Keywords
droplet evaporation method - crystallization patterns - homeopathy - mineral extracts
- vegetal extracts - low potencies
Introduction
In homeopathic basic research, the mainstream of studies concerns high potencies.
Effects of dilutions beyond the Avogadro limit, being inconsistent with the present
state of scientific knowledge, represent an interesting topic for scientific investigation.
Moreover, based on Hahnemann's Organon,[1] the “power” of a remedy should increase with its dilution; thus, studying the effectiveness
of high potencies, rather than low potencies, seems to be reasonable. From this perspective,
low potencies seem to be less interesting. However, the fact that they still contain
substantive material allows one to study characteristics of this very substance as
well as substance-specific changes due to the successive dilution and potentization
steps.
Phase-transition-induced pattern formation is a process that forms the basis of different
methods applied in homeopathic basic research.[2] One such method is the droplet evaporation method (DEM), where the sample to be
analyzed is applied on a substrate in the form of droplets and left for drying. The
desiccated residues of such droplets, containing often surprisingly ordered patterns,
comprise the main output of the method and serve as a data source for further analysis.
Until now DEM was applied on three experimental models, testing high potencies: (1)
evaporation of wheat seed leakage droplets prepared by soaking wheat seeds in homeopathic
samples[3]
[4]
[5]
[6]; (2) evaporation of a droplet sequence made out of five droplets of a given homeopathic
preparation, where each successive droplet is placed on the dry residue of the preceding
droplet[7]; and (3) evaporation of a single droplet of a diluted (not succussed) substance.[8]
In contrast to common analytical methods aiming at isolation, identification, and
quantification of defined material compounds, phase-transition-induced pattern formation
is a complementary scientific approach aiming at studying and characterizing the wholeness
of a given sample, which can be seen to be more than the sum of its parts. The wholeness
of an element of nature is, amongst others, basically characterized by its physical
form. Phenomenological science describes forms of nature by using qualitative and
quantitative research methods to identify characteristic elements that are unique
and specific for a given element of nature.
Here we propose a DEM experimental model consisting of the evaporation of a single
droplet of a given homeopathic preparation per se (i.e., without any pre-treatment or addition of reagents) and apply DEM for the first
time to investigate low potencies. The present study included a pilot study, where
a wide choice of substances of mineral, vegetal, and animal origin, used for the preparation
of homeopathic potencies, was screened by means of DEM in the potency range 1x to
6x for their pattern-forming properties. The main study aimed at testing DEM's ability
to distinguish between four pre-selected substances in increasing dilution/succussion
levels ranging from 2x to 6x. The image analysis consisted of calculation of the gray-level
distribution (GLD) (the quantification of the gray levels across the whole image yields
an estimate of the structure's size) and the textural parameters inverse difference
moment (IDM) and entropy (i.e., measures of the image's homogeneity and disorder,
respectively). The model was tested also for repeatability on different experimental
days and for stability by means of control experiments.
Materials and Methods
Experimental Design
The experimental design ([Fig. 1]) included a pilot study and a main study.
Fig. 1 Flowchart for the pilot and the main study.
The pilot study consisted of screening tests, in which decimal potencies up to 6x
of 18 substances ([Table 1]) were analyzed by means of DEM regarding their pattern-forming properties. From
each potency, 20 droplets were deposited on two slides, evaporated, and analyzed visually
for pattern-forming properties. Based on the results of the pilot study, four substances
(Baptisia [B], Echinacea [E], Luffa [L], and Spongia [S]) were chosen for the main study (selection criteria are described in the Results
section).
Table 1
Substances used in the pilot and main study, their origin, solute, and production
method according to the European Pharmacopeia
|
Substance
|
Origin
|
Solute
|
Manufacturing
|
|
Pilot study
|
|
Aurum chloratum (1x)
|
Mineral
|
H2O
|
3.1.1 (Ph. Eur.)
|
|
Kalium bichromicum (2x)
|
Mineral
|
H2O
|
3.1.1 (Ph. Eur.)
|
|
Natrium sulfuricum (powder)
|
Mineral
|
−
|
|
|
Silicea (powder)
|
Mineral
|
−
|
|
|
Zincum valerianicum (2x)
|
Mineral
|
Ethanol 100%
|
3.1.1 (Ph. Eur.)
|
|
Lilium tigrinum (Ø)
|
Plant
|
Ethanol 50% (v/v)
|
1.1.3 (Ph. Eur.)
|
|
Baptisia (Ø)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.5 (Ph. Eur.)
|
|
Cimicifuga (Ø)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.5 (Ph. Eur.)
|
|
Cypripedium pubescens (Ø)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.5 (Ph. Eur.)
|
|
Echinacea (Ø)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.5 (Ph. Eur.)
|
|
Ignatia (1x)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.8 (Ph. Eur.)
|
|
Luffa (1x)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.8 (Ph. Eur.)
|
|
Passiflora incarnata (Ø)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.5 (Ph. Eur.)
