# Method for estimating effectiveness of periodically repeated treatment and prophylaxis in inflammatory periodontium diseases in population group

FIELD: medicine.

SUBSTANCE: method involves carrying out periodontium state diagnosis before and after applying measures during their first repetition period. Intensity of periodontium transitions from one state to another one is additionally determined as reciprocal values of intervals between neighboring mean ages inherent in corresponding nosologic periodontium forms and, after having applied the measures, as ratios of patient number having periodontium state with no inflammation signs to the number of patients having inflammation signs before applying measures multiplied by the number of repetitions. Measures efficiency is determined by applying Markov process techniques as average of distribution of relative patient number having periodontium state with no inflammation signs. It is thought that the more the expected value the higher is the treatment effectiveness.

EFFECT: reduced time and financial costs.

4 dwg, 3 tbl

The invention relates to medicine, namely to the dentist, and can be used to assess the efficiency of the periodically repeated treatment and prevention of inflammatory periodontal diseases (HICP) in the population.

Among the important scientific and practical tasks in the field of prevention and treatment in HICP occupies a special place justification appropriate recommendations for the use of hygiene products. The solution to this problem provides the appropriate ways to assess their effectiveness.

Currently there is no way to assess the effectiveness of recurrent treatment-and-prophylactic measures in HICP in groups based on a mathematical model of the HICP in the state space, allowing for a time the influence of risk factors and ongoing curative and preventive measures for the indicators of oral health, as this model has not been developed.

There is a method of assessing the effectiveness of recurrent treatment-and-prophylactic measures in the HICP populations, including diagnosis of the state of periodontal before and during the events in each period of their repetition. Repeated evaluation of results must be carried out with a given repetition period t is the significance of a long time to determine the influence of risk factors and ongoing curative and preventive measures for the indicators of oral health (Periodontics - 2004 - No. 2, pp.96-102, Periodontics - 2004 - N 3 (32) - P.10-13). The method is the closest solution to the invention and can be adopted for the prototype.

The disadvantage of this method is that its implementation requires significant financial and time resources due to multiple repetitions of research.

The objective of the invention is to reduce time and material costs by identifying the influence of risk factors on the age-related changes in periodontal to events and evaluating their effectiveness in the first period of events in a period of time sufficient for the onset of saturation of preventive and curative effects on the periodontium.

The problem is solved in that in the known method of evaluating the effectiveness of recurrent treatment-and-prophylactic measures in the HICP population by diagnostic States of the periodontium to events and for their conduct with regard to the repetition period of the events, according to the invention, diagnosis of conditions of the periodontium carried out before and after events in the first period of their recurrence, and additional diagnostic data prior events determine the intensity of transitions from periodontal status in the status return value is of intervalof between adjacent middle ages, typical relevant nosological forms of periodontal, and after the events in the first period as the ratio of the number of patients with conditions of the periodontium without inflammation among patients with inflammation to events, multiplied by the repetition period, and evaluate the effectiveness of interventions using the mathematical apparatus of Markov processes as the mathematical expectation of the relative number of patients with conditions of the periodontium without inflammation, believing that the higher the expectation, the higher the effectiveness of interventions.

Studies have shown that the process of development of the HICP in populations subject to the provisions of limit theorems for the total flux is characteristic of all the signs of a Markov process (Wenzel E.C., Ovcharov L.A. Theory of random processes and its engineering applications. - M.: Nauka, 1991, s, 128, 129). The inventors propose a mathematical model of the pathogenesis of HICP for estimating the transition probabilities of the periodontal condition of the absence of inflammatory symptoms depending on the intensities of transitions from periodontal status in the state before and after the event, using the mean ages of the groups, characteristic of nosological forms of periodontitis, which is a new significant feature of the invention. New essential submit that the lump is also holding events only in the first period, that is, one-time events in a period of time sufficient for the onset of saturation of preventive and curative effects on the periodontium. Mathematical models characteristic graph of States of the Markov process represented in figure 1. The vertices of this graph correspond to the following main nosological forms of periodontal: 1 - intact periodontium (PI); 2 - chronic generalized catarrhal gingivitis (HHCG); 4, 6, 8 - chronic generalized periodontitis (HGP), respectively, lightweight (HGP LS), medium (HGB SS), heavy (HGP TC) degrees in the acute phase and 3, 5, 7 - in remission; 9 - tooth loss. Arcs of the graph corresponds to the intensity of transitions from one state to:

λ_{1}-λ_{8}- intensity transitions from periodontal intact periodontal or remission in a state of inflammation or acute (up events);

β_{1}-β_{4}- intensity transitions of the periodontium of the acute stage or inflammation in remission or intact periodontium (after the event).

