Homeopathic preparations are used in homeopathy and anthroposophic medicine. Although there is evidence of effectiveness in several clinical studies, including double-blinded randomized controlled trials, their nature and mode of action could not be explained with current scientific approaches yet. Several physical methods have already been applied to investigate homeopathic preparations but it is yet unclear which methods are best suited to identify characteristic physicochemical properties of homeopathic preparations. The aim of this study was to investigate homeopathic preparations with UV-spectroscopy. In a blinded, randomized, controlled experiment homeopathic preparations of copper sulfate (CuSO4; 11c–30c), quartz (SiO2; 10c–30c, i.e., centesimal dilution steps) and sulfur (S; 11×–30×, i.e., decimal dilution steps) and controls (one-time succussed diluent) were investigated using UV-spectroscopy and tested for contamination by inductively coupled plasma mass spectrometry (ICP-MS). The UV transmission for homeopathic preparations of CuSO4 preparations was significantly lower than in controls. The transmission seemed to be also lower for both SiO2 and S, but not significant. The mean effect size (95% confidence interval) was similar for the homeopathic preparations: CuSO4 (pooled data) 0.0544% (0.0260–0.0827%), SiO2 0.0323% (–0.0064% to 0.0710%) and S 0.0281% (–0.0520% to 0.1082%). UV transmission values of homeopathic preparations had a significantly higher variability compared to controls. In none of the samples the concentration of any element analyzed by ICP-MS exceeded 100 ppb. Lower transmission of UV light may indicate that homeopathic preparations are less structured or more dynamic than their succussed pure solvent.
Homeopathy and anthroposophic medicine are complementary medical systems that use high or ultra-high dilutions, also known as homeopathic preparations or homeopathic potencies. These homeopathic preparations are prepared by logarithmically diluting and succussing a mother tincture, typically in water or water-ethanol mixtures. The dilution level that will ultimately be used may be beyond the Avogadro number, for example, the probability for even a single molecule of the mother tincture to be present in the dilution is virtually zero. Although several randomized placebo-controlled double-blind clinical trials reported effects of homeopathic preparations superior to placebo [
It is often argued that the effects of homeopathic dilutions are either unspecific or placebo, since common scientific theories and models cannot account for any specific effects of homeopathic dilutions.
Within the last years, several working hypotheses have been developed to reveal the mode of action of homeopathic preparations but none of them has been validated so far [
In addition, considering the conditions of modern life, the question about the stability of homeopathic preparations arises. It is yet unclear whether certain factors such as pharmaceutical procedures (e.g., autoclavation), artificial magnetism, ionizing radiation (e.g., scanner at airports, train stations) or devices emitting non-ionizing radiation (e.g., mobile communication) might affect the stability and quality of homeopathic preparations. Given these uncertainties, there clearly is need for further research.
One important step is the investigation of physical properties of homeopathic preparations using standard techniques. Previous studies (for a review see [
In addition, it is not yet clear which measurement methods are best suited to determine specific physicochemical properties of homeopathic preparations (in case there are any). UV-spectroscopy is a little investigated method that yielded promising results in own previous pilot measurements.
The aim of our study was to investigate homeopathic preparations of copper sulfate, sulfur and quartz with UV-spectroscopy and compare them to controls.
The experiments were carried out at two laboratories in the USA, at the University of Illinois at Urbana Champaign (Lab 1) and at the National High Magnetic Field Laboratory, Tallahassee, FL (Lab 2).
Lab 1 was a standard wet laboratory; while in Lab 2 all samples were prepared in a metal-free class 100 HEPA-(High Efficiency Particulate Air) filtered clean room. Clean flow boxes had class 5. It was intended to test whether the two different laboratories and their conditions may have an influence on the results.
In Lab 1 we used distilled water as potentization medium. In Lab 2 water was prepared according to standard procedures in trace analytics. De-ionized water (DI-water) was prepared from tap water using two ion-exchange columns (Culligan, Northbrook, IL, USA) for a first de-ionization and a subsequent Millipore system (Super-Q water purification system with four cartridges: 1. Super-C for organic removal, 2. Ion-Ex, and 3. Ion-Ex for inorganic removal, and 4. Durapore for bacteria and particle removal), resulting in water of 18 MΩcm. Quartz distilled water (QD-water) was prepared by subsequent sub-boiling distillation of the DI-water (Seastar Chemicals Inc., Sidney BC, Canada).