|
|
Cocculus (1x)
|
Plant
|
Ethanol 90% (v/v)
|
1.1.8 (Ph. Eur.)
|
|
Valeriana (1x)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.8 (Ph. Eur.)
|
|
Apis (1x)
|
Animal
|
Ethanol 70% (v/v)
|
Monograph (GHP)
|
|
Lachesis (2x)
|
Animal
|
Glycerol 85%
|
Monograph (GHP)
|
|
Spongia (1x)
|
Animal
|
Ethanol 70% (v/v)
|
1.1.9 (Ph. Eur.)
|
|
Main study
|
|
Baptisia (1x)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.5 (Ph. Eur.)
|
|
Echinacea (1x)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.5 (Ph. Eur.)
|
|
Luffa (1x)
|
Plant
|
Ethanol 70% (v/v)
|
1.1.8 (Ph. Eur.)
|
|
Spongia (1x)
|
Animal
|
Ethanol 70% (v/v)
|
1.1.9 (Ph. Eur.)
|
Abbreviations: Ø–mother tincture; 1x, 2x—decimal dilutions; Ph. Eur.—European Pharmacopoeia;
GHP—German Homeopathic Pharmacopoeia; 3.1.1, 1.1.3, 1.1.5, 1.1.8, 1.1.9—methods of
preparation according to Ph. Eur.
The aim of the main study was to test DEM's capacity to differentiate between Baptisia, Echinacea, Luffa, and Spongia in five potencies, from 2x to 6x. For each potency level, one experiment (chamber
run) was performed, in which the potency droplets of each of the four substances were
deposited on three slides (12 slides per chamber run). Five chamber runs were performed
to analyze the potencies 2x to 6x. The whole experimentation was repeated on three
different experimental days. Additionally, in the potency range where DEM showed differentiation
potential, control experiments (chamber runs) were performed to investigate the system
stability, using potencies Echinacea 2x, Baptisia 3x, and Luffa 4x.
The patterns collected in the main study were subjected to computerized pattern evaluation
followed by statistical analysis.
Substances for the Preparation of Investigated Potencies
All substances used in the present study were provided or manufactured according to
the European Pharmacopoeia (Ph. Eur.), Homoeopathic Preparations,[9] or to the monographs in the German Homoeopathic Pharmacopoeia (GHP)[10] by Hevert-Arzneimittel GmbH & Co. KG (Nussbaum, Germany). The choice of the substances
was based on both their use in the homeopathic products Sinusitis Hevert SL and Calmvalera (drops and tablets) and their diversity regarding provenance (mineral, plant, or
animal origin) and expected crystallographic properties.
As shown in [Table 1], the following substances were used:
-
For the pilot study, 18 substances in the form of powders, mother tinctures, or 1x
or 2x potencies;
-
For the main study, four substances (Baptisia, Echinacea, Luffa, and Spongia) in 1x coming from the same batch as those used in the pilot study and manufactured
as follows: Baptisia 1x and Echinacea 1x with method 1.1.5, Luffa 1x with method 1.1.8, and Spongia 1x with method 1.1.9.
Experimental Procedure
The experimentation was performed in the laboratories of the Society for Cancer Research
(Arlesheim, Switzerland). The experimental procedure included the following steps:
preparation of potencies, preparation of slides, droplet deposition and evaporation,
photographing of patterns, and data extraction and processing.
Preparation of Potencies
The preparation of 1x potencies followed the substance-specific guidelines[9]
[10] ([Table 1]). Mineral powders and plant mother tinctures with manufacturing indication 1.1.8.
(Ph. Eur.) were diluted in the ratio 1:9; 0.8 g of the substance was weighed and placed
in a sterile glass cylinder (SBR-ET, Mix Cyl. 10 mL, B; Brand GmbH + CO KG, Wertheim,
Germany) with stopper (untargeted volume 13 mL); subsequently 7.2 mL purified water
according to Pharm. Eur. 9.4[9] (“purified water in bulk,” X-SEPTRON LINE 10 VAL, BWT AQUA AG, Aesch, Switzerland)
was added. By contrast, plant mother tinctures with manufacturing indications 1.1.3
and 1.1.5 (Ph. Eur.) were diluted in the first dilution step in the ratios 3:7 (to
2.4 mg substance, 5.6 mL water was added) and 2:8 (to 1.6 mg substance, 6.4 mL water
was added), respectively. The cylinder was closed tightly and shaken by hand by performing
10 quick, vertical, movements in the air. Subsequent potencies (2x–6x) of all substances
were prepared in the dilution ratio 1:9. After the settling of any foam, the cylinder
was re-opened and 0.8 mL of the potentized solution was taken for the preparation
of the next potency, as described previously. Water had to be used as solvent, since
ethanol decreases the droplet's contact angle, which disturbs the pattern formation.
The potencies were prepared fresh for each experiment. The samples were prepared unblinded.
