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Table of Contents
ORIGINAL ARTICLE
Year : 2020  |  Volume : 8  |  Issue : 3  |  Page : 162-176

Mathematical interpretation of the pharmacodynamics of homeopathic medicines


Ex-Research Assistant, Uvocorp LLC, Kiev, Ukraine

Date of Submission04-Jun-2020
Date of Decision14-Jul-2020
Date of Acceptance03-Aug-2020
Date of Web Publication11-Nov-2020

Correspondence Address:
Mr. John Michel Warner
Berdychivska Street 1, Kiev.
Ukraine
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/JISM.JISM_55_20

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  Abstract 

According to Hahnemann, homeopathic medicines must be great immune-responses inducers. In crude states, these medicines pose severe threats to the immune system. So, the immune system of an organism backfires against the molecules of the medicinal substances. The complex immune-response mechanism activated by the medicinal molecules can handle any threats which are similar to the threats posed by the medicinal molecules. The intersectional operation of the two sets: medicine-induced immune-responses and immune-responses necessary to cure diseases shows that any effective homeopathic medicine, which is effective against any disease, can induce immune responses that are necessary to cure the specific disease. In this paper, this mechanism has been exemplified by the action of Silicea in the human body. Also, a neuroimmunological assessment of the route of medicine administration shows that the oral cavity and the nasal cavity are two administration-routes where the smallest doses (sometimes even few molecules) of a particular homeopathic medicine induce the most effective and sufficient (in amount) purgatory immune-responses. Administering the smallest unitary doses of Silicea in the oral route can make significant changes in the vital force line on the dose-response relationship graph. The dose-response relationship graph further implicates that the most effective dose of a medicine must be below the lethality threshold. If multiple doses of any medicine are administered at the same intervals, the immune-system primarily engages with the medicinal molecules; but along the passage of time, the engagement line splits into two: one engages with the medicinal molecules and another engages with diseases. The immune system’s engagement with the diseases increases along the passage of time, though the engagement with the medicinal molecules gradually falls with the administration of descending doses. Necessarily, I have shown through mathematical logic that the descending doses, though they seem to be funny, can effectively induce the most effective immune responses.

Keywords: Hahnemann’s postulation, homeopathic medicines, homeopathy, immunology, mathematical interpretations, mechanism-of-action, pharmacodynamics


How to cite this article:
Warner JM. Mathematical interpretation of the pharmacodynamics of homeopathic medicines. J Indian Sys Medicine 2020;8:162-76

How to cite this URL:
Warner JM. Mathematical interpretation of the pharmacodynamics of homeopathic medicines. J Indian Sys Medicine [serial online] 2020 [cited 2020 Dec 3];8:162-76. Available from: https://www.joinsysmed.com/text.asp?2020/8/3/162/300490




  Introduction Top


Despite innumerous examples of successful cures by the homeopaths around the world, Homeopathy is not recognized as a scientific treatment method by the mainstream medical frontiers because of the lack of a scientifically proved theoretical basis and laboratory evidences. Regarding this lack of scientific evidences of the efficacy of homeopathic medicines, Anthony King, a critic of the popular journal Nature Research, says, “The principles of homeopathy were created in 1796 and today rely on belief, not scientific evidence.”[1] Critics like Anthony King cannot be blamed much for their failure to understand the mechanism-of-action of homeopathic medicines, because they often failed to dissolve the following maze satisfactorily. That is, if a patient suffers from bacterial fever and if the smallest dose of a medicinal substance which also can produce fever is administered to him, why will the fever producing substance not increase his bacterial fever? Is it not ridiculous that the fever-producing substance will reduce the bacterial instead of increasing it? In Aphorisms 26 and 29, Hahnemann endeavored to answer these questions in an attempt to explain the mechanism-of-action of his medicines.


  Hahnemann’s Postulation and Organism’s Immunity against Simultaneous Threats Top


Indeed, Hahnemann’s explanation of the mechanism-of-action of his medicines is even more difficult because it requires the readers to understand it holistically in terms of the homeopathic concepts such as vital force, vital functions, the Jupiter Analogy, vital principle, miasm, etc which are, indeed, the philosophical predecessors of the modern immunological terminologies such as immune system, immune functions, states of immune deficiencies, pathogens, etc. Despite this difficulty, an attempt to understand Hahnemann-explained mechanism-of-action in terms of the holistic vital force (this vital force is, in no way, the medieval vitalism) necessarily reveals that, in Aphorism 26 and 29, Hahnemann did not merely explain his medicines but also discovered an epoch-making discovery of a complex biological phenomenon as it is in the following postulation:So in homoeopathic cure this vital principle, which has been dynamically untuned by natural disease, is taken over by a similar and somewhat stronger artificial disease, through the administration of a potentized medicine that has been accurately chosen for the similarity of its symptoms. The (weaker) natural dynamic disease is extinguished and disappears; from then on it no longer exists for the vital principle, which is controlled and occupied only by the stronger artificial disease; this in turn presently wanes so that the patient is left free and cured.[1]

In this statement, Hahnemann did not simply explain how like cures like; rather he discovered accurately how the vital force (immune system) behaves when an organism is challenged by multiple threats simultaneously. Indeed, the statement “like cures like” is a layman’s perception of Hahnemann’s great discoveries of complex biological functions of an organism against pathogens and its curative responses against the ailments. It is meant to reduce the complexity of Hahnemann’s philosophy which is shrouded around the mechanism-of-action of homeopathic medicine. However, it simplified the mechanism but not without severely destroying the essence. The statement “like cures like” is as easy for a layman to understand as it is ridiculous for a modern immunologist. Indeed, for an immunologist, the reverse, that, the vital force cures two like ailments with like immune strategies, is more plausible. Indeed, a modern immunological interpretation of Hahnemann’s postulation necessarily tells about the behavior of an organism’s immune system when threatened by multiple challenges as follows:If the immune system (vital force) detects two (almost) similar threats simultaneously, the immune responses (actions of vital principles) which are metered by the severer one consider both threats as one unitary target and treat them with the same defense and recuperative strategies. During the immune responses in action, the less severe infection will be cured faster than the severer one.