In Lab 1 we used copper sulfate (CuSO4
In Lab 2 hydrochloric acid (HCl) was sub-boiling double-distilled HCl, prepared from reagent grade HCl (certified ACS PLUS, normality 12.1, A 2005–212, from Fisher Scientific, Fairlawn NJ, USA). Nitric acid (HNO3) was twice two-bottle distilled HNO3, prepared from reagent grade HNO3 (certified ACS PLUS, normality 15.8, A 1445–212, from Fisher Scientific, Fairlawn NJ, USA). Ethanol used was Ethyl Alcohol USP, Absolute-200 Proof (Aaper Alcohol and Chemical Co., Shelbyville, USA). Lactose was ordered from Dixa AG, St. Gallen, Switzerland, quartz powder (SiO2) from Weleda AG, Schwaebisch Gmuend, Germany, copper sulfate (CuSO4
In Lab 1 the potentization vessels were 100-ml narrow-necked bottles with conical shoulder, made from boro-silicate glass, hydrolytic class 1 and thus highly resistant to ion leaching (DURAN, Schott, from VWR International, Dietikon, Switzerland). In Lab 1 the vessels were cleaned using detergent, alcohol and distilled water. In a control measurement the vessels were filled with water that was succussed and transmission was measured using UV-spectroscopy. The data were analyzed and no relevant outliers were detected.
In Lab 2 vessels for all liquids were 500-ml narrow-necked bottles with conical shoulder, also made from boro-silicate glass, hydrolytic class 1 (DURAN, Schott, from VWR International, Dietikon, Switzerland). All 40 vessels used were numbered permanently in order to be able to retrace the use of every individual vessel during the entire study. In a control measurement the vessels were filled with water, then the water was succussed in these vessels and transmission of UV light was measured. The data were analyzed, and no relevant outliers were detected. After production of one series of homeopathic preparations and the corresponding controls, all vessels were cleaned (see below) and re-used in randomized allocation for the next series. Trituration (potentization of solid compounds) was performed with a porcelain mortar and pestle.
For the ICP-MS measurement 4-ml polypropylene vials (Omni vials Polypropylene (PP), Cole-Parmer, Vernon Hills IL, USA) were used.
To minimize ion release from the vessel walls, all vessels were pretreated in Lab 2 as customary in inorganic trace analytics. In Lab 2 the treatment of the potentization vessels before the first use included: Rinse 3× with DI-water, fill 1/4 of height with 1.2 N HCl (12.1 N, Fisher Scientific, 1 : 10 diluted with QD-water), put vessels on hot plate (125°C) for 8 h in a clean flow box, remove HCl, rinse 3× with DI-water, rinse 3× with QD-water.
In Lab 2 cleaning of the potentization vessels before S potentization consisted of: rinsing 3× with QD-water. Potentization vessels before CuSO4 potentization: rinsing 3× with DI-water and 3× with QD-water. Vessels having contained homeopathic dilutions with concentrations higher than 10–10 were rinsed 6× with DI-water and 3× with QD-water.
ICP-MS-vials and pipette tips: 24 h in 7.9 N HNO3 (15.8 N, Fisher Scientific, 1 : 1 diluted with QD-water) on hot plate (100°C), rinse 3× DI-water, rinse 3× QD-water.
In order to complement earlier investigations using nuclear magnetic resonance, we decided to investigate homeopathic preparations of quartz (SiO2) like Demangeat [
Homeopathic preparations were produced in such a way that they met current legal regulation for homeopathic remedies [
Quartz (SiO2) and copper sulfate (CuSO4) were prepared as c-preparations (centesimal homeopathic preparations, 100-fold dilution), S as x-preparations (decimal homeopathic preparations, 10-fold dilution) in order to allow a comparison with previous investigations [
In Lab 1 the potentization medium was distilled water, while in Lab 2 it was quartz distilled water with 1% ethanol.
Trituration (potentization of solid compounds) was performed by hand for 60 min according to standard pharmaceutical procedures (prescription no. 6 of the German Homeopathic Pharmacopoeia [
Potentization was performed by hand according to standard pharmaceutical procedures with the multiple glass method [
For each set of homeopathic preparations (SiO2, S or CuSO4), 4 (Lab 1) and 10, respectively (Lab 2), independent controls were produced, using the same potentization medium and shaken equally to the homeopathic preparations. This procedure resulted in a preparation called “agitated potentization medium”. In Lab 2, five of the controls were prepared before the preparation of the homeopathic preparations and five controls after, in order to control for a possible cross-contamination and other interference in the course of the production process.