Preparation of Slides
Microscope slides of 76 × 26 mm (Menzel, pre-cleaned, cut edges, Thermo Scientific;
Gerhard Menzel, B.V. & Co. KG, Braunschweig, Germany) were de-greased by washing them
with a dishwasher liquid, then thoroughly rinsed with hot tap water, and placed in
four consecutive purified water baths. Each slide was wiped dry with a laboratory
wiper (Kimtech Science; Kimberly-Clark Professional, Roswell, Canada) just before
droplet deposition.
Droplet Deposition and Evaporation
As depicted in [Fig. 2], 3 μL droplets of the tested potency were deposited on a slide in two parallel rows,
seven droplets per row, by the use of a micropipette of 20 µL capacity (Eppendorf
Research Plus, Eppendorf, Hamburg, Germany). Evaporation took place in an incubator
(KBF 720, cooled incubator with controlled humidity system, WTB Binder Labortechnik
GmbH, Tuttlingen, Germany) with an inner plexiglass-chamber with a semi-permeable
cover placed on a vibration absorbing base. In the inner chamber, 12 microscope slides
were placed in three columns and four rows, and left for evaporation at 26°C and 44%
relative humidity (rH) for 1 hour. In the main study, the slide distribution inside
the chamber followed a quasi-randomization design to provide a uniform arrangement
of the samples within the rows and to eliminate any gradients in the evaporating conditions
within the chamber.
Fig. 2 Graphical representation of the chamber-run design. The evaporation chamber was organized
in four rows (A–D) and three columns (1-3) in which 12 slides were placed (slide a1, a2, … d3). On
each slide, 14 droplets were deposited for evaporation.
Photographing of Patterns
The droplet residues were photographed in dark field at magnification 100X using an
optical microscope (Zeiss Laboratory.A1; Carl Zeiss Microscopy GmbH, Jena, Germany)
with an attached camera (Moticam 5.0 MP; CMOS; Motic Electric Group Co., Ltd, Xiamen,
China). In the pilot study, additionally bright-field and 25X, 50X, 200X, and 400X
magnifications were used to photograph some structure details. The photographs were
saved in jpeg format.
Droplets with disturbed crystallization due to presence of contaminating particles
or due to edge effects on the slide were not photographed. In the main study, per
experiment (one chamber-run, [Fig. 2]), 168 droplets were prepared (14 droplets × 12 slides). The three independent main
experiments for the potencies 2x to 6x yielded 408, 448, 360, 359, and 359 images,
respectively; the control experiments for potencies 2x to 4x yielded 128, 144, and
125 images, respectively. In total 2,331 images were subjected to the computerized
pattern evaluation.
Data Extraction and Processing
Images deriving from the main study were analyzed by means of the software ImageJ
(v. 1.50b) (National Institutes of Health, Bethesda, Maryland, USA)[11] with the plug-in Texture Analyzer (v. 04).[12] The analysis consisted of: (1) calculation of the GLD, which was performed on images
subjected to a background extraction by means of the sliding paraboloid with rolling
ball radius set at 50 pixels; and (2) calculation of the texture analysis parameters
IDM and entropy on images subjected to a background extraction and converted into
8-bit type. Texture analysis was performed by running the GLCM algorithm, which is
based on spatial dependence of pixels in a gray-level co-occurrence matrix with estimation
of image features using second-order statistics, considering distances between pixel
pairs of 4 pixels and angles of 90 degrees.
Statistical Analysis
The data deriving from the computerized image analysis were analyzed by means of analysis
of variance (ANOVA) (one-way ANOVA with the factor randomization group, or two-way
ANOVA with independent factors substance and experimental day, or row and column). In the case of two-way ANOVA, an interaction term between the
independent factors was included in the statistical model to assess stability and
reproducibility. All statistical calculations were performed with CoStat (v. 6.311)
(CoHort Software, Monterey, California, USA).
Pairwise mean comparison was performed with the protected Fisher's least significant
difference test (pairwise comparisons were evaluated only if the global F-test was
significant at p < 0.05). This procedure gives a good safeguard against type I as well as type II
errors, and thus balances well between false-positive and false-negative conclusions.[13]
Results
Pilot Study
The screening experiments showed that all 18 substances delivered patterns in all,
or some, of the analyzed consecutive potencies up to 6x.
The patterns deriving from potencies of mineral origin ([Fig. 3]) showed the greatest variety of forms, for instance: (1) creeping crystals, with
ramifications extending outside the droplet with connection to the droplet border
in Natrium sulfuricum 2x ([Fig. 3A]); (2) structures formed outside the droplet border without any visible connection
to it, probably on diffusion basis in Aurum chloratum 2x ([Fig. 3B]); (3) filament-like crystallization in Aurum chloratum 4x ([Fig. 3C]); (4) crack patterns in Silicea 1x ([Fig. 3D]); and (5) solid rhomboidal or cuboid-shaped crystals in Zincum valerianicum 3x and Kalium bichromicum 3x, respectively ([Fig. 3E], [F]). The patterns from potencies at different dilution levels prepared out of the same
mineral substance also showed prominent differences between each other (e.g., Kalium bichromicum 3–5x in [Fig. 3G–I], respectively).