Hahnemann’s observation on this behavior of the immune system is quite reasonable. Modern critics like Anthony also failed to understand this precious discovery because they are too busy to understand how “like cures like” (which is apparently ridiculous), while overlooking how the immune system of an organism behaves when it is threatened with similar threats (one natural and another medicine induced). Tons of laboratory evidences can be produced and experiments can be conducted to prove this claim of Hahnemann. But that is out of the scope of my paper. In this paper, I will simply interpret Hahnemann-explained mechanism-of-action of homeopathic medicines, especially Silicea, from a mathematical and immunological perspective. I further will show that Hahnemann-explained mechanism-of-action mathematically abides by the rules of physics and modern immunology.


  Immunological Properties of Homeopathic Medicines Top


The mechanism-of-action of a homeopathic medicine requires a substance to fulfill several criteria to be qualified as medicines. For Hahnemann, germs (in Hahnemann’s words, disease agents) play a secondary role in causing a disease; rather it is some deficiency of the vital force which is the root cause of the disease. Hahnemann believed that disease which “is not exclusively a surgical case consists of a particular pathological, dynamic untunement of feelings and functions in our vital force (vital principle).”[2] So, it will not be unreasonable to believe that homeopathic medicines are not supposed to kill germs. It is apparently paradoxical that, according to Hahnemann, any substances which can terrify, control, and occupy the vital force artificially more than any natural disease can be considered as the raw materials of homeopathic medicines.

In bold line, the first criterion of homeopathic medicine is that the raw forms of homeopathic medicines (with the exceptions of few such as natrum mur, acid phos, etc.) must be highly toxic, poisonous and, therefore, they are strong immune-response inducers, as in aphorism 18, Hahnemann says, “medicines can cure disease only if they possess the power to alter the way a person feels and functions.”[3] The underlined phrase, “the power to alter the way a person feels and functions” is almost analogous to the power of inducing strong immune responses. Again, he describes the essential characteristics of homeopathic medicines as follows: “Every real medicine can at all times and in all circumstances affect every living person and bring about its particular symptoms in him (even clearly perceptible ones if the dose is large enough).”[4] So, it is clear that Hahnemann wanted his medicines to have the ability to “affect every living person and bring about its particular symptoms” and, therefore, to induce strong immune-responses. If we suppose that a medicine T creates a set of threats to an organism, so the set T will be as follows:

T = {Ta, Tb, Tc, Td, Te, Tf, Tg, Th ………}

where Ta, Tb, and Tc etc are threats to organism.

Against this set of threats, the set of immune responses is TR:

T = {Ra, Rb, Rc, Rd, Re, Rf, Rg, Rh ………}

where Ra, Rb, and Rc are organism’s immune response against specific threats.

Hahnemann clearly emphasized that the artificial disease must be stronger than the natural disease as he says, “the artificial disease brought on by a medicine does not have only to be stronger in order to cure the natural disease.”[1] If we suppose again, a splinter or a fishbone has got stuck in the throat/leg of a patient and there is poking pain in the injured area. For some unknown reasons, the patient’s immune system is not producing enough phagocytes which are supposed to consume the splinter and to produce pus (or some phagocytes around the foreign body) to throw it out. The set of splinter/fishbone’s threats to the body is P:

P = {Tc, Te, Tf, Th}

Now, the immune responses against the threats {Tc, Te, Tf, Th} of P should be as follows:

PR = {Rc, Re, Rf, Rh}

As Hahnemann says, the medicinal threat set T must be stronger than the ailing threat set P. Therefore, the immune-response set TR must be stronger than the response set PR both qualitatively and quantitatively. For some unknown reason, the organism’s immune system fails to produce the necessary immune-response set PR. So, PR is almost zero. That is,



The second criterion is that the substance’s property of being toxic and of inducing immune-response must be strong but quickly subsiding so that the vital force does not remain occupied with the medicines for long. In aphorism 18, he describes which properties a substance should have to be the medicine, as he says, “medicines can cure disease only if they possess the power to alter the way a person feels and functions.”[1] Interestingly, Hahnemann wanted his medicines to be strong enough to terrify the organism. But the surprising twist in his claim is that he wanted the terrorizing property of the medicine to subside quickly. Hahnemann demanded that the organism’s immune system (vital force) must react against the medicinal threat set vehemently but the threat itself will exist for a short duration, as he says in the following statement from Aphorism 29: “The vital force frees itself much more easily from artificial diseases than from natural ones, although the former are stronger, because the disease-agents called medicines producing the artificial diseases have a short action.”[1] Strangely, Hahnemann wanted his medicines to have such peculiar property. Indeed, we will try to interpret what happens inside the organism during the administration of medicines with such peculiar property and see if we can justify Hahnemann’s claim. According to Hahnemann’s claim, the medicinal threat T is weaker in terms of longevity (though stronger qualitatively and quantitatively; it can induce strong immune response) than the disease threat set P. So the following is true:



TR response for T threat ……………………………… (c)

PR response for P threat ………………………………. (d)

As T threat is easily subsiding and short-living in statement (c) and we have supposed that, in spite of the threat set P, organism’s immune-response set PR is absent either partially or completely, the following is true:

TR response for almost zero threat ……………………(e)

Almost zero response for P threat ………………………(f)

Now, as the events of statement (e) and statement (f) occur simultaneously in the same organism, the TR response which has been infuriated by the short-living medicinal threat T will address the disease threat P (where the necessary PR response is absent). So the strong immune-response inducing but easily subsiding property of Hahnemann’s medicine is mathematically proved to be quite effective.