Randomization was effectuated through randomly (random numbers from a computer) allocating the numbered potentization vessels to the homeopathic preparation levels or controls to be produced. After preparation, the bottles were placed in random order, and the codes were kept secret on a hidden allocation list on paper. Thus, the experiment was blinded. Codes were only revealed after the end of the measurements and data reduction. The measured homeopathic preparations are diluted to such a degree that they cannot be distinguished from controls by any of the human senses.
Samples of 3 ml of each homeopathic preparation and control were pipetted into ICP-MS-vials to which 15
For analysis, a Sector ICP-MS Finnigan MAT Element (Thermo Electron, Karlsruhe, Germany) with PFA inlet system, Teflon spray chamber, and PFA nebulizer with a flow rate of 100
Samples were measured in random order in runs of 10 samples. Blank and external standard samples (all analyzed elements in a concentration of 1 ppb) were measured at the beginning, in the middle and at the end of each run.
After measurement, data reduction was performed according to standard procedures of analytical chemistry [
At Lab 1, a Perkin-Elmer
Table
The preparation and measurement process.
Substance | CuSO4 Series 1 | CuSO4 Series 2 | SiO2 | S |
---|---|---|---|---|
Location of preparation | Lab 1 | Lab 2 | Lab 2 | Lab 2 |
Clean room | No | Yes | Yes | Yes |
Type of vessel | 100 ml | 500 ml | 500 ml | 500 ml |
4/25 | 10/20 | 10/21 | 11/20 | |
Spectroscopy instrument | ||||
First measurements location | Lab 1 | Lab 2 | Lab 2 | Lab 2 |
First measurements age (days) | 0.1 | 20 | 7.5 | 6 |
Second measurements location | Lab 1 | |||
Second measurements age (days) | 61 |
Two separate series of CuSO4 homeopathic preparations and controls were prepared, while there was one series of samples for sulfur (S) and quartz (SiO2). Lab 1 is a wet laboratory at the University of Illinois at Urbana Champaign and Lab 2 is a 100HEPA clean room at the National High Magnetic Field Laboratory, Tallahassee, FL. At Lab 1 a Perkin-Elmer
Data was averaged across the three and five repetitions, respectively, and across two bands, that is, from 190 to 290 nm and from 215 to 290 nm. In the band, from 190 to 215 nm, measurements are less stable since these wavelengths are at the border of the measuring range of the UV spectrometer and, consequently, between 190 and 215 nm, the instrumental noise is higher than above 215 nm. But since the effects may possibly be stronger below 215 nm, because the UV absorption of water is higher here, the band below 215 nm was once included and once left out.
All statistics were calculated in SPSS 15.0. The difference in light transmission between homeopathic preparations and controls was tested using a
ANOVA was used to analyze variability between and within samples for CuSO4.
In addition, between the different CuSO4 series, the correlation (Pearson & Spearman) was determined.
In Figures
The results of the different measurements.
