The mathematics of dilution.

The major objection to homeopathic medicine is that the doses of medicine prescribed in some cases are too dilute for any active ingredient to be present. The medicines would hence be rendered inactive, necessitating novel explanations for the action. A further examination of dilution in the light of the Langmuir equation shows that homeopathic medicines may not be as dilute as a simplistic application of Avogadro's Principle suggests, due to surface effects.

"Torque-like" action of remedies and diseases on the vital force and their consequences for homeopathic treatment.

INTRODUCTION: Within the developing theoretical context of quantum macroentanglement, a mathematical model of the Vital Force (Vf) has recently been formulated. It describes the Vf in terms of a hypothetical gyroscope with quantized angular momentum. This enables the Vf's state of health to be represented in terms of a "wave function" derived solely from secondary symptom observables produced in response to disease or homeopathic remedies. So far, this approach has illustrated the biphasal action of remedies, resonance phenomena arising out of homeopathic provings, and aspects of the therapeutic encounter. METHOD: In this paper, the effects of a therapeutic remedy and disease states on the gyroscopic angular momentum characteristics of the Vf were investigated by mathematical manipulation the Vf "wave function." RESULTS: The formulation of the Vf in terms of a quantized gyroscope permits disease to be represented as a braking "torque" decreasing the Vf's angular momentum, causing it to "precess" (i.e., express symptoms). The therapeutic remedy, however, provides an accelerating "torque," increasing the Vf's angular momentum and decreasing precession (i.e., reducing symptom expression). CONCLUSIONS: According to this model, symptom expression corresponds to precession of the Vf "gyroscope." Conversely, complete removal of symptoms is equivalent to cessation of Vf "precession." However, if overprescribed or given in unsuitable potency, the curative remedy (which may also be formulated as a wave function but this time derived solely from changes in Vf secondary symptom observables) may cause the Vf to express proving symptoms. Thus, with only observation of symptoms and changes in them to indicate, indirectly, the state of a patient's Vf, the safest treatment strategy might be for the practitioner to proceed via gradual removal of the symptoms. This is congruent with Hahnemann's later development and use of the LM potencies, as described in his final 6th edition of The organon.

Patient-Practitioner-Remedy (PPR) entanglement, Part 8: 'Laser-like' action of the homeopathic therapeutic encounter as predicted by a gyroscopic metaphor for the vital force.

BACKGROUND: A preliminary mathematical model for the Vital Force had been developed based on the idea of a metaphorical gyroscope, combined with earlier notions derived from Weak Quantum Theory (WQT) and Patient-Practitioner-Remedy (PPR) Entanglement. This combination generates a hypothetical 'wave function' as a description of the state of the Vital Force that is intimately related to the secondary symptom picture of the therapeutic remedy, and is capable of illustrating certain empirical observations of the homeopathic process, including the bi-phasal action of remedies and some of the results gained from provings. OBJECTIVE: The goal of this present study was to further develop the idea of a Vital Force 'wave function' by generating insights into its mode of reaction to therapeutic intervention by a practitioner. METHODS: In orthodox quantum theory, the time-dependent Schrödinger equation, in which a particle's wave function is operated upon by the Hamiltonian total energy operator, provides information concerning the temporal evolution of the wave function. By analogy, a secondary-symptom-dependent Vital Force equation is postulated in which the Vital Force 'wave function' is operated upon by a so-called 'homeopathic operator'. RESULTS: By inserting the previously developed wave function for the Vital Force into the secondary-symptom-dependent Vital Force equation, another equation is generated mathematically reminiscent of longitudinal mode standing waves set up in the resonant cavity of a laser. CONCLUSION: In the language of therapeutics, it is often said an essential part of the curative process is that practitioners act as 'mirrors' for their patients. Previous papers in this series have shown that this reflective practitioner activity is more than a poetic analogy. Borrowing from the mathematical formalism of quantum theory, with its ideas of entangled, coherent wave-functions as metaphors for the homeopathic process, this mirror-like activity can be seen to be an integral part of the curative therapeutic encounter. The preliminary theoretical investigation reported here develops the metaphor further by suggesting that the effect of this practitioner mirror-like activity on a patient's Vital Force during the therapeutic encounter, might be likened to the sequence of operations by which lasers function. The analogy seems compelling, as an essential feature of laser operation is the arrangement of parallel mirrors placed at both ends of the laser's resonant cavity.

Apple II program to simulate the response-time profile of non-depolarising muscle relaxants.

We have developed a BASIC program for the Apple II microcomputer which can simulate the effect (degree of paralysis) time curve obtained following bolus intravenous administrations of pancuronium. The program is based on a combined pharmacokinetic/pharmacodynamic model and has practical application to the anaesthetist under operating room conditions. Knowing the disease state of the patient and the doses and times of administration of pancuronium the microcomputer can predict the degree of paralysis which exists at any time and so assists in the timing of the next dose of relaxant and in deciding when to effect reversal.