Fig. 3 Examples of pattern-forming phenomena in evaporating droplets of potencies of mineral
origin: (A) creeping crystals (marked by an arrow) in Natrium sulfuricum 2x; (B) structures beyond the droplet border (marked by arrows), not connected to the droplet,
in Aurum chloratum 2x; (C) filament-like structures in Aurum chloratum 4x; (D) cracks in Silicea 1x; (E) rhomboidal crystals in Zincum valerianicum 3x, (F) cuboid-shaped crystals in Kalium bichromicum 3x; and (G–I) examples of different textures in Kalium bichromicum 3x–5x, respectively. Images in magnification 25X (D); 50X (B, C); 100X (E); 200X (A, F); and 400X (G–I). Images are in dark field, with exception of (E) in bright field.
The patterns from potencies of vegetal origin ([Fig. 4A–I], [K]) seemed to be more uniform. The 1x potencies showed transparent films (e.g., Passiflora incarnata 1x, [Fig. 4A]) or agglomerates as in Cimicifuga 1x ([Fig. 4I]); also, thick film-like deposits with regular hexagonal spaces were noticed (Cypripedium pubescens 1x; [Fig. 4G]). Potencies in the range 2x to 4x showed in most cases (in 6 out of 10 vegetal substances)
dendritic, ramified, fractal-like structures in the droplet center, as in Passiflora 2x to 4x and Lilium tigrinum 3x, 4x ([Fig. 4B–F]); or (in 1 out of 10 vegetal substances), also placed in the droplet center, regular
aggregates with branching, as Cypripedium pubescens 3x ([Fig. 4H]).
Fig. 4 Examples of structures formed in potencies of organic origin: (A, B) whole droplets without a structure and containing a fractal-like structure in Passiflora incarnata 1x and 2x, respectively; (C, D) fractal-like, branched structures in Passiflora incarnata 3x and 4x, and (E, F) Lilium tigrinum 3x and 4x; (G) hexagonal branched formations surrounded by a thick film in Cypripedium pubescens 1x; (H) organized, branched deposit in Cypripedium pubescens 3x; (I) agglomerates in Cimicifuga 1x; (J) circles due to stepwise evaporation in Apis 4x; and (K) structures in Echinacea 5x. (L) Example of structures formed in a droplet of purified water. Images in magnification
25X (A–B), 50X (H), 100X (D–G, I–L), and 200X (C). Images are in dark field, with exception of (G) in bright field.
Patterns from the analyzed potencies of animal origin (Apis, Lachesis, and Spongia) greatly resembled each other and contained mainly circles, probably formed as a
result of step-wise shrinking of the droplet perimeter during evaporation ([Fig. 4J]). Lachesis 3x could not be analyzed due to high glycerol content in the droplets, which prevented
the evaporation.
The patterns showed substance-typical features in potency-range 1x to 3x and, albeit
in smaller degree, also in 4x; patterns from mineral potencies showed in many cases
some substance-typical features also in 5x. Beyond this range, the patterns resembled
those of pure solvent (e.g., Echinacea 5x in [Fig. 4K] and purified water in [Fig. 4L]).
For the main experimentation, we chose four substances, out of which three were of
vegetal origin, creating dendritic, fractal-like structures in the droplet center
in potencies 2x to 4x (Baptisia [B], Echinacea [E], and Luffa [L]), and one was of animal origin (Spongia [S]).
Differentiation Experiments
Visual Pattern Evaluation
Pattern examples formed in evaporated droplets of 2x to 6x potencies of B, E, L, and
S are shown in [Fig. 5]. It can be seen that patterns obtained from the four substances differed remarkably
at the potency levels 2x and 3x, and also—though somewhat less pronounced—at 4x. For
potency levels 5x and 6x, the differences between the B, E, L, and S patterns ceased
to be distinguishable, and the patterns resembled those of the solvent (purified water;
[Fig. 4L]).
Fig. 5 Examples of the patterns formed during evaporation of droplets of potencies from
Luffa, Baptisia, Echinacea, and Spongia in dilutions 2x–6x. Images in magnification 100X.
Computerized Pattern Evaluation
As shown in [Table 2], the differences found between B, E, L, and S patterns by analyzing their GLD, IDM,
and entropy by two-way ANOVA with independent factors substance and day were highly
significant for the potency levels 2x (F values for the factor substance were highest) and decreased gradually with increasing
the potency level. A clear differentiation of samples was possible until the potency
4x. For the potency levels 5x and 6x, the F values for the factor day were higher than those for the factor substance, which
means that the day-to-day variation was larger than the influence of the substances
tested. For all potency levels, the interaction between the independent factors substance
and day was highly significant, which means that the differences between B, E, L,
and S varied to a certain extent for the individual experiments ([Fig. 6]).