The third criterion is that the homeopathic medicine should be able to produce the set of immune-responses which is similar to the symptoms of the natural disease. It is not unknown why Hahnemann was inspired to claim the ability to produce similar symptoms as one of the essential properties of homeopathic medicines. Hahnemann’s observations of natural phenomena which he narrated in Aphorism 46 might have inspired him to reach such conclusion. Not only must the medicines induce strong immune responses (disease symptoms), but also the symptoms they induce must be almost similar to the disease symptoms, as Hahnemann says: “the artificial disease brought on by a medicine does not have only to be stronger in order to cure the natural disease. Above all it must have the greatest possible similarity to the natural disease being treated.”[1] Let us try to delve deep into why Hahnemann admired this “greatest possible similarity” property of his medicine.

Similarity of symptoms means the similarity of immune-responses. If several doses of diluted T are administered at the oral route, the nociceptors of the neuroimmune system will immediately detect the threats posed by the molecules of T. Infuriated by the possible threats, the immune system will start the response set TR {Ra, Rb, Rc, Rd, Re, Rf, Rg, Rh ……..} against the threat set T {Ta, Tb, Tc, Td, Te, Tf, Tg, Th ……..}. Now, the threat sets T and P have some elements in common, the intersection of T and P will be:



Or,



Or, {Tc, Te, Tf, Th}

According to Hahnemann’s postulation, if the “vital force” (or immune system) encounter multiple similar threats at a time, the immune responses are determined by the severe ones and all the immune threats are addressed by the same immune responses. So, when the immune system is threatened by the molecules of T, it addresses the threats with PR response-set {Ra, Rb, Rc, Rd, Re, Rf, Rg, Rh ……..}. As threats {Tc, Te, Tf, Th} are common in both of the threat sets, the PR response set {Ra, Rb, Rc, Rd, Re, Rf, Rg, Rh ……..} will cure the threats of the medicinal molecules along with the threats posed by the foreign body splinter.


  Exemplifying the Mechanism-of-Action of Homeopathic Medicines with Silicea Top


The immune response to the lower potency of Silicea is very much similar to the immune response which a foreign body (inert) normally induces in human body. The array of immune responses that are induced by a foreign body along the duration from the intrusion to the expulsion is also induced by the different doses of Silicea. In Aphorism 29, Hahnemann mentions two disease forces: (a) natural disease (the weaker one) which is caused by the natural disease-agent or outer malefic disease force and (b) artificial disease that is similar and somewhat stronger artificial and caused by potentized medicines. The effect of the medicine on the organism is, indeed, one kind of strong but short-active disease. So the balance between the vital power and disease power is as:

Vital power ≈ disease power

Or, Ability of the immune system ≈ power of the disease-agent

Or, AIS ≈ PDA (1)

If we try to conjure a graphical picture of the abovementioned equation, we will see [Figure 1] that the ups and downs of the Engagement curve of vital force/immune system with pathogen/pathogenic conditions are determined by several factors such as psychological and physical well-being, lifestyle, occupation, eating habit, etc. The graphical presentation is as follows:
Figure 1 (original): The oscillation of vital force from birth to death of a man. Man’s vital force may fluctuate throughout his whole life. Understanding the balance between the vital force and the debilitating effects of the disease agents is very important because the general state of this balance affects and determines the nature and quality of the specific immune response against any diseases and disease-agents. Any point on the curve during the fall of the vital force makes the organism vulnerable to any disease agent

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The abovementioned equation is too general to depict the complex relationship between the immune system (vital force) and the disease-agent; yet it can render an overall picture of the sickness of a man. In disease, the immune system is supposed to be in a losing state as follows:

AIS<PDA

Or, PDA>AIS

where

AIS = ability of the immune system and

PDA = power of disease-agent.

The reversal of this balance depends on both the ability of the immune system and the power of the disease-agent. According to Hahnemann, a homeopath’s sole target is to reverse the balance between vital force and disease-agent. This sacred effort can be impeded by factors of the vital force and the disease. For example, the vital force in the diseased state is directly and indirectly controlled by the following factors:

AIS = MS + HF + PF + CS + SM

where

AIS = ability of the immune system,

MS = miasmState,

Hf = hereditary factors,

PF = psychological factors,

CS = constitutional state,

SM = Suppressive medication, and

C = Causation

Similarly, we can sum up the factors that constitute the power of the disease-agent as follows:

PDA = AEI + ASH + RFB + TFB

where

PDA = power of disease-agent,

AEI = ability to evade the immune system,

ASH = ability to stay in the host,

RFB = reproducibility of the foreign bodies, and

TFB = toxicity of the foreign bodies.

So, if in any condition where one or more than one of the variables is such that the equation can never be reversed into AIS < PDA because the immune system is not able to get the upper hand over the disease force in the battle unless an interference in favor, surgery may be necessary. Now, we will see how the homeopathic medicine Silicea induces immune responses to different doses along different durations. In this regard, we will know more specifically the steps which the immune system takes to clear out any foreign body from the host. Normally, for the immune system, the Silicea or Silicon Dioxide (SiO2) is an antigen which will be ingested by macrophages which will start an inflammatory response by producing interleukin-1, tumor necrosis factors (TNFs), leukotriene B4 and other inflammatory cytokines.[5] Referring to the Silicon-dioxide-induced immune-responses, Suzzane et al. further says,We identify Nalp3 as being an important innate immune receptor involved in the recognition of silica and asbestos by macrophages. Stimulation of macrophages with either silica or asbestos resulted in the robust secretion of IL-1β in a manner dependent on the Nalp3 inflammasome.[5]

So, each of the immune responses elicited by Silicea is very much important for a homeopath, because his sole target is to manipulate any of them to achieve the desired result in treatment. Obviously, we must lead more researches to discover the dose-response relationship of Silicea as well as other homeopathic medicines. But in this paper, I will simply describe the theoretical aspects of the dose-response relationship of Silicea. If we consider the abovementioned equation for Silicea as a disease force, we will get the following:

AIS<PDA

Or, AIS >AEI + ASH + RFB + TFB

(Because PDA = AEI + ASH + RFB + TFB)

where

AIS = ability of the immune system,

PDA = power of disease-agent,

AEI = ability to evade the immune system,

ASH = ability to stay in the host,

RFB = reproducibility of the foreign bodies, and

TFB = toxicity of the foreign bodies.