The invention is illustrated by drawings figure 1-4.

Figure 1 shows the graph of States of the Markov process.

Figure 2-4 presents the performance characteristics recurrent treatment-and-prophylactic m the activities in the HICP populations using toothpaste "New Pearl Mint", "The new Pearl Cedar complex and toothpaste "Parodontax-F" respectively.

The method is as follows.

The Markov process of pathogenesis HICP is defined in accordance with the system of linear differential equations for the state probabilities. As the initial conditions for this system depending on the allocated periodontal diagnoses can be the following: this equality is one of the probability of finding the process at time t=0 the unit. To the initial state, in our case, can be 1-8 status. Interest of the state, reflecting the effectiveness of therapeutic and preventive measures, are States 1 and 3, 5, 7 (intact periodontium; chronic generalized periodontitis, respectively, mild, moderate, severe in remission). To resolve composed of a system of differential equations for interested States under the given initial conditions is applicable operator method (Wenzel, Y.S., Ovcharov L.A. Theory of random processes and its engineering applications. - M.: Nauka, 1991, s-144). According to him using the direct Laplace transform of the system of differential equations is converted to a system of algebraic equations, which is easily resolved relative to the images of the desired probabilities. By means of reverse conversions is of Laplace received the originals of the desired probability, as a function of time.

With this in mind, for initial States 1 and 2 we obtain the following transition probabilities in state 1 at the current time:

For initial States 3 and 4, and the final state 3 are:

and for 5, 6, and end state 5:

For initial conditions 7 and 8, and the final state 7 transition probabilities in the state 7 in the current time expressed as

In mathematical expressions (1)to(8),,,- the roots of quadratic equations, which are determined by the formulas(9)-(12):

To obtain estimates of these probabilities do the following. Based on the distribution of patients according to nosological diagnoses to events build distribution nosological diagnoses by age. Appreciate the well-known formulas average age (mathematical expression is practical expectations),
typical nosological forms of periodontal for a given group of the population, and characterized them confidence intervals. The difference between these ages determine the average times of transitions of the periodontium from one nosological form to another without the events. The inverse values of these times are the corresponding intensities (λ_{1}that λ_{2}that λ_{3}that λ_{5}that λ_{7}) transitions of the periodontium from one nosological form to another.

Values λ_{4}that λ_{6}that λ_{8}determine by monitoring population or taken from clinical practice.

For assessing β_{1}that β_{2}that β_{3}that β_{4}conduct activities in a period of time sufficient for the onset of saturation of preventive and curative effects on the periodontium. According to the results of events during this time determine the relative frequency of transition of chronic generalized periodontitis of the stages of escalation in remission and chronic generalized catarrhal gingivitis in intact periodontium and characterized them confidence intervals. These relative frequencies are found through the relationship of the number of patients with conditions of the periodontium without inflammation (intact periodontium or the corresponding remission among patients with inflammatory to the rosedene events.
Using these relative frequencies (probabilities are not functions of time) and a period of repetition of events evaluate intensity β_{1}that β_{2}that β_{3}that β_{4}by multiplying the values of the relative frequencies of the return value of the specified period of repetition. After determining the values of all intensities included in the formulas (1)to(8), evaluate the effectiveness of interventions as the mathematical expectation of the relative number of patients with conditions of the periodontium without inflammation, believing that the higher the expectation, the higher the effectiveness of interventions. To calculate the mean using the following formula

where:

N - number of patients in the population;

R - the number of the selected forms of diseases of the periodontium;

n_{z}the number of patients with z-the nosological form of periodontal;

P_{z}(t) is the probability of transition of the periodontal condition of z-the nosological forms in nosological form with missing inflammatory symptoms, including z form if she is. This probability is estimated by the formula(1)-(8).

The method is illustrated by the following example.

Example. The assessment of the effectiveness of recurrent treatment-and-prophylactic measures p and inflammatory periodontal diseases in populations, including every 6 months (recurrence interval) professional hygiene of the oral cavity using an ultrasonic scaler and brush with polishing paste Detartrin, patient education rules and methods of brushing teeth with a toothbrush and toothpaste, and the constant use by patients brushes "New Pearl Total" and one of the toothpastes:

- "New Pearl Mint (complex 1);

- "New Pearl Pine Complex (complex 2);

- "Parodontax-F" (set No. 3).

Studies evaluating the effectiveness of activities conducted within one month. Diagnosis of conditions of the periodontium was performed by determining the indices of plaque Green - Wermillion, gingivitis Silness - Loe, periodontal Russel, bleeding Muhlemann & Sax and ultrasonic dopplerography.

