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Differential Treatment mathematical model_3163

By Stephen Sanders,2014-10-30 15:10
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Differential Treatment mathematical model_3163

Differential Treatment mathematical model

     Key Words syndrome differentiation;,, mathematical

    model;,, quantify dialectical;,, quantitative set of square,,,,

     Abstract: Differential Treatment of the traditional process of "disorders ? Card ? Therapeutic Methods ?

    Prescriptions" do a further decomposition, described in detail the elements of disorder and dialectic between the "weighted sum" relationship between the dialectical elements and permit the "logic combination "relationship with the disease and

    permit the derivation of the relationship between disease factors, disease factors and the corresponding set of square elements of the relationship between the drug effect as the offset between the lesion factor (in partial correction)

    relations, the dialectical model of the past have expanded to dialectical model of the complete set of square.

     Key words: Differential Treatment; mathematical model; quantify the dialectical; quantitative set of square

     In recent years, standardization and quantification of traditional Chinese medicine has made significant progress, to a certain extent, explain in traditional Chinese medicine can not only qualitative but also quantitative, this mathematical model provides for the establishment of favorable conditions.

    Conversely, mathematical models in turn to Chinese medicine to provide standardized and quantitative frame of reference. The establishment of mathematical models and standardization and quantification of the mutual promotion and common development.

     1 Model Overview

     Early (in the early 20th century, 80 years) There are two main mathematical models: the weighted sum of model and the

    logical combination model. These two models are only used to describe the relationship between disease card, that is only a description of syndrome differentiation process "Disease ?

    Card ? Governance Act ? Prescriptions" in the "disorders ?

    card," are dialectical model. 80 years since the late 20th century, the model research and development is slow, and were

    confined to the dialectical model. Differentiation of the previous model is the integration and expansion of the "disorders ? Card ? Therapeutic Methods ? prescriptions"

    for further decomposition, as shown in Figure 1, to enable a

    more comprehensive description of the contents of syndrome differentiation and treatment. The model input is present in patients with clinical symptoms and medical history information, the output is prescriptions. The following discussion on model decomposition.

     Figure a model structure (omitted)

     2 Differentiation and Disease Identification

     "Syndrome" is based on Chinese medicine theory, through the cross-checks pentad (symptoms, signs, etc.) analysis, to determine their disease-bit and the nature of disease

    pathology, etc. - Certificate hormone (Note: This study was called "dialectical elements"), and were made to permit the diagnosis of cognitive process of thinking [1,2]. Figure 1 E and L is the model of the dialectical part of the. E, defined

    as follows:

     ei = fi (x1, x2, ... xn) (1)

     Equation (1) According to the symptoms and signs (hereinafter referred to as "symptoms") elements of the calculation Syndrome (liver, spleen, food product, cold, air stagnation, Yang, etc.). Where ei dialectical elements in the collection on behalf of the first i items of dialectical elements; xj symptoms of the collection on behalf of the first j one symptom; fi is a nonlinear function. When ei reach the required threshold, the dialectical elements of the

    establishment.

     Dialectic is not currently identified as elements and

    non-linear relationship between the various symptoms, unable to establish fi, they can be used for temporary use (2) type instead of (1) type.

     wi = Σn jbi, jxj (2)

     Type (2), wi is the first i items of dialectical elements eiwi weights, when wi reach the required threshold value, the dialectical element ei established; xj symptoms of the collection on behalf of the first j months severity of

    symptoms, take [0,1] interval value; bi, j on behalf of j a symptom of the first i-dialectical elements of the diagnostic value (referred to as "weights"), taking [0,1] interval value.

     L is defined as follows:

     L = ? i ((? j (wi, j ? ti, j)) ? (? j (| X ? Si, j

    | ? pi, j)) ?) | X ? N | = 0) ? (? j (wi, j ? ti, j)) ?

    (? j (| X ? Si, j | ? pi, j))) (3)

     Equation (3) is based on this treatment in patients with symptoms and syndromes when the elements and the last treatment when the symptoms and syndromes elements to

    calculate the name of a certificate diagnosis of whether to set up. Calculation result is a logical value: "true" or "false." "True" indicates that the establishment permits were diagnosed, "false" means not valid. A diagnosis of whether to

    set up certificate name can depend on a number of dialectical standards, as long as a standard to be met, the card name that the establishment of the diagnosis.