For Silicon Dioxide particles, the virulence factors AEI, ASH, and RFB are almost equal to zero. So, the immune system can easily get dominance over the particles, and therefore, over TFB. However, when the balance is AIS < PDA, the immune system is in offensive mode. But when the balance is reversed into AIS > PDA, it returns to the nursing mode. In both modes, the immune system reacts differently. For a single dose of Silicea, the VF graph [Figure 2] will be as follows:
Figure 2 (original): Immune-response curve for unitary Silicea dose

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Obviously, this immune response is unitary which is made theoretically speaking against a single Silicea molecule. So, if the unitary or molecular immune response is µ, then IR or VF is as follows:

IR (orVF) = nµ

where n is the number of threatening molecules of Silicea. So, if you increase the number of Silicea particles in the dose, the response curve will expand along both X- and Y-axis. In the following graph, the P point on the curve indicates a stage where the immune system starts to be subdued and incapacitated by the disease force or medicinal pathogens because the immune system cannot overcome a dose which is larger than PR and because the immune system needs to have an immune response (to neutralize such a large dose), which is beyond its capacity.

Here, I must acknowledge Hugo Paul Friedrich Schulz and Rudolf Arndt’s contribution to the development of the abovementioned graph. At any point on the OP slope [Figure 3], the immune system behaves differently against different doses. The more the dose increases (up to RP), the more violently the immune system reacts. So, when the dose increases along the OP slope, the symptoms (medicinal aggravations) of the medicinal pathogens are more and more visible towards the P end and along the PS slope, the inhibitory effect of the medicines increases along the increase of the dose. Hahnemann tells about this inhibitory effect of large doses in the following: “A medicine given in too large a dose, though completely homoeopathic to the case and in itself of a beneficial nature, will still harm the patient by its quantity and unnecessarily strong action on the vital force”.[6] The required time which the immune system takes to overcome the dose also increases towards the end. At the same time, you must note that the stimulation of the immune system increases along the OP slope towards the P end. Hence, we need a position B [Figure 4] which indicates the minimum dose of the medicinal antigen and the correlated highest possible stimulation of the immune system to avoid the medicinal aggravation.
Figure 3 (original though the basic concept comes from Friedrich Schulz and Rudolf Arndt’s Law): This response curve shows how the immune response increases if the doses/number of molecules increases. But if the dose exceeds the maximum dose/lethality threshold, it starts inhibiting the vital force/immune system

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Figure 4 (original though the basic concept comes from Friedrich Schulz and Rudolf Arndt’s Law): The response curve in this graph is almost similar to [Figure 3]], but it shows the most effective dose B on the OP slope

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Another dilemma which a homeopath has to deal with is to decide the dose which will stimulate the immune system to produce so much immune response which will be adequate enough to take initiative against the existing invasion of the external disease force. It means that the dose should be large enough to start the desired immune response and not be large so much that it starts to put extra pressure on the immune system. This claim about the quality of the dose has also been affirmed by Hahnemann in the following lines: “the dose of….homoeopathic remedy….can, as a rule, not be made so small that it is not stronger than the natural disease, that it is cannot at least partially overcome it, that it cannot at least partially extinguish it in the feelings of the vital principle, that it cannot start the process of cure.”[7] If we understand how homeopathic medicines cure we will be able to determine the effective dose for different pathogenic conditions. In this regard, we will consider the intrusion of the aforementioned tiny, thin, and sharp metal into the tissue of the sole as the pathogenic condition. Even after several days of its intrusion, the immune system has not been able to clear it out. Simply it is causing a bit of stitching pain. A homeopath will most probably prescribe Silicea to produce pus to clear out the foreign body. But it is apparently ironical that a homeopath will use a different dose of Silicea to absorb pus. We will explain it in the following part. We have seen the immune response against Silicea. We will also see the nature of the immune response against the foreign body and explain how the interaction between the two types of immune responses helps the physician to achieve the goal. For the aforementioned pathogen, the immune system is taking unusually long time to produce necessary immune responses. But normally the response curve like the green one [Figure 5] should be steeper within a narrower timeframe along the x-axis. But the response curve for the pathogen is staggering over an unusually longer period like the red one. Whereas a healthy immune system will start an innate immune response within 4h after the intrusion, this immune system did not start innate immune response even though several days passed.
Figure 5 (original): Response–time curve for Silicea: In healthy state, the immune response against any disease agent should be steeper like the green one. It is assumed that in the diseased state, the immune-response curve is as dull as the red one