Fig. 6 Graphical representation of the results (mean values ± standard error) of the parameters
gray-level distribution (GLD; left graphs), inverse difference moment (IDM; middle graphs), and entropy (right graphs) for 2x–6x potencies of Luffa, Baptisia, Echinacea, and Spongia (rows) on the three experimentation days.
Table 2
The F-test results of the ANOVA for the parameters GLD, IDM, and entropy of droplet evaporation
patterns obtained from Baptisia, Echinacea, Luffa, and Spongia in potency levels 2x–6x
|
Substance
|
Experimentation day
|
Interaction substance x exp. day
|
|
F-Value
|
p-Value
|
F-Value
|
p-Value
|
F-Value
|
p-Value
|
|
Potencies 2x
|
|
GLD
|
186.59
|
<0.0001***
|
0.72
|
0.4855
|
7.98
|
<0.0001***
|
|
IDM
|
930.75
|
<0.0001***
|
0.95
|
0.3856
|
9.09
|
<0.0001***
|
|
Entropy
|
684.52
|
<0.0001***
|
1.33
|
0.2666
|
11.13
|
<0.0001***
|
|
Potencies 3x
|
|
GLD
|
170.99
|
<0.0001***
|
22.88
|
<0.0001***
|
5.09
|
<0.0001***
|
|
IDM
|
312.93
|
<0.0001***
|
12.73
|
<0.0001***
|
9.05
|
<0.0001***
|
|
Entropy
|
354.31
|
<0.0001***
|
16.69
|
<0.0001***
|
8.15
|
<0.0001***
|
|
Potencies 4x
|
|
GLD
|
195.73
|
<0.0001***
|
1.61
|
0.2010
|
3.83
|
0.0010**
|
|
IDM
|
154.83
|
<0.0001***
|
2.51
|
0.0825
|
8.26
|
<0.0001***
|
|
Entropy
|
172.90
|
<0.0001***
|
1.93
|
0.1461
|
7.35
|
<0.0001***
|
|
Potencies 5x
|
|
GLD
|
1.19
|
0.3115
|
2.37
|
0.0948
|
3.95
|
0.0008***
|
|
IDM
|
3.58
|
0.0142*
|
22.82
|
<0.0001***
|
8.97
|
<0.0001***
|
|
Entropy
|
3.13
|
0.0258*
|
18.30
|
<0.0001***
|
8.85
|
<0.0001***
|
|
Potencies 6x
|
|
GLD
|
4.54
|
0.0039**
|
24.55
|
<0.0001***
|
9.00
|
<0.0001***
|
|
IDM
|
4.85
|
0.0025**
|
61.61
|
<0.0001***
|
14.02
|
<0.0001***
|
|
Entropy
|
6.81
|
0.0002***
|
60.72
|
<0.0001***
|
16.53
|
<0.0001***
|
Abbreviations: ANOVA, analysis of variance; GLD, gray-level distribution; IDM, inverse
difference moment.
Note: Effects of substance and experimentation day as well as their interaction are given for each parameter and potency level (*p < 0.05; **p < 0.01; ***p < 0.001).
The mean values for the parameters GLD, IDM, and entropy for each investigated substance
and dilution level are given in [Table 3], alongside pairwise statistical comparison. For the potency level 2x, sample differentiation
was possible for all three outcome parameters. For the potency level 3x, IDM was able
to differentiate all samples, whereas entropy could not differentiate B and S, and
GLD could not distinguish B, E, and S. For the potency level 4x, IDM and entropy did
not distinguish between B and S; however, GLD ranked these two samples differently.
For the potency levels 5x and 6x, some differences for two or three substances were
significant; however, as shown by the F-values in [Table 2]—as also in [Fig. 6] depicting the results of GLD, IDM, and entropy for each substance within the three
experimental days—these differences were not stable in the course of the experiments.