     Type (3) of the wi, j from (2)-type derived, which

    corresponds to the dialectic of the first i standard of the first j elements of a dialectical; ti, j is the wi, j is required to achieve a threshold; X is that the patient in this second treatment when the symptoms of a collection, Si, j is the first i standard of the first j Syndrome symptoms of a

    subset of, pi, j is the first i standard of Syndrome, the patient should have Si, j in the minimum number of symptoms; N represents a denial of the permit were diagnosed symptoms (identification of disease) collection. w'i, j, and t'i, j

    corresponds to the dialectic of Article i, the standard treatment when the patient last dialectical elements and required to achieve the threshold, X 'is the last treatment,

    when patients with symptoms of a collection, p'i, j is the first article i dialectical criteria, the patient should be the last treatment with S'i, j in the minimum number of symptoms.

     Diseases and syndromes identified using the same model.

     Three elements of governance law and the lesion

     Lesions element refers to the drug's efficacy (bias) of

    the targeted disease-bit, illness, etc., such as: upper and lower limbs, liver, Shaoyang, where cold, cold, inner wind, outside air, food product, blood deficiency, gas inverse, gas trap and so on. Lesions element is in the light of drug

    efficacy (bias) and bias and drug corresponding to each, based on the elements of the dialectical refinement. Figure 1 E, f, M elements used to calculate the disease.

     f is a single mapping function, from the "(disease, certificate) elements of" a collection of maps to the

    governing law set. An "element of the disease," only with a government counterpart wears. Although the card can have a law, but surely there is only one governing law is the most appropriate. In fact, f is a reversible mapping, namely,

    "Diseases of elements on the"-one correspondence with the

    governing law.

     Governing law is a license for the specific treatment of disease. From the wording of the terms governing the method by a number of phrases, each phrase with one or more

    corresponding drug's efficacy, each has a drug's efficacy against a disease factor, it is essentially a rule France for a number of pathological factors. Such as "heat-clearing and

    dampness, qi and stomach" by "heat", "dampness", "qi and stomach," composed of three phrases, which correspond to the drug's efficacy: heat, dampness, qi. These three elements of drug efficacy against disease are: where heat, in wet, air stagnation.

     Governing law is in the long-term medical practice, by

    Syndrome-depth understanding and analysis, highly summarized and extracted, and it not only against the disease, currently being shown by lesion factor (which may be calculated in the model E), but also for the lesions did not show the elements

    (potential pathogenesis, disease transfer, etc.) There are also seeking this treatment, rousing and so on. So, for a single card in terms of diseases, from governance law against disease elements (set A2) compared with lesions from the E calculated elements (set A1) more comprehensively and

    accurately reflect the disease state, this time, there must be A1A2. But for folders and cards, need to be A1 and A2 for special merger - with the right to merge (similar to fuzzy sets combined), from Figure 1 in the M to achieve this merger

    to be a collection of pathological elements of A, in order to fully reflect the pathological state of . The so-called "right

    to merge with," refers to seeking and which set of A1 and A2, if the same element of a disease have emerged in the two collections, then take the weight is greater. "Take the right to merge" operator is defined as (a collection "and" with the Boolean operator ? "plus" a combination of operator ?), the

    operator is defined as follows:

     A = A1A2 = (ew | ew ? A1 or ew ? A2;

     If ew1 ? A1 and ew2 ? A2, then ew = emax (w1, w2)) (4)

    reposted elsewhere in the paper for free download http://

     4 Prescription

     Group party is a collection of A selection factor for the disease, and prescription drugs, the composition of herbs, so

    herbs in the drug's efficacy (bias) was synthesized just be able to "offset" (in partial correction) A factor in the disease.

     Prescriptions for the relationship between the elements and the lesion is a complex and diverse non-linear

    relationship, mainly including the following three aspects: ?

    the overall effectiveness of herbs and elements of the relationship between the lesions, namely, how to calculate the required elements under the lesions of various effects and their effectiveness (the effectiveness of weight); ?