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Now we will see how different doses of Silicea affect this troubled response curve (the red one in [Figure 5]). Earlier we have learnt that Silicea particles have their own response curve (the green one in [Figure 5]). As a pathogen, Silicea particles are endowed with a particular type of toxicity. So, a dose of Silicea within the medicinal limit can create a pathogenic environment which is strong enough to elicit an immune response which will be able to cover the threat caused by the foreign body. This immune response further will be divided into arrays: the first array of responses will gradually clear out the threat caused by the Silicea particles and gradually will die out. But the second array of immune responses is so much stirred and infuriated by the Silicea particles that it will be further amplified by the signal of threat caused by the foreign body. This ability to be amplified by the signal sent by the damage cells is further dependent on the threat posed by the medicinal dose, the site of administration of the drug, the immune ability, miasms, psychological well-being, and strength of the immune signal. Now we will see how different doses of Silicea affect this troubled response curve. Earlier we have learnt that Silicea particles have their own response curve. As a pathogen, Silicea particles are endowed with a particular type of toxicity. So, a dose of Silicea within the medicinal limit can create a pathogenic environment which is strong enough to elicit an immune response which will be able to cover the threat caused by the foreign body. This immune response further will be divided into arrays: the first array of responses will gradually clear out the threat caused by the Silicea particles and gradually will die out [Figure 6]. But the second array of immune responses is so much stirred and infuriated by the Silicea particles that it will be further amplified by the signal of threat caused by the foreign body. This ability to be amplified by the signal sent by the damage cells is further dependent on the threat posed by the medicinal dose, the site of administration of the drug, the immune ability, miasms, psychological well-being and strength of the immune signal.
Figure 6 (original): The green curve shows the rise of the immune-response induced by the Silicea particles. Later, the response curve will split into two: one, which is for the Silicea particles, will gradually die out and another which is supposed to address the existing ailments will die after it addresses the ailments

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Generally, an infuriated immune system will spring to actions and address any impending threat. It will take the steps which are necessary in any particular context. For example, if the stirred immune system finds the site of injury in its initial state (the unaddressed foreign body, damaged cells, and presence of cell-signaling chemicals), it is supposed to initiate responses which will capture the foreign body, neutralize and eat it. It will call for more help. It further will search for more threats; if there is any, it will send more specialized forces (adaptive immune responses) which will analyze the foreign body and estimate the potential threat from it. Then it will develop strategy to defend the body from future attack. Either during this whole process or at the end of the process, the immune system will adopt nursing mode. Ideally if the stirred immune system starts (provided that it is not suffering from any major drawbacks) addressing the threat, it will complete the whole cycle of its functions [Figure 1]. For different Silicea doses, the curve behaves differently. Look at the following two graphs [Figure 7] and [Figure 8] for two different doses (smaller doses and larger doses) of Silicea:
Figure 7 (original): Immune-response curve for repeated smaller dose

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Figure 8 (original): Immune-response curve for repeated large Silicea dose

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Please note that the time covered by the response curve for the larger dose along the x-axis is larger than the time taken by the response curve of the smaller dose. So, repeating the dose for a number of times will necessarily change the nature of the response curve. For example, if the successive doses occur within the innate-response period of the preceding one and if the doses are large enough not to be cleared out by innate or adaptive immune system alone, both innate and adaptive responses will remain active [Figure 8]. In [Figure 8], the Green curve indicates the adaptive immune response, whereas the blue one refers to the innate response. So though larger doses can easily develop offensive immune responses, nursing/caring responses are continuously postponed by them because they remain busy with the offenses. On the contrary, smaller doses complete the whole phase of infection and cure within a shorter timeframe. During the infection phase, the immune responses are instigated, whereas during this nursing mode, the nervous system releases some neurotransmitters such Dopamine, serotonin, oxytocin, endorphins, and many others which create the feelings of happiness and well-being. So, smaller doses or higher potencies can bring the mental well-being prior to the physical cure than the larger doses or lower potencies can do. This finding is quite compatible with Hahnemann’s observation:The signs of improvement in the emotions and mind can be expected immediately after the medicine has been taken only if the dose was small enough (i.e., as small as possible) an unnecessarily larger dose even of the most homeopathically appropriate remedy, apart from its other ill effects, acts too violently and initially disturbs the mind and emotions too strongly and too long for the patient’s improvement to be noticed immediately.[8]

To elicit adaptive immune response the dose must be large enough to fail the innate immune response. It is because the failure of the innate immune response to clear out the threat evokes the adaptive immune response to develop. So if a man comes to a homeopath to clear out a foreign body, the homeopath should prescribe the larger doses. But suppose the same patient revisits the doctor with an infection where there is enough suppuration, and white clammy discharge. These symptoms are indicative of that the immune system has already reached the adaptive immune phase which is, for some reasons, failing to finish the task of healing the infection. For achieving this object of stimulating the adaptive immune response, we need a dose which can complete the whole response phase within a very short time. So, the dose must be repeated during the span from the start of adaptive immune response to the end of nursing mode. Here, the homeopaths must keep it in their mind that as smaller doses cannot elicit adaptive immune response, it is necessary to initiate the adaptive immunity with larger doses. This strategy should be taken if the patient never took the medicine earlier. May be, gradually reducing the dose may help in this regard:

As secondary cell-mediated immune response is specific and, therefore strong, the doses up to a certain amount seem to manifest no visual effects on the symptoms of a disease. Sometimes it happens that larger doses (lower potency) often do not seem to work after the administration of lower doses (higher potency). Also the homeopaths very often face a situation that a medicine worked very well for several days, now it is not working at all. Explanation of such events is quite obvious. After a certain period of the administration of any homeopathic medicine, the immune system develops the adaptive immune response against the medicinal particles [Figure 9]. The time taken by the immune system to develop adaptive immune response and the process of developing the immune response is almost same as the adaptive defense against the bacterial or viral infections. The adaptive immune system is quicker, more specific, and more effective. It can handle larger doses up to a certain limit. So, the same dose which once worked very well to induce innate response is not working anymore now. In this situation, any large dose which is beyond the capacity of the adaptive immunity and larger than the dose which would once easily induce innate response, is supposed to induce the innate response again. The locked dose (which is quickly addressed by the adaptive immunity) fails to induce any stimulatory environment, because the repetition of the same dose at equal interval cannot create a chaotic and alarming environment which the repetition of the different dose at different intervals can create. As increasing the dose puts an extra pressure on the immune system, this target of creating chaotic and alarming environment (which is supposed to induce immune responses and which the locked dose is now failing to create the chaotic and alarming environment) can also be achieved by decreasing the doses at a regular basis [Figure 10]. In general an adaptive immune response on any exposure after the second one is equal to what it is for the preceding one. So, frequent recurrence of descending doses poses a fake severity of the invasion or the infection against which the immune system takes the alertest stance. Moreover, the descending doses gradually decrease the immune system’s engagement with the medicinal particles and increase the amount of lymphocytes and other necessary defensive-nursing functionalities in the host. This environment is strong enough to address the infection which our patient is suffering from.
Figure 9 (original): Inducing adaptive immunity against chronic disease with medicines is a good strategy to fight off long-term ailments. Decreasing doses can be administered for long enough time in order to allow the immune system to grow adaptive response like the red curve. The blue one for the medicine gradually dies out