Substance | Location | Age (days) | Type | Wavelength range 190–290 nm | Wavelength range 215–290 nm | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Mean ± SD | Difference ± SEM | 95% CI | Mean ± SD | Difference ± SEM | 95% CI | |||||||
CuSO4 | Lab 1 | 0.1 | Control | 4 | 86.5472 ± 0.0472 | 0.0528 ± 0.0297 | 0.1173 | −0.0170 to 0.1226 | 89.4182 ± 0.0495 | 0.0451 ± 0.0290 | 0.1745 | –0.0272 to 0.1175 |
0.1 | Preparation | 25 | 86.4944 ± 0.0898 | 89.3730 ± 0.0756 | ||||||||
Lab 1 | 61.0 | Control | 4 | 86.4850 ± 0.0459 | 0.0955 ± 0.0365 | 0.0176 to 0.1734 | 89.4168 ± 0.0571 | 0.0656 ± 0.0356 | 0.1080 | –0.0186 to 0.1498 | ||
61.0 | Preparation | 25 | 86.3895 ± 0.1420 | 89.3512 ± 0.1060 | ||||||||
Lab 2 | 20.0 | Control | 10 | 97.2199 ± 0.0503 | 0.0497 ± 0.0237 | 0.0010 to 0.0983 | 98.9036 ± 0.0236 | 0.0351 ± 0.0116 | 0.0113 to 0.0589 | |||
20.0 | Preparation | 20 | 97.1703 ± 0.0783 | 98.8685 ± 0.0396 | ||||||||
SiO2 | Lab 2 | 7.5 | Control | 10 | 97.4888 ± 0.1162 | 0.0645 ± 0.0498 | 0.2084 | −0.0386 to 0.1675 | 99.0687 ± 0.0440 | 0.0323 ± 0.0187 | 0.0972 | –0.0064 to 0.0710 |
7.5 | Preparation | 21 | 97.4243 ± 0.1542 | 99.0364 ± 0.0572 | ||||||||
S | Lab 2 | 6.0 | Control | 11 | 97.2549 ± 0.3379 | 0.1257 ± 0.1355 | 0.3626 | −0.1539 to 0.4054 | 99.0085 ± 0.0963 | 0.0281 ± 0.0388 | 0.4758 | –0.0520 to 0.1082 |
6.0 | Preparation | 20 | 97.1292 ± 0.3991 | 98.9804 ± 0.1152 | ||||||||
Pooled all | Labs 1 and 2 | All | Control | 39 | 0 ± 0.1903 | 0.0836 ± 0.0364 | 0.0111 to 0.1562 | 0 ± 0.0604* | 0.0456 ± 0.0129 | 0.0199 to 0.0712 | ||
Preparation | 111 | −0.0836 ± 0.2095 | −0.0456 ± 0.0902* | |||||||||
Pooled CuSO4 | Labs 1 and 2 | Various | Control | 18 | 0 ± 0.0494* | 0.0758 ± 0.0189 | 0.0381 to 0.1136 | 0 ± 0.0395* | 0.0544 ± 0.0142 | 0.0260 to 0.0827 | ||
Preparation | 70 | −0.0758 ± 0.1249* | −0.0544 ± 0.0897* | |||||||||
Pooled Lab 2 | Lab 2 | Various | Control | 31 | 0 ± 0.2129 | 0.0819 ± 0.0503 | 0.1076 | 0.0183 to 0.1821 | 0 ± 0.0626 | 0.0322 ± 0.0149 | 0.0024 to 0.0620 | |
Preparation | 61 | −0.0819 ± 0.2547 | −0.0322 ± 0.0769 |
The column “Difference ± SEM” contains the difference between the homeopathic preparations and controls, which indicates the effect of homeopathic preparation on the UV-light transmission. The 95% CI does not include the zero value for statistically significant differences. There were significant differences between some of the CuSO4 homeopathic preparations and controls. Thus, the measurements at both locations that were done some days after preparation showed significant differences between homeopathic preparations and controls but not the measurements performed on the first day after preparation. The UV-transmission was also lower for both SiO2 and S, but not significant. The pooled data, once all data, once only the data for CuSO4 and once only for data from Lab 2 exhibit significant differences in transmission between homeopathic preparations and controls. Asterisk signifies a significant Levene's test, which indicates that the variance was significantly different between homeopathic preparation and control. Bold typeface indicates significance
Copper sulfate (CuSO4) homeopathic preparations and controls: The averaged UV transmissions from 190 to 290 nm of the two separate preparations (series 1 and 2) are displayed in percentage. The controls are on the left, the homeopathic preparations on the right side. For the Series 1 with age 61 days and Series 2 the difference between homeopathic preparations and controls was significant.
The UV transmissions of the quartz (SiO2) and sulfur (S) homeopathic preparations and their respective controls.
The UV transmission for CuSO4 preparations was significantly lower than in controls in two out of three measurements for the band of 190–290 nm, and in one out of three measurements (Lab 2) for the band of 215–290 nm. Pooling all three CuSO4 measurements led to highly significant (
The transmission was also lower for both SiO2 and S, but not significant. Pooling all measurements (CuSO4, SiO2 and S) again led to significant differences between homeopathic preparations and controls for both bands. Pooling all the measurements of Lab 2 yielded significant differences for the band of 215–290 nm.
The effect size was remarkably similar for the homeopathic preparations of all substances, that is, the difference between homeopathic preparations and controls ranged from 0.0457–0.1257% for the band of 190–290 nm and from 0.0281–0.0656%.