[New method for selectivity optimization in thin layer chromatography and its application in pharmaceutical analysis].

A new experimental design method named the step climbing method (SCM), as well as a new global criterion (NRC), are proposed for the selectivity optimization of thin layer chromatography. The method offers chromatographers a convenient means to decide the optimum developer composition for thin layer chromatography. The principle of the method is described, and examples of applications in pharmaceutical analysis are given to certify the feasibility of the method. Clearly, it may also be used for the selectivity optimization in high performance liquid chromatography.

Towards a new model of the homeopathic process based on quantum field theory.

BACKGROUND: Quantum theory's notions of non-locality and entanglement have previously informed attempts to model the therapeutic process. Of these, Weak Quantum Theory (WQT) and Patient- Practitioner-Remedy (PPR) entanglement are developing into mathematically- based models of homeopathy. OBJECTIVE: The present study attempted to identify fundamental concepts within quantum field theory (QFT) that could be used to broaden the scope of PPR entanglement models, prior to constructing a more rigorous mathematical treatment. METHODS: In QFT, particles and forces are considered as fully interacting relativistic quantum matter and force fields, respectively. These interactions are visualized graphically as spacetime Feynman diagrams. Further, these interacting field systems can have ground states with broken symmetry; the so-called Higgs field being responsible for this symmetry breaking. In the new model, patient, practitioner and remedy are imagined as fully interacting quantum-like fields; patients and practitioners in terms of quantum matter-type fields, and remedies and diseases as quantum interaction-type fields. RESULTS: Disease manifestation by the Vital Force (Vf) could be an event similar to spontaneous symmetry breaking in QFT: the curative remedy acting to restore the broken symmetry of the Vf field. Entanglement between patient, practitioner, and remedy might be representable as Feynman-like diagrams. CONCLUSION: QFT demonstrates that quantum properties can be physical without being observable. Thus, an underlying similarity in discourse could exist between homeopathy and quantum theory which could be useful for modelling the homeopathic process. This preliminary investigation also suggested that key elements of previous quantum models of the homeopathic process, may become unified within this new QFT-type approach.

[Relations of physicalism and vitalism in biology: contribution to the year of Darwin 1982]. / Zum Verhältnis von Physikalismus and Vitalismus in der Biologie: Ein Beitrag zum Darwin-Jahr 1982.

With help by an axiom established and some descriptions before this paper, it is possible to model successful processes of growth. In this description, it will be tried to explain in generally form this axiom and to classify it into our scientific system of world. With that comes a dialectical relation between Physicalism and Vitalism. Both continuous and statistical methods are known as possible and necessary forms of description of biological processes. By that the method of Newton can be transferred analogous into Biology with help from the field of information definited before this paper. The developed theoretical conceptions for analysis of growth are conformed also with the demands of system theory by v. Bertalanffy and they will derivated also from his system theory. This work will be finished with firstly ideas for application of this results and with relations of this theory and dialectic.

[On the inhibition of cholinesterases by pancuronium (author's transl)]. / Zur Cholinesterase-Hemmung durch Pancuronium

1. The inhibition by pancuronium of acetylcholinesterase (AChE) and of plasma cholinesterase (ChE) was investigated in vitro regarding a) the sensitivity of both enzymes; b) the mechanism and constants of inhibition; and c) the relationship between the neuromuscular blocking and the anticholinesterase activity of pancuronium. 2. Pancuronium is a reversible inhibitor of both AChE and ChE. The inhibitory potency regarding ChE ([I]50=2.7 X 10(-7) M; Ki=4.2 X 10(-8) M) is highly selective and about 1000-fold higher than compared to AChE ([I]50=2.4 X 10(-4) M; Ki=3.5 X 10(-5) M). 3. The kinetic analysis by means of an Lineweaver-Burk plot and an Arunlakshana-Schild plot displayed a pure competitive mechanism of inhibition. 4. The inhibition of AChE and ChE is thought to be induced by a reversible binding of pancuronium to the anionic subsite of the active center, thus decreasing the formation of the primary enzyme-substrate complex. 5. The clinical administration of pancuronium for muscular relaxation during anaesthesia (0.01-0.08 mg/kg) will result in a concentration of approximately 10(-7)=10(-6) M in the extracellular fluid. Thus, an inhibition of plasma ChE can be expected to occur under clinical conditions, however, probably without practical significance.

A pharmacokinetic explanation for increasing recovery time following larger or repeated doses of nondepolarizing muscle relaxants.