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Figure 10 (original): Graph showing how decreasing smaller doses of Silicea can keep the immune response almost constant along the x time-axis against the quickly falling doses

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  Immunological Interpretation of Descending Dose of Homeopathic Medicines Top


Prescribing descending dose is another apparently weird practice in homeopathy. A commoner will be in utter maze when he or she is advised to take few drops of medicine from the bottle and subsequently to add the same amount of water to it. Though the homeopaths believe that the strength of the medicines is increased by doing so, such practice can be legitimatized by an immunological and mathematical interpretation. Let’s develop a mathematical model for the repetitive descending doses of Silicea. Suppose, at equal intervals, the doses of Silicea, S decreases geometrically as follows:

(1)

Against each of these doses, the immune response will remain almost the same, though it will decrease very slightly. So, the consecutive immune response will be as follows:

(2)

However, over a certain period of time, the summations of the doses (for 3 doses in this case) and immune responses should be as follows:





[INLINE :9]

(3)

The summation of immune responses is as follows:

R + R−x + R−2x

(4)

If the doses of Silicea do not decrease at regular intervals, the doses (3 doses) and immune responses will be as follows:

S + S + S

(5)

And,

R + R + R

(6)

Please take a look at statement (3) where the three doses of Silicea decrease consecutively and geometrically [Figure 10]. Though the doses decrease, the respective immune response R will not decrease so fast as the doses do. So, if the x is negligible in statement (4), the summation of immune responses is almost 3R. Comparing statement (5) and statement (6), we can conclude that if the same doses, which are administered over a period of time, keep the respective immune responses engaged fully with the doses. But if the doses decrease, a part of the 3R–3x (the summation of the immune responses is 3R as 3x is almost negligible) will engage with the 13s/9 dose. The engaged part of the immune response is assumedly 13R/9. So, the rest of the total immune response (i.e., 3R − 13R/9 = 14R/9) will stay free to be engaged with the existing ailments. It shows that the decreasing doses are more effective to address the disease. Indeed, prescribing decreasing doses of a selected medicine, though popular, often seems to be funny and often homeopaths fail to explain why the decreasing doses work so effectively. However, this mathematical model of decreasing doses show that homoeopathy believes in increasing the vital force’s initiatives against a disease gradually by decreasing the drug-dependency.


  The Most Effective Route of Administration of Homeopathic Medicines Top


Hahnemann started the method of potentization to reduce the toxicity of the medicines and to increase the strength (indeed, efficacy) of the medicine. Hahnemann opined that taking a medicine through the steps of potentization helps to break the healing power free. Potentization, indeed, decreases the toxicity. Potentized dose contains relatively lower number of molecules. So, the organism’s immune system can easily get rid of the few molecules. Regarding the question why the immune-system or the vital force becomes so infuriated by some negligible number of molecules, Hahnemann assumed that thrashing and beating the molecules through the process of potentization breaks free the healing power lying inside the molecules. However, why negligibly few molecules can infuriate the immune system to respond violently lies in the answer of which route of administration offends the immune system the most.

An effective site should be the one where the lowest dose of medicinal particles stimulates the immune system the most. Obviously, a dose of medicinal particles will receive quicker and stronger immune reactions in a highly immune area than what it receives in a low immune area. In this regard, a sound knowledge of Neuroimmune system can be helpful to perceive what the most effective site of drug-administration is. The nervous system plays a very important role in the development of immune responses. The initiation of the immune response is intensively determined and controlled by the central nervous system (CNS) [Figure 11]. In an article, “The Sympathetic Nerve--An Integrative Interface Between Two Supersystems: The Brain and the Immune System,” Elenkov et al. (2000) assesses the role of the CNS in the development of an effective immune defense: “During an immune response the brain and the immune system ‘talk to each other’ and this process is essential for maintaining homeostasis.”[10] Indeed, the hypothalamic-pituitary-adrenal (HPA) axis and the sympathetic nervous system (SNS) are two main routes of communications between the CNS and the whole immune system. Almost all the immune organs are intimately connected with the CNS through peripheral nervous system (PNS). Look at what Dantzer and Wollman (2003) tell about the relationship in their article:The concept that the brain can modulate activity the immune system stems from the theory of stress. Recent advances in the study of the inter-relationships between the central nervous system and the immune system have demonstrated a vast network of communication pathways between the two systems.[11]
Figure 11: Human brain and central nervous system.[9] Source: Martin P R., et al, 2003. Available from: https://pubs.niaaa.nih.gov/publications/arh27-2/134–142.htm

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They further explained how the lymphoid organs are connected with the autonomic nervous system and how the immune functions are regulated by the membrane receptors which bind to the neurotransmitters and neuropeptides [Figure 12]. Immune functions such as cell proliferation, chimiotactism, specific immune responses and many other vital ones are activated and regulated by the integrated neuroendocrine-immune network. In an article, “Relationships between the brain and the immune system,” Dantzer and Wollman (2003) further narrate:The communication pathways that link the brain to the immune system are normally activated by signals from the immune system, and they serve to regulate immune responses. These signals originate from accessory immune cells such as monocytes and macrophages and they are represented mainly by proinflammatory cytokines. Proinflammatory cytokines produced at the periphery act on the brain via two major pathways: (a) a humoral pathway……; (b) a neural pathway, represented by the afferent nerves that innervate the bodily site of infection and injury. In both cases, peripherally produced cytokines induce the expression of brain cytokines that are produced by resident macrophages and microglial cells. These locally produced cytokines diffuse throughout the brain parenchyma to act on target brain areas so as to organise the central components of the host response to infection (fever, neuroendocrine activation, and sickness behavior.[11]
Figure 12: Image showing how the immune cells communicate the CNS. Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5205568/