    Prescription drugs with the overall effectiveness of the relationship between the various effects, namely, how the various effects of the various drugs to calculate the overall effectiveness of herbs; ? ? and ? How to choose according

    to prescription and drugs and their dosage. Ruoqiang Prescription expressed as a collection D = (dv | d, said

    drugs, v said the amount of), then the relationship could be indicative defined as follows:

     divi = fi (e1w1, e2w2, ..., emwm,

     ci1ri1, ci2ri2, ..., cimrim,

     d1v1, d2v2, ..., dnvn,

     y1u1, y2u2, ..., ymum) (5)

     ij entry cij and the unit dosage of the effectiveness of the effectiveness of rij; dkvk indicated that they had an opt-

    in prescriptions of drugs and their dosage, in which k ? i;

    yjuj that it has an opt-in prescriptions overall effectiveness of all drugs in the first j items of the effectiveness of yj and the effectiveness of uj.

     Equation (5) a function f as shown in the study may need

    long to get a precise definition, it may ultimately not get a precise definition of (not possible). To solve the problem step by step approximation method is used, that is, over time, gradually establish an equation (5), closer and closer, and can achieve sub-linear function instead of f. At present, it can be divided into two parts to achieve, and simplified as in Figure 1 g, and F.

     Figure 1 g is an invertible map, which is based on disease factors and the set of square elements of the collection A collection of C-one correspondence between the

    relationship: C = g (A) = (cw | cw = g (ew), ew ? A). Set of

    square elements is the efficacy of drugs, sexual taste go through, lifting floating and sinking, the role of parts, etc. (hereinafter collectively referred to as "bias"), such as: upper and lower limbs, liver, Shaoyang, temperature, the cold-

    dispelling, interest-wind, Qufeng, digestion, blood, Jiangni, lifting depression, etc.; They are against the lesion elements: the upper and lower limbs, liver, Shaoyang, where

    cold, cold, inner wind, outside air, food product, blood deficiency, air reverse, gas trap and so on. Determine the set

    of square elements of the principle that: ? the elements in

    each group between the parties with minimal effect on the cross; ? all the set of square elements to cover "in medicine" and "Prescription study" all the textbooks, the efficacy of drugs and prescriptions, sexual taste Tropism, lifting floating and sinking, the role of parts and so on. Map g does not change the weights, so that each set of square elements of cw exactly equal to the weight of it against the weight of pathological elements of ew, which aims to make the final formation of prescriptions just to offset the effect of lesion composition.

     Under the set of square elements of a collection C = (c1w1, c2w2, ..., cmwm) to select group of party drugs. In Figure 1 F is the model selected group of some of our drugs, but also the most complex parts. The following discussion of the F decomposition.

     Set up a collection of the final forming of prescriptions for the Y = D1 D or Y = D1 D2 D, where D1, D2-based side, D

    for the addition and subtraction, each set contains the drug name and dose. The former type that use only a basic party; after the ceremony, said the basis of need to choose two sides as a co-parties, such as stomach bleeding disease in the stagnation of cards selected based side to Shixiaosan Danshen cited. Will be the basis of a first side (the first i in the first base side) of the bias expressed as a set of DCi = (ci1ui1, ci2ui2, ... cimuim), where cij for the first item ij bias, uij for the first i in the first recipe the first item

    bias ij effect; to a blindly drugs (the first i smell of drugs) is expressed as a set of bias DCi = (ci1ri1, ci2ri2, ... cimrim), where cij for the first item ij bias, rij taste of drugs for the first i first item bias ij the effect

    of dosage units, called "bias factor." The selected drug group's first target is: the final form of the herbs Y is just the effect of the bias is equal to the corresponding set of square elements of the weight. The Prescription of a bias equal to the basis of side effect of D1, D2 of the side effects of various drugs with D, the effect of the bias and, as equation (6) as follows:

     Σk i = 1uij Σh i = 1rij × vi = wj (6)

     Equation (6), k = 1 or k = 2, uij for the first i in the first base side Di's first ij the effect of item bias, rij taste for the D, the first drug i first item bias ij coefficient, vi is D the first i taste the drug dosage, wj

    item j for the first set of square elements of weight.

     Defined set of square factor set for the XE = (z) ? X ?

    C ? Y. Where X is the time of treatment in patients with symptoms of this collection; z is the diagnosis of patients with evidence of this name; C is C, the value of the various elements of the right omitted after (without the right values)

    set of square elements of sets, namely, C = (c | cw ? C), and

    C is based on patients with lesions of this element of g mapped out through the set of square elements of sets; Y is the Y amount spent each Herbs (only constituted by drug name) is a collection of prescriptions.