Table 3
Mean values of the parameters GLD, IDM, and entropy for 2x–6x potencies of Luffa, Baptisia, Echinacea, and Spongia
|
N
|
GLD
|
IDM
|
Entropy
|
|
Potencies 2x
|
|
Luffa
|
103
|
32.217 (a)
|
0.141 (d)
|
8.008 (a)
|
|
Baptisia
|
101
|
22.961 (b)
|
0.348 (c)
|
6.162 (b)
|
|
Echinacea
|
109
|
15.061 (c)
|
0.594 (b)
|
4.253 (c)
|
|
Spongia
|
95
|
3.573 (d)
|
0.826 (a)
|
1.871 (d)
|
|
Potencies 3x
|
|
Luffa
|
115
|
15.715 (a)
|
0.552 (d)
|
4.796 (a)
|
|
Baptisia
|
100
|
5.451 (b)
|
0.787 (b)
|
2.265 (b)
|
|
Echinacea
|
111
|
3.788 (c)
|
0.863 (a)
|
1.585 (c)
|
|
Spongia
|
122
|
4.263 (bc)
|
0.758 (c)
|
2.453 (b)
|
|
Potencies 4x
|
|
Luffa
|
90
|
7.623 (a)
|
0.817 (c)
|
2.163 (a)
|
|
Baptisia
|
90
|
0.993 (c)
|
0.887 (b)
|
1.292 (b)
|
|
Echinacea
|
90
|
1.364 (bc)
|
0.915 (a)
|
1.015 (c)
|
|
Spongia
|
90
|
1.939 (b)
|
0.888 (b)
|
1.330 (b)
|
|
Potencies 5x
|
|
Luffa
|
92
|
1.398 (a)
|
0.890 (c)
|
1.244 (a)
|
|
Baptisia
|
89
|
1.089 (a)
|
0.903 (ab)
|
1.125 (ab)
|
|
Echinacea
|
90
|
1.155 (a)
|
0.906 (a)
|
1.097 (b)
|
|
Spongia
|
88
|
1.415 (a)
|
0.892 (bc)
|
1.240 (a)
|
|
Potencies 6x
|
|
Luffa
|
91
|
1.192 (b)
|
0.903 (a)
|
1.105 (b)
|
|
Baptisia
|
90
|
1.789 (a)
|
0.890 (b)
|
1.287 (a)
|
|
Echinacea
|
89
|
1.436 (ab)
|
0.902 (a)
|
1.149 (b)
|
|
Spongia
|
89
|
1.089 (b)
|
0.906 (a)
|
1.103 (b)
|
Abbreviations: N, number of droplet patterns; GLD, gray-level distribution; IDM, inverse difference
moment.
Note: a, b, c, d (per quartet of means of the different substances at a given potency),
differing letters: statistical differences between involved groups at p < 0.05; same letters: absence of statistical differences between involved groups
(p > 0.05).
Positive Control Experiments
For the control experiments, we chose E2x, B3x, and L4x: that is, potencies that yielded
fractal-like branch structures in the potency range where the outcome parameters significantly
differentiated most samples. The F-Test of ANOVA for the parameters GLD, IDM, and
entropy of E2x, B3x, and L4x patterns from the control chamber runs ([Table 4]) revealed that the position of the slides (independent factors row and column) inside
the chamber ([Fig. 2]) during evaporation had no significant influence on E2x; however, for B3x row and
column were significant for two parameters, and for L4x the factor column was significant
for all parameters. This means that row and/or column drifts may influence experimental
outcome in the set-up chosen. Randomized allocation of the samples to row and column
positions is therefore necessary to avoid systematic errors. Correspondingly, the
applied randomization design eliminated the gradients for B3x and strongly decreased
it for L4x ([Table 4]).
Table 4
Analysis of variance of the control experiments
|
Column
|
Row
|
Interaction column x row
|
Randomization group
|
|
F-Value
|
p-Value
|
F-Value
|
p-Value
|
F-Value
|
p-Value
|
F-Value
|
p-Value
|
|
Echinacea 2x
|
|
GLD
|
0.49
|
0.6147
|
2.16
|
0.0967
|
2.51
|
0.0252*
|
2.94
|
0.0356*
|
|
IDM
|
1.75
|
0.1790
|
2.59
|
0.0563
|
1.00
|
0.4253
|
0.75
|
0.5236
|
|
Entropy
|
1.53
|
0.2211
|
2.46
|
0.0658
|
1.35
|
0.2422
|
0.87
|
0.4565
|
|
Baptisia 3x
|
|
GLD
|
1.48
|
0.2312
|
4.76
|
0.0035**
|
3.68
|
0.0020**
|
0.32
|
0.8078
|
|
IDM
|
13.32
|
<0.0001***
|
6.95
|
0.0002***
|
4.70
|
0.0002***
|
1.55
|
0.2046
|
|
Entropy
|
7.50
|
0.0008***
|
1.71
|
0.1664
|
4.84
|
0.0002***
|
2.08
|
0.1059
|
|
Luffa 4x
|
|
GLD
|
0.62
|
0.5383
|
6.46
|
0.0004***
|
1.63
|
0.1433
|
3.43
|
0.0192*
|
|
IDM
|
1.22
|
0.2991
|
12.38
|
<0.0001***
|
2.87
|
0.0123*
|
2.49
|
0.0633
|
|
Entropy
|
0.82
|
0.4432
|
11.04
|
<0.0001***
|
2.50
|
0.0262*
|
2.16
|
0.0963
|
Abbreviations: GLD, gray-level distribution; IDM, inverse difference moment.
Note: F-test results for the parameters GLD, IDM, and entropy of patterns obtained
in three control chamber-runs (Echinacea 2x, Baptisia 3x, and Luffa 4x) for the factors column, row, their interaction, and for the randomized group
allocation (* p < 0.05; **p < 0.01; ***p < 0.001).