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It is very much clear from the progress of modern researches on the role of the brain in the initiation of the immune response against any foreign body that the distance between the CNS and the site of infection plays a crucial role in the quality of the immune response [Figure 13]. The nearer the site of infection is to the CNS, the stronger the response is. Furthermore, the nearer the site of infection is to the CNS, the shorter the time which the immune system takes to develop is. Almost all the organs which are involved in the remote regulation of necessary biological and immunological functions of distant target organs through the neuroendocrine signaling system are located in or nearer to the CNS. Scientists believe that the hypothalamus plays as the neural control center for all endocrine systems, whereas the thalamus plays the role of a signal relay-station which relays sensory signals, that is, motor signals to the cerebral cortex[12] and regulating consciousness, sleep, alertness, and other important biological functions. Obviously, the time and the intensity of the response to any infection are related to the distance of the CNS from the site of infection.
Figure 13: Process of feeling pain and the role of the CNS in producing immune responses. Source: http://endocomprehensive.blogspot.com/2013/12/

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It is very much clear from the progress of modern researches on the role of brain in the initiation of the immune response against any foreign body that the distance between the CNS and the site of infection plays a crucial role in the quality of the immune response. The nearer the site of infection is to the CNS, the stronger the response is. Furthermore, the nearer the site of infection is to the CNS, the shorter the time which the immune system takes to develop is. Almost all the organs which are involved in the remote regulation of necessary biological and immunological functions of distant target organs through the neuroendocrine signaling system are located in or nearer to the CNS. Scientists believe that the hypothalamus plays as the neural control center for all endocrine systems, whereas the thalamus plays the role of a signal relay-station which relays sensory signals i.e. motor signals to the cerebral cortex[12] and regulating consciousness, sleep, alertness and other important biological functions. Obviously the time and the intensity of the response to any infection are related to the distance of the CNS from the site of infection. So, the theorization is quite obvious as follows:

IIR α DSOI

Or, IIR = m / DSOI

where

IIR = intensity of immune response and

DSOI = distance of the site of infection from the CNS.

Intensity of immune response is inversely related to the distance of the site of infection from the CNS. Similarly, the time which is taken by the immune system to develop against any infection is also inversely related to this distance as follows:

TIR α DSOI

Or, TIR = m / DSOI

where

TIR = time of immune response and

DSOI = distance of the site of infection from the CNS.

The Central Nervous System plays a significant role in the immune system. So the distance between the CNS and the site of infection or site of administration is important for a number of reasons. Firstly, the hypothalamus controls the immune-responses through neuroendocrine routes, such as the HPA axis and Sympathetic nervous system (SNS), etc.[13] Proinflammatory cytokines which released into the peripheral circulation system travel through the blood brain barrier and interacts with CNS and the distance and the diameter of the nerve fiber affect the time which is taken by the neurotransmitters to reach the CNS [Figure 13] and [Figure 14]. So, the distance which the proinflammatory and anti-inflammatory cytokines travel through to reach the Hypothalamus and the pituitary gland plays a crucial role in determining the quality and intensity of the immune response.
Figure 14: Diameter of the nerve fiber and the respective speed of carrying the signals to the CNS. It purports that the nearer to the CNS the medicines are administered, the severer the threat momentum is. Source: http://endocomprehensive.blogspot.com/2013/12/

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Secondly, the distance between the site of medicine-administration and the CNS is important because the sensory nervous receptor, namely nociceptor, which is responsible for “responding to potentially damaging stimuli” by sending signals to the CNS through the spinal cord to the brain needs to be close to the thalamus as well as the CNS to get quicker and more effective immune responses [Figure 13]. The effective development of the immune defense against any infection or damaging stimuli crucially depends on the successful transmission of the chemical messages to the brain. If the transmission of the casualty is successful, the brain receives it as some unpleasant feelings such as pain, inflammation, etc. Being provoked by the pain-message, the brain (the CNS) takes further defensive initiatives against the injury through an Integrated Network of Organs Regulatory System (INORS). The distance between the CNS and the site administration also plays a crucial role in inducing the desire immune response. The signal of damaging stimuli travels all the way to the brain through different nerve at certain speeds as following. So, it is very much reasonable to assume that the site which will supposedly induce the most effective immune response is the nearest to the CNS.

According to this distance relativity of the effectiveness of the immune response, the oral and the nasal cavities are the most effective sites of administration. Moreover, being the only two gateways which are used to get supply from external world, the oral and nasal cavities are believed to be highly fortified with innumerous nociceptors that are always alert against any trespasses of harmful chemicals and microorganisms. Nociceptors are supposed to “detect signals from damaged tissue or the threat of damage and indirectly also respond to chemicals released from the damaged tissue.”[14] The TRP channels of the chemical nociceptors within the oral and the nasal cavities can detect a wide range of chemical stimulants such as capsaicin, acrolein, external toxins, ligands, certain fatty acid ligands, etc. Even if the damaging stimuli do not exceed the pain threshold, the immune system continues the detection and defending the noxious chemical molecules.