The population was represented by employees of one of the largest enterprises in the amount of 640 people aged 20 to 70 years. Among them with PIS was 12 people, with HHCG - 28, with HGP drugs in the acute stage - 219, and in remission - 56; HGP SS in the acute stage - 210, and in remission - 53; HGP TC in the acute stage - 49, and in remission - 13. Prior to the events was obtained normalized distribution of patients according to nosological diagnoses is presented in table 1.

Table 1 | |||||

Age (years) | FE | HGKG | HVPLS | HGPS | HPTS |

20-25 | 0,0909 | 0,27 | 0,64 | --- | -- |

26-30 | 0,0968 | 0,226 | 0,516 | 0,129 | to 0.032 |

31-35 | 0,0652 | 0,087 | 0,674 | 0,174 | -- |

36-40 | --- | 0,05 | 0,45 | value (0.475) | 0,025 |

41-45 | --- | 0,015 | 0,43 | 0,48 | 0,075 |

46-50 | --- | --- | 0,35 | 0,56 | 0,09 |

51-55 | --- | --- | 0,44 | 0,47 | 0,09 |

56-60 | --- | --- | 0,22 | 0,51 | 0,27 |

61-65 | --- | --- | 0,27 | 0,33 | 0,4 |

66-70 | --- | --- | 0,29 | 0,42 | 0,29 |

After normalization of the data given in table 1, were obtained the average age of the patients characteristic nozologicheskie periodontal, values are presented in table 2.

Table 2 | |||||

Name of indicator | FE | HGKG | HVPLS | HGPS | HPTS |

The average age of patients (years) | 27,0 | 27,2 | 40,7 | a 50.5 | 53,6 |

From table 2 it is seen that the average time interval between FE and HGCH for a given group of the population is 0.2 years (2.4 months), and between HGCH and HGP mild - 13.5 years (162 months). The transition from HGB mild to average is 9.8 years (117,6 months) and from it to heavy for 3.1 years (37.2 months). The intensity of these transitions is equal to the inverse value of the found interval. Confidence intervals for estimates of these average ages with a probability of 0.9 for the experimental data collected are from 1 to 2 years. It should be noted that these confidence intervals are dependent on sample size and is not truncated by age groups are significantly less than the difference between the middle ages.

Treatment and preventive measures were carried out for 250 patients. By comparing the original nosological forms at the beginning and at the end of the month (when therapeutic effect is already virtually the ski has not increased) were obtained relative frequency shift nosological forms of periodontal transitions from States 2, 4, 6, 8 1, 3, 5, 7 (table 3).

The intensities of the transitions of the periodontium from state to state on these relative frequencies were determined through multiplying them by the intensity of the complex, which was assumed to be equal 0,1667 (planned repetition period is 6 months). The repetition period is selected based on the analysis of known results: it was believed that the time transitions HGP of remission in the stage of exacerbation of the average is 6 months, and the time interval between HGP severe and loss of teeth - 5 years.

Table 3 | |||

Types of transitions | The relative frequency shift nosological forms | ||

Complex №1 | Complex №2 | Complex №3 | |

2→1 | 0,2 | 0,7 | 0,76 |

4→3 | 0,2 | 0,8 | 0,82 |

6→5 | 0,15 | 0,75 | 0,74 |

8→7 | 0,1 | 0,5 | 0,6 |

In table 3: 2→1 - transition from HGCH in FE; 4→3, 6→5, 8→7 - transitions, respectively, from HGP mild, moderate or severe in the acute stage in the study is remission.

Using the data presented in table 1-3, using a computer to assess the efficacy of e(t) developed by the authors of the C program-oriented language programming in MatLab. The results are shown in figure 2-4.

Comparison of the results obtained by calculation and the results of the clinical examination at 1 year, shows that they coincide with an accuracy of 94%, with significantly reduced time and expense by estimating the efficiency of a single of their implementation.

A method of evaluating the effectiveness of periodically repeated treatment and prevention of inflammatory periodontal diseases in populations by diagnosing conditions of the periodontium to events and for their conduct with regard to the repetition period of the events, wherein the diagnosis of the state of periodontal carried out before and after events in the first period of their recurrence, and additional diagnostic data prior events determine the intensity of transitions from periodontal status in the state as the reciprocal of the spacing between adjacent middle ages, characteristic of the appropriate nosological forms of periodontal, and after the events in the first period as the ratio h is als patients with States without periodontal inflammation among patients with inflammation to events, multiplied by the repetition period, and evaluate the effectiveness of interventions using the mathematical apparatus of Markov processes as the mathematical expectation of the relative number of patients with conditions of the periodontium without inflammation, believing that the higher the expectation, the higher the effectiveness of interventions.

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