UV transmission values between homeopathic preparations in terms of the SD had a higher variability in homeopathic preparations compared to controls. These differences in SD were not significant for any series by itself. However, when the CuSO4 data were pooled, the mean SD was a factor 2.53 (
ANOVA for the three CuSO4 series showed for data between 190–290 nm a between-group (homeopathic potency level and control) mean square of 0.0192 (
There were no significant correlations between the three CuSO4 series, which indicates that there is no specific pattern of higher or lower transmission for different potency levels.
The ICP-MS analysis showed that the samples produced were highly pure, that is, in Lab 1, the concentrations of all ions were <100 ppb and, in Lab 2, <10 ppb. In the following, the elements are sorted according to their mean concentrations in decreasing order.
In Lab 1, the mean concentrations of elements between 21 and 10 ppb were: 11B, 24Mg, 23Na, 44Ca; between 10 and 1 ppb were: 28Si, 65Cu, 27Al; and below 1 ppb were: 66Zn, 208Pb, 137Ba, 88Sr, 48Ti, 56Fe, 85Rb, 7Li and 133Cs.
In Lab 2, most elements were below the detection limit of approximately 1 ppb. Only 11B and 23Na were detectable at mean concentrations between 1 and 4 ppb. The CuSO4 samples were particularly clean, that is, only 11B was detectable at concentrations <2 ppb.
Thus, the use of the clean room and sophisticated procedures improved the purity by one order of magnitude. There were no significant differences in the ion concentrations between homeopathic preparations and controls.
In our results we found significant differences, that is, a lower transmission of UV light, in two series of homeopathic CuSO4 preparations. Also for potentized SiO2 and S we observed differences in transmission pointing in the same direction although they were not significant. The question arises whether these differences could be due to artifacts, that is, trivial physicochemical explanations? To clarify this, the following aspects need to be considered.
Both UV spectrometers were double-beam instruments, which enhance the stability of the measurements and thus increase the reproducibility of the measurements.
The instrumental drift that was monitored throughout the measurements was negligible and it was not necessary to corrected for it in the data analysis. The drift during the CuSO4 measurements was even smaller than for the other homeopathic preparations. Therefore, the results are not biased by an instrumental drift.
The humidity of the air may influence UV transmission measurements because water is absorbing light. Since the humidity affects the measurement and the reference beam of double-beam spectrometers in the same way, its influence is negligible. In addition, the measurements were carried out under stable weather conditions and did not exceed 4 h; a time in which a considerable change in humidity in an air conditioned laboratory is minimal.
Room temperature may influence UV-spectroscopy measurements. However, the room temperature was constant throughout the measurements.
The amount of dissolved oxygen in water, that is, the diluent, affects its UV-spectroscopic absorption properties, but since this factor affects both controls and homeopathic preparations in the same way, it can be ruled out.
The reproducibility of the measurements was good; in a pilot study in Lab 2, the error for the range between 190 and 290 nm was 0.0059% (empty cuvette) and 0.119% (cuvette filled with water and refilled for each measurement) and for the range between 215 and 290 nm was 0.0045% (empty cuvette) and 0.076% (cuvette filled with water and refilled for each measurement). This shows that the reproducibility of the instrument is higher and that refilling the cuvette affects the reproducibility more than the instrumental factors. This high reproducibility was also demonstrated by the fact that measurements carried out in two different laboratories with two different instruments and two different homeopathic preparations of CuSO4 led to similar effects.
Most importantly, all mentioned factors would have affected both homeopathic preparations and controls in the same way and could be, even if they had occurred, ruled out due to the randomization.
To test whether the samples were contaminated by traces of dust or inorganic contaminants, all samples were also measured by ICP-MS. These measurements showed that the contamination was negligible for both Lab 1 and Lab 2 (<100 ppb, resp., <10 ppb for all ions, data not shown). In addition, contamination in Lab 2 was particularly low for CuSO4 homeopathic preparations (<2.6 ppb for all ions). Previously, quantitative concentrations of contaminating ions such as Na, Si, Mg, Al, Li and Fe were reported for brown glass bottles [
Therefore, the detected differences in transmission are not due to contamination. Since this factor applies to both controls and homeopathic preparations in the same way, it can be excluded.
All samples were blinded and blinding was only disclosed after data analysis was completed. Moreover, all measurements were carried out in a randomized order. Therefore we can exclude bias caused by the experimenter.