The authors used pharmacokinetic and pharmacodynamic modeling to explain the time course of neuromuscular blockade following single or multiple doses of three nondepolarizing muscle relaxants. Published and unpublished pharmacokinetic and pharmacodynamic data for 13 normal subjects were used to simulate the duration of neuromuscular blockade (time from administration of the muscle relaxant to 25% recovery of control twitch tension) following six successive doses of atracurium (150-400 micrograms/kg initially, followed by 100 micrograms/kg), vecuronium, or pancuronium (30-80 micrograms/kg initially, followed by 20 micrograms/kg). With atracurium, duration of action was similar for the second and sixth doses, regardless of the initial dose. With vecuronium (initial doses of 30-80 micrograms/kg) and pancuronium (initial doses of 30-60 micrograms/kg), duration of action was longer after the sixth dose than after the second; with larger initial doses of pancuronium (70 and 80 micrograms/kg), duration of action was similar following the second and sixth doses. The authors also determined two recovery times (time for twitch tension to recover from 5-25% and from 25-75% of control value) for varying single doses of atracurium, vecuronium, or pancuronium. When the dose of atracurium was increased from 200 to 400 micrograms/kg, neither recovery time increased. When the dose of vecuronium was increased from 40 to 80 micrograms/kg, 5-25% recovery time increased from 6.0 +/- 2.5 min to 8.8 +/- 4.0 min (mean +/- SD) and 25-75% recovery time increased from 8.7 +/- 4.3 min to 12.6 +/- 4.4 min.(ABSTRACT TRUNCATED AT 250 WORDS)

[Attempt at a mathematical definition of pachycurare dosage. Application for pancuronium and AH 8165]. / Essai de définition mathématique de la posologie d'un pachycarare. Application pour le pancuronium et l'AH 8165

Correlations among the elements indispensable to the choice of an average dose of pachycurare are established for surgical needs. Weight and duration of the surgery jointly allow to foresee with approximately 80 p. 100 accuracy the effective dose required for a surgical curarization controlled according to clinical and electromyographical criteria. After calculation of the average consumption of pachycurare per unit of time, a group of curves is established by successive integrations of additional doses representing a family of parabolae corresponding to a second-degree equation: P = alpha + beta t + gamma t2 where P: the cumulative dose for a determined period of time, per kg of body weight and thus total dose if t: the duration of the surgery, t: the time variable, alpha, beta and gamma: significant calculated coefficients. This analytical function established for the use of Pancuronium - bromide in surgery, is also being tried for the curarizing substance: AH.8165.

A pharmacodynamic model for pancuronium.

It has been demonstrated that a simple two-compartment kinetic model may account for the changes in plasma concentration of pancuronium after i.v. administration. However, it can be shown that this simple model does not account satisfactory for the observed changes in muscle twitch response. By the addition of a receptor (biophase) compartment, twitch response can be reconciled with model behavior and the characteristics resemble those predicted by animal studies. The complete model is applied to the problem of total renal failure, and shows that patients with this condition are likely to be marginally resistant to small doses of pancuronium, with a normal rate of recovery. However, larger doses are likely to result in delayed recovery, the duration of effect increasing in a dose-dependent manner.

Un cas de pathogenesie induite par le Lithium carbonicum / A case of pathogenesy of Lithium carbononicum

Age de 61 ans, un homme est traite por un syndrome cyclothymique au Lithium carbonicum, en doses de 900mg/jour (3x300mg), depuis vingt ans. A la consultation, le malade presente des troubles respiratoires, des modifications du trajet EEG, des changements des epreuves fonctionnelles respiratoires et renales, une alteration de la fonction hematopoietique, du ionogramme sanguin et des images echographiques renales. Ce tableau clinique et paraclinique a ete attribue au traitement prolonge par le Lithium. Apres la reduction graduelle du traitement par le Lithium, jusqu'a la suppression et l'introduction concomitante du traitement homeopathique, l'evolution clinique et paraclinique a ete satisfaisante. Les resultats obtenus ont confirme l'incrimination du Lithium dans le tableau clinique general

La homeopatia y las ciencias elementales / The homeopathy and basic sciences

Si la homeopatia no esta totalmente reconocida por la "medicina oficial"no es porque no sea facilmente explicable o sus principios o postulados sean dificiles de entender, sino que, mas bien, es porque los homeopatas no la sabemos explicar al resto des colectivo medico, con una terminologia que nos sea comum. Pienso que si Hahnemann viviese en la actualidad su vocabulario si referiria al utilizado en las ciencias elementales (Matematicas, Fisica, Quimica, etc.) y evitaria toda terminologia que pudiera dar lugar a pensamientos misticos, religiosos, filosoficos, etc. porque la homeopatia es una Ciencia y como tal debe ser exenta de todo movimiento doctrinario o fundamentalista.(AU)