As homeopathic medicines produce different symptoms during the proving, it will not be irrational to think that the damaging effects of the molecules of homeopathic medicines are quickly detected by the nociceptive system of the sensory nervous system. So the scholars who wonder how it is possible for the negligible number of molecules of medicine to bring so great changes are indeed driven by some bestial impulse of filling their patients’ belly with medicinal syrups. But homeopathy is free of such idiocy. Hahnemann might not have any knowledge of the noniceptive process of the sensory nervous system. But he was quite aware that the smallest doses of the poisonous molecules will be detected by the immune system (vital force). So he wanted to keep the subtle counter immune response (vital response) which is evoked by the subtle dose of the medicine uncorrupted and uncontaminated; as usually he advocated that: “Considering the smallness of the dose, everything that could have any medicinal action must be removed from the diet and the daily regimen, so that the subtle dose is not overwhelmed and extinguished, not even disturbed, by any foreign medicinal influence” (Aphorism 259).[15] However, from the abovementioned discussion, it can further be claimed that infection or administration of homeopathic medicine on any innervated organ initiate immune responses are stronger than those which are produced by infection or administration of medicine on any paralyzed organs.

Thirdly and finally, the site of administration in a highly immune or defense area will necessarily evoke the most effective and intensive immune response. Traditionally it is supposed that organs such as tonsil, adenoid, lympathic duct and lymph nodes, etc within the thoracic cage and the skull are the most important ones and, therefore, are highly defended. Take a look at the positions of the immune organs in the following picture [Figure 15]. Another reason behind such defense structure of the immune organs is that they are to defend the oral and the nasal cavities for sterilizing the only permitted routes of intakes of external substances. So, the defense system needs to stay alert and to focus its defense effort on preventing any harmful intrusion. The immune system intimately interacts with the nervous system to keep these areas safe. Being the nearest to the Central Nervous System and the brain, the immune system can efficiently grow an interactive and communicative defense against any external harmful stimuli or substances.
Figure 15: Image showing the density of the position of the immune organs to the CNS. Source: Laura Jayne Watson, “Immune Response”, https://geekymedics.com/immune-response/

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Furthermore, almost all of the organs or glands which directly or indirectly regulate remote target organs for maintaining a healthy state are located in the brain. Functions such as maintaining core temperature through thermoregulation, blood glucose regulation, human iron metabiolism, blood-gas regulation, blood-oxygen levels, Baroreflex and Renin–angiotensin system, maintaining sodium, potassium and calcium levels, maintenance of the neuroendocrine functions through H-P-A axis and many other are directly regulated by the CNS. Any slightest intrusion (or infection) of any harmful external stimuli at the oral and the nasal cavities can easily induce immune responses and affect these functions within the shortest possible time. For example, if administered intravenously at the hand or leg, any amount of toxic substance which is far less than the pain threshold may not be capable of exerting any effects on the nerve. But the same amount will induce a noticeable effect on the nervous system as well as the homeostatic functions of the body. Indeed, the effective site of administration should be the one which helps the lowest dose of MA most effectively to affect the immune system and to produce the expected purgatory antibody. According to this assessment, oral and nasal cavities are supposed to be the perfect sites of administration of homeopathic medicines.


  Conclusion Top


Obviously, all these interpretations are purely theoretical and further researches are necessary to discover the specific effects of this medicine. Such mathematical interpretation of the effects of homeopathic medicines on organisms necessarily can answer many questions that have remained unanswered so far. For example, we now know why oral and olfactory administration of homeopathic medicines is more effective than the intravenous injection. We further can argue if some medicines need to reach the stomach to be effective. Even further researches can be conducted to Also, the mathematical interpretation of the homeopathic medicines, presented in this paper, can help us to explain why several molecules of some toxic crude medicines can set the patients free off some functional diseases so rapidly and, at the same time, to explain homeopathic treatment takes so much time to cure.

I hope this immunological and mathematical interpretation of the mechanism-of-action of homeopathic medicines like Silicea will help researchers to embrace Hahnemann’s therapeutic philosophy and reexamine the efficacy of homeopathic medicines in curing ailments. It will further help researchers to use the discoveries of modern immunology to explain the medicinal properties of a smaller dose of toxic substances. Indeed, this mathematical model of the mechanism-of-action will help the doctors to understand why painkillers should not be prescribed, when the antibiotics will fail and how homeopathic medicines invalidate the use of antibiotics. Physicians can use the mathematical model of Hahnemann’s vital force to assess the stage of the patient’s immune deficiency and to select the relevant medicines. Last but not the least, this model will help the physicians to guess why their prescribed medicines are supposed to fail the desired results.

Financial Support and Sponsorship

Nil.

Conflicts of Interest

There are no conflicts of interest.



 
  References Top

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Hahneman S Organon of medicine, 1842. Translated by Josh Kunzli, Alain Naude, and Peter Pendleton. Los Angels, CA: J.P. Tarcher, Inc. Distributed by Houghton Mifflin Company, Boston, MA; 1982Aphorism-29  Back to cited text no. 2
    
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Hahneman S Organon of medicine, 1842. Translated by Josh Kunzli, Alain Naude, and Peter Pendleton. Los Angeles, CA: J.P. Tarcher, Inc. Distributed by Houghton Mifflin Company, Boston, MA; 1982 Aphorism-18  Back to cited text no. 3
    
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Peyman O, Josiah G, Seraj E-O, Huafeng L, Juan G, Mohamed S, Mary P, Jerry Y Neuroimmune interaction in inflammatory diseases. Clin Med: Circ Respirat Pulmon Med 2008;2: 35-44.  Back to cited text no. 13
    
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Dafny N Pain principles. In: Sensory System. McGovern Medical School at UTHealth, Department of Neurobiology and Anatomy; 1997. Available from: https://nba.uth.tmc.edu/neuroscience/m/s2/chapter06.html. [Last accessed on 2020 May 03].  Back to cited text no. 14
    
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Hahneman S Organon of medicine, 1842. Translated by Josh Kunzli, Alain Naude, and Peter Pendleton. Los Angeles, CA: J.P. Tarcher, Inc. Distributed by Houghton Mifflin Company, Boston, MA; 1982 Aphorism-259  Back to cited text no. 15
    


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15]



 

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