[Figure 7] compares the values of the pattern evaluation parameters GLD, IDM, and entropy for
2x to 4x potencies of B, E, L and S analyzed on the third experimental day (three
slides per substance for each potency-level, placed randomly in the chamber) with
the values for the control runs of E2x, B3x, and L4x (evaluated following the same
randomization design). For example, in [Fig. 7], graph 2x/GLD, the blue bars for L, E, B, and S indicate the mean values of GLD
of L2x, E2x, B2x, and S2x evaporated on three slides each in one chamber run performed
on the third experimental day, and the black symbols indicate the mean GLD values
for the control E2x evaporated on slides placed in the same locations as L2x, E2x,
B2x, and S2x in a control chamber run performed on the same day.
Fig. 7 Graphical representation of the mean values (± standard error) of the parameters
gray-level distribution (GLD; left graphs), inverse difference moment (IDM; middle graphs), and entropy (right graphs) for the potencies 2x–4x for Luffa, Baptisia, Echinacea, and Spongia (blue bars) and for the controls Echinacea 2x (upper row), Baptisia 3x (middle row), and Luffa 4x (lower row), (black markers, and lines), evaporated in the same chamber positions
as the respective potencies.
Discussion
Evaporation-Induced Pattern-Formation in Potencies of Mineral versus Organic Origin
The pilot study provided a wide range of structures formed during the droplet evaporation
of the 18 investigated substances in consecutive decimal potencies up to 6x.
The structure formation in evaporating droplets may follow different scenarios depending
on both the evaporation environment (e.g., temperature, relative humidity, pressure,
substrate characteristics) and the droplet composition (e.g., substance and its degree
of dilution, the liquid viscosity, electrical conductibility, droplet surface tension).
In our experiments, the evaporation temperature and relative humidity were controlled
and kept as constant as possible throughout all the experimental series; therefore,
differences in patterns will rather depend on the droplet composition.
A visual inspection of the images revealed that potencies of mineral origin delivered
the largest variety of structures ([Fig. 3]), whereas in patterns obtained from vegetal and animal potencies this variety of
observed forms was less marked ([Fig. 4]). As regards potencies of mineral origin, out of the observation of forms it can
be said that different pattern-forming mechanisms took place, involving inter alia: (1) classical crystal growth mechanisms relying on attachment of monomers and leading
to the formation of solid, geometric crystals[14] (e.g., rhomboidal crystals in Zincum valerianicum 3x, [Fig. 3E]; cuboid-shaped crystals in Kalium bichromicum 3x; [Fig. 3F]); (2) formation of structures outside the droplet border (creeping crystals in Natrium sulfuricum 2x; [Fig. 3A])[15] and formation of structures outside the droplet without any visible attachment to
the droplet, probably on a diffusion basis (Aurum chloratum 2x; [Fig. 3B]); (3) formation of filament-like structures (Aurum chloratum 3x; [Fig. 3C]); and (4) formation of cracks due to tensions appearing in desiccating films (Silicea 1x; [Fig. 3D]).[16]
In potencies of vegetal origin, the predominant pattern-forming process seemed to
be diffusion-limited aggregation relying on the attachment of clusters which, in the
course of droplet evaporation, following Brownian motion, attach themselves to protruding
structures leading to dendritic growth and the formation of so-called randomized fractals:[17]
[18] that is, branched structures. These structures were generally placed in the droplet
center ([Fig. 4B]) and their branches were thin and well-defined ([Fig. 4C, E, F]), comparably thick ([Fig. 4H]), or agglomerate-like ([Fig. 4I]) (depending probably on the sizes and characteristics of the aggregating molecules).
As regards typical pattern-forming processes in potencies of animal origin, it is
not possible to make a statement based on the present study, since it involved only
three such potencies (Apis, Lachesis, and Spongia). However, all these potencies were characterized by very poor pattern-forming properties
and created circles only, probably due to step-wise shrinking of the droplet perimeter
during evaporation ([Fig. 4J]).
Dendritic structures, similar to those obtained here from potencies of vegetal origin,
have been observed also in previous studies regarding DEM applied to wheat seed leakages,[3]
[4]
[5]
[6]
[19]
[20] where this specific kind of crystallization showed to be sensitive toward stress
induced by poisoning,[20] homeopathic treatment influences,[3]
[5] the number of strokes applied in-between the dilution steps,[6] and force-like effects of homeopathic preparations.[4] In these studies, the use of a biological model (wheat seed leakage model) enabled
work with high potencies. The results obtained showed a correlation with wheat seed
viability, indicating that the droplet pattern characteristics corresponded to the
biological effects of the applied treatment. In the present study on low potencies,
we applied DEM as a physical model to characterize the physico-chemical properties
of the tested substances.
Based on past experience, we decided to concentrate on dendritic structures also in
the present investigation of low potencies per se. Therefore we chose for the main study three substances of vegetal origin (Baptisia, Echinacea, and Luffa) due to their ability to create dendritic, fractal-like structures in the droplet
center in the potency range 2x to 4x. To complement these three substances of vegetal
origin with one substance of animal origin, we further added Spongia to the main study.