In Lab 1 we used vessels of hydrolytic class 1, which are highly resistant to leaching. Although they were not pre-treated as in Lab 2 the homeopathic preparations and controls were very pure with a concentration of ions <100 ppb.
Since all glassware at Lab 2 that was used for the preparation and storage of the samples was treated according to trace analytics prior to their use, leaching of ions from the vessel walls is minute. The only vessels that were not treated according to the trace analytics protocol were the cuvettes. The residence time of a sample in a cuvette, however, was less than 2 min. We consider this time to be too short to induce a considerable leaching. Had a leaching been taken place by the repeated filling and emptying of the cuvettes during the measurements we would have noticed that as a drift in the values. Moreover, since the measurements were done in a randomized order, and a possible leaching effect would affect both homeopathic preparations and controls in the same way. Therefore, this cannot explain the differences found.
Since there are no trivial artifacts that could lead to the significant differences between homeopathic preparations and controls what does this effect mean? The UV transmission values were lower and significantly different, compared to controls for CuSO4 homeopathic preparations that were measured more than two weeks after preparation. For SiO2, S and the first CuSO4 series, which were all measured within two weeks after the preparation, all had lower transmission values for homeopathic preparations compared to controls, but these differences were not significant.
It seems that homeopathic preparations have a lower UV transmission compared to controls. A lower transmission in UV-spectroscopy corresponds to a higher absorption of light. In general, absorption is explained either as an electron being moved to a higher energy level by a quantum of light or by an increase in the vibrational energy of a molecule. The sharp absorption edge between 160 and 200 nm corresponds to an electronic transition between non-bonding and anti-bonding states (
Several working hypotheses to describe the mode of action of homeopathic preparations have been proposed including theories based on placebo, water structure (clusters or clathrates), silica contamination and entanglement models of quantum theory, but none of these has been validated so far [
Placebo can be ruled out in our study as well as silica contamination.
Some studies and theories suggest that there might be particular structures (clusters) in water, which are causative for the homeopathic effect [
The entanglement theory, which is based on a weak quantum theory, is one possibility explored by many authors [
We would like to emphasize that at the moment it is unclear, whether any theoretical model is able to explain our findings. Therefore, the mode of action of homeopathic preparations remains unclear. The observation in our experiment that the homeopathic preparations are less structured may serve as an indicator for future models on homeopathic dilutions.
In several previous studies differences in UV absorption of homeopathic preparations and controls were observed. Effects pointing at the same direction were reported in one study [
The transmission values for the homeopathic preparations had a higher variability between homeopathic preparations in comparison with the controls. Although this effect was not significant for any of the homeopathic preparation series by itself, it was significant once the CuSO4 data was pooled. The higher variability could indicate that the degree of dynamization depends on the homeopathic preparation level. This may indicate that a homeopathic preparation series expresses peaks and troughs, an effect that was discovered earlier [
SiO2 and S homeopathic preparations were prepared from triturations, while CuSO4 directly from the dissolved mother substance. Since significant differences were only observed in CuSO4 preparations (Tbale
The measurements of CuSO4 immediately after sample preparation in Lab 1 did not show a significant effect, while after 20 days the effects were significant (Table
The transmission of UV light for homeopathic preparations of CuSO4 was significantly lower than in controls. The transmission was also lower for both homeopathic preparations of SiO2 and S, but not significant.
UV transmission values between homeopathic preparations had a significantly higher variability compared to controls.
Thus, experimental evidence accumulates that highly diluted homeopathic preparations, that is, diluted beyond the Avogadro limit, exhibit particular physicochemical properties different from shaken pure solvent. The exact nature of these properties is not yet known; our current working hypothesis is an increase in the solvent's molecular dynamics for homeopathic preparations. All high-quality experimental data obtained so far by several independent working groups for different homeopathic preparations, involving studies with high- and low-field 1H NMR relaxation time, 1H-NMR-spectroscopy, and thermodynamics are compatible with this “dynamization hypothesis”.
Software Foundation, Darmstadt, Germany; Wala Heilmittel GmbH, Boll, Germany; Dr Reckeweg & Co. AG, Bensheim, Germany. The sponsors had no influence whatsoever upon design, realization, evaluation and publication of the study.
The authors like to thank Vincent Salters, Afi Sachi-Kocher, Ted Zateslo and Jeroen Sonke for practical support and valuable discussion during the ICP-MS-measurements, and Hans J. Schneider-Muntau for general support.