     Basis for the definition side set of attributes for the FA = Z ? DC. Where Z is the set of the basis of the indications side, Z = (z1, z2, ..., zn); DC is a DC in the weights of the elements omitted after (non-bias effect) the

    partial nature of collection, DC = (c | cu ? DC).

     Attribute set for the definition of drug YA = Z ? XS ?

    XT ? YP ? YQ ? DC. Where Z is the set of the drug's

    indications, XS is the set of indications, XT is a contraindication set; YP is a commonly used drug compatibility

    (the drug) name of the drug sets, YQ is the name of the drug incompatibility set; DC is the drug non-bias bias coefficient

    sets.

     FY defined as all of the available prescription drugs and all the available collections.

     Prescription drug selection algorithm The basic steps are as follows:

     ? Y = Ф.

     ? will be the first prescription for each FY of the attribute set with the set of square factor set match, that is, according to equation (7) Calculate the matching value;

    the FY properties of drugs in each set of blind-side factors

    and the group set match, that is, according to equation ( 8) Calculate the match. Selected matches the largest value of a prescription drug fd or blindly d. If you selected the prescription, then turned to ?; of drugs, if elected, then

    turned to ?.

     | Z ? (z) | × rz | DC ? C | × rc-| DC-C | × rd (7)

     | Z ? (z) | × rz | XS ? X | × rs | DC ? C | × rc |

    YP ? Y | × rp - | DC-C | × rd - | XT ? X | × rt - | YQ ?

    Y | × rq (8)

     Where rz, rc, rd, rs, rt, rp, rq is a pre-determined rate

    through the statistics and experiences of the coefficient.

     ? According to the d corresponding to the bias set of square elements of the weights, using equation (9) Calculate the corresponding set of square elements of the required

    dosage of the drug v, and then select those in greatest use as a drug.

     v = min (vu, (vl (vu-vl) / (wm-wl) × (w-wl)) / r) (9)

     Where vl ~ vu is d dosage, vl is the smallest effective amount, vu is the maximum safe dosage; r is the coefficient of bias; w is the bias corresponding to the set of square elements of the weights, is also the group side elements of the lesions targeted by the weight of the elements. Pathological factors (ie set of square elements) divided into

    mild, moderate and severe three grades, respectively wl, wm, ws said the three levels of the lower limit, they are pre-

    determined rate through the statistics and experience.

     ? Y = Y (dv).

     ? using equation (10) from the d corresponding to the

    partial nature of the right set of square elements of the value of the bias by subtracting the effect of d are obtained do not offset the value of the residual power. Then, turning to ?;

     w = max (0, w-((v × r-vl) × (wm-wl) / (vu-vl) wl)) (10)

     ? Y = Y fd.

     ? using equation (11) from the fd of the bias corresponding set of square elements of the right to subtract the value of the bias of the effect of fd, find the remnants do not offset the weight.

     w = max (0, w-u) (11)

     ? If the set of square elements of a collection of C, the elements of the right side of each group the value of w have all been 0, then the end; otherwise turn to ?.

     Prescription drug selection algorithm for the final formation of prescriptions for the Y = (d1v1, d2v2, ...,

    dnvn).

     5 Conclusion

     Development of the disease processes and drug effects on the process of the human body is an extremely complex nonlinear system, such a system, between the symptoms and the symptoms, drugs and drug between the various effects of drugs, and between drugs and symptoms there is an extremely complicated between all the non-linear relationship. Failure

    to describe such a non-linear relationship, the adoption of the method of successive approximation, using sub-linear

    relationship to replace the non-linear relationship is

    feasible. This model is a preliminary study of this approach.

     This model there are the following deficiencies: ?

    efficacy did not reflect the relationship between the relevant

    and complex effects, such as "warm inside" and "cold-

    dispelling" between "gas-breaking" and "Qi", between "Qi" and the "blood circulation" between other; ? cited did not

    reflect how the choice of drug. Yet to be further expanded and improved.

     References

     1 Zhu Feng, Gan Huijuan. An Analysis of the contents of certificate elements. Medicine Herald, 2005,11 (1): 11.

     2 Zhu-feng. Common symptoms of the measurement of dialectic. Liaoning Journal of Traditional Chinese Medicine,

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