isotopic form of silica possesses a spin (I=1/2) but its contribution to the signal is negligible due to its low natural abundance (4.7%) and the distance of its resonance frequency (8.46 MHz/T) from that of the proton (42.7 MHz/T). As for ¹⁷O isotope (I=5/2) of silica, which could influence relaxation via its electric quadrupolar momentum, its concentration is negligible compared to that of oxygen atoms in water (1/95000 in the first potency). Protons and ¹⁷O isotopes of lactose C₁₂H₂₂O₁₁ could affect both signal and relaxation more than silica since the first potency (3CH) contained 2.92.10^-3 M lactose; however this represents 1700-fold less protons and oxygen atoms than in water and a negligible amount in the subsequent dilutions. In fact, this first Sil/Lac potency did not differ in relaxation times from higher dilutions. (ii) Mn/Lac. Mn possesses a spin (I=5/2) but the influence on signal and relaxation may be neglected due to the distance of its resonance frequency (10.49 MHz/T) and to the small amount present in the first potency (1.82.10^-7 M). As for lactose, it was 1000-fold less abundant than in Sil/Lac dilutions. (iii) Hist. The possible magnetic influence of protons and of 14N (I=1) and 15N (I=5/2) isotopes of histamine can reasonably be neglected at concentrations as low as 9.8.10^-8 M.

Paramagnetic Solutes or Contaminants. Paramagnetic contaminants in sodium chloride, silica or lactose may induce, at micromolar concentrations, up to 20 ms changes in relaxation times, that would be non negligible, if any, in our experiments. But the paramagnetic effect is essentially a reduction in relaxation times, contrary to what was observed; moreover, differences in relaxation times persisted at very high dilution levels where contaminants of solutes could no more be present. The absence of a particular behavior of the paramagnetic solute Mn/Lac (which, even, exhibited the smallest changes in relaxation) does neither argue for the responsability of paramagnetic contaminants of solutes for the observed NMR modifications. Dissolved O₂ was the main paramagnetic agent present in our experiments; the protocol used aimed to minimize the PO₂ fluctuations in the samples of a given series but we cannot formally exclude a minute variation of the oxygen dissolution in the course of the preparation, not detectable at the PO₂ determination, but which could have influenced relaxation times. A modification in the oxygen solubility within a series could result from room temperature fluctuations or from interaction with the molecules of solute, the number of which decrease with the dilution/agitation process. The relaxant effect of paramagnetism generally affects mainly T2 and particularly above the MHz domain for contaminants such as Mn⁺⁺ or Cr⁺⁺⁺ (Morgan and Nolle, 1959), resulting in a higher T1/T2 ratio. But the observed simultaneous increase in T1/T2 and T1 appears paradoxical since the increase in T1/T2 suggests a higher amount of paramagnetic agents in dilutions compared to solvent and the increase in T1 suggests the reverse. The effect of pH can neither be neglected as it influences differentially the T1 and T2 via ¹⁷O quadrupolar relaxation (Meiboom, 1961) leading to a T1/T2 increase; but this parameter was not examined.

Preparation Conditions. The control samples, water and saline, underwent simultaneous and strictly identical dilution/agitation, filtering, sealing, storage and measurement. Moreover new batches of solvent were used for each series. These conditions statistically compensated the influence of (i) the barometric influence on O₂ dissolution (ii) any possible contamination from the glass test tube and especially silica which form a gel on contact with glass and alter the chemicophysical properties of water (so-called poly-water; Menès, 1970; Prigogine, 1971) (iii) contaminants of solvents (iv) filtering and sealing procedures.

Thus, there is no obvious experimental bias to explain our results. Effects of pH, of dissolved O₂ (the dissolution rate of which being enhanced) or of paramagnetic contaminants in the successive dilutions/agitations cannot be formally excluded but, if present, would probably constitute a common and non specific phenomenon, unable to explain the differentiation of substances, especially at dilution level higher than 10¹⁸. In the absence of satisfactory answer, one cannot exclude a modification of the solvent structure in diluted/agitated samples; the increase in T1 suggests a decrease in correlation times. When substances such as urea, acetamide and numerous, especially monovalent, ions are dissolved in water, they break hydrogen bonds thus increasing the mobility of water molecules. This so-called negative hydration state has been described using techniques as different as diffusion, conductivity, viscosity, ultrasound absorption, and NMR T1 relaxation time (Hammes and Swann, 1967; Engel and Hertz, 1968; Brun et al, 1969). This phenomenon is concentration-dependent, with many substances acting as destructuralizers at low concentration (increasing T1 compared to pure water) but generating a structure at higher concentration (lowering T1). While this hypothesis of water destructuralization, suggested by T1, is not supported by the non variation of T2, it is neither refuted since T2 is an experimental less reliable parameter than T1 and since several factors acting differently on T1 and T2 may be intricated to produce the observed result.

Whatever the phenomenon described here, true modification of molecular interactions or common chemicophysical changes induced by the dilution/agitation process, the NMR relaxation, associated with a rigorous protocol and an appropriate statistics, emerges as an unsuspected sensitive technique to study water protons in very high diluted aqueous solutions, prepared according to the successive 100-fold hahnemanian principle required for homeopathy.

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^{* Communication presented at the 8th GIRI Meeting, December 1994, Jerusalem, Israel.}