Differentiation of Potencies in Range 2x to 6x
In the differentiation experiments of the four substances B, E, L and S in dilutions
from 2x to 6x, DEM showed to be discriminative for the potency levels 2x to 4x, whereas
in 5x and 6x differences due to the substance could no longer be detected ([Fig. 4K]), and the patterns resembled those of pure solute (purified water; [Fig. 4L]). As shown in [Table 2], the F values from ANOVA for the factor substance were high for the potencies 2x to 4x (from
170 to 930) and larger than those for the factor day and the interaction between the
two factors substance and day; for the potencies 5x and 6x, this ratio reversed and
the F values for the factor substance were smaller than those of the factor day and the
interaction between substance and day.
For the potency level 4x, the differentiation between B and S was possible only by
one pattern evaluation parameter (GLD), and it was visually apparent that the patterns
of these two potencies resembled the pattern of pure solute ([Fig. 4L], [Fig. 5]). It therefore may be supposed that the limit of DEM's ability to differentiate
between potencies of different origin may depend on the substance characteristics.
Repeatability of the Experiments and Robustness of the Model
The differentiation experiments were performed on 15 different days (3 days for each
potency level 2x to 6x). As can be seen in [Fig. 6], the reproducibility was quite good for the potency levels 2x to 4x, whereas for
5x and 6x the samples could no longer be differentiated. It is worthy of notice that
there were significant inversions of the substance effect between the experimentation
days for all potency levels ([Table 2]). Such inversions may be due to: (1) some methodological or technical instability,
in which case they might be eliminated by further optimization of the experimental
design and work flow; or (2) some—in this experiment uncontrolled—external factors
modifying the pattern of the potency response in the DEM model.
In the potency range 2x to 4x for the four substances, the robustness of DEM was scrutinized
by means of control experiments, which were designated as chamber runs with only one
potency, E2x, B3x, and L4x. These control experiments revealed that there were gradients
in the chamber, probably due to slight differences in evaporation conditions (temperature,
relative humidity), causing differences in the patterns deriving from different positions
within the chamber. To neutralize these effects, the slide distribution followed a
quasi-randomization design to provide a possibly uniform distribution of the sample
replicates within the chamber rows and columns ([Fig. 2]), avoiding at the same time two sample replicates being deposited on slides lying
nearby. As shown in [Table 4], for the potencies 3x and 4x the factor row had a strong significant influence on
the pattern evaluation parameters (also the factor column for the textural parameters
for 3x); this influence could be neutralized in the randomization group. [Figure 7] depicts additionally the differences between the B, E, L, and S samples for the
same potency dilution as the control samples evaluated with the same randomization
design. Future experiments should include further optimization of the chamber set-up
to minimize or eliminate these gradients.
Future Perspectives
Low homeopathic potencies represent an interesting field of study, providing the possibility
to investigate the material that is still present in these dilution levels, thus shedding
new light on the procedure of homeopathic potentization by investigating the effects
of the first dilution/succussion steps on the material potentized.
In the present study, we showed that DEM applied to potencies per se was able to differentiate phenomenologically between potencies derived from different
substances in the potency range 2x to 4x. In this investigation, only one batch of
each substance was studied. Further investigations will have to compare independent
batches (mother tinctures prepared from material from different harvesting years and/or
areas) to determine possible generalization from the differences between mother tinctures
as observed in this study.
Further investigations could include questions such as: (1) effects related to the
physical processes applied during potency preparation (potentization manner [manual
versus mechanical]; potentization intensity [number of applied strokes]; possible
influence of the potentization vessel [shape and material]); (2) effects related to
the time (hour/day/month) of potency preparation; (3) influence of the storage on
the potency; and (4) contribution of single remedies to the patterns formed by homeopathic
combination medicines.
The different, non-dendritic, pattern-forming phenomena observed in the pilot study
in potencies of mineral origin—for instance the classical nucleation mechanism, creeping
crystals, and cracks ([Fig. 3])—represent also an interesting and new field of investigation. So far, all methods
based on evaporation-induced pattern formation applied in homeopathic basic research
have concentrated on fractal structures formed in the course of diffusion-limited
aggregation (e.g., dendritic structures); it is not known if other non-dendritic pattern-forming
phenomena might also be sensitive to the effects of potencies.
Conclusions
In the present study, we proposed DEM for the first time for analyzing low potencies
per se and showed that the evaporation-induced pattern formation in droplets may represent
a suitable tool for their phenomenological characterization, due to the fact that
they still contain material. Formation of patterns in evaporating droplets has previously
been used to analyze effects of high and ultra-high potencies by means of experimental
models including test organisms, or applying a sequence of droplets dried one on another
residue. Low potencies, retaining enough material for the pattern formation, allow
the application of the method without the use of any test organisms or additives.
The reported experimental protocol may serve as a basis for further studies in this
field, such as comparison of potencies versus dilutions, or studies on homeopathic
combination remedies with regard to the influence their single remedy components may
have on the pattern of different mixtures.
