A method for establishing a numerical model of heparin anticoagulant coating release

Abstract

The present invention discloses a method for establishing a numerical model of heparin anticoagulant coating release, belonging to the technical field of anticoagulant coatings for medical instruments. The present invention first proposes two factors affecting the heparin release rate of the model, namely the coating area and free heparin. During the modeling process, the influence mechanisms of the two factors on the model are different, and the two factors are considered separately. When considering the coating area factor, the initial parameters of the coating are used as the initial variables, and the change amount of the subsequent coating area is obtained by an iterative method. When considering the free heparin factor, the shear rate thrombus growth model is used to calculate the heparin consumption. The establishment of the model coefficients can make the model applicable to different types of heparin anticoagulant coatings. Through this model, the time variation laws of the heparin coating release rate and release amount can be analyzed, providing a numerical model basis for the theoretical and applied research on heparin coatings.

Description

Technical Field

[0001] The present invention belongs to the technical field of anticoagulant coatings for artificial blood vessels, and specifically designs a method for establishing a numerical model for the release of heparin anticoagulant coating pipelines Background Art

[0002] In medical devices such as extracorporeal circulation equipment, cardiac pacemakers, hemodialysis machines, artificial valves, and artificial hearts, when synthetic materials come into direct contact with blood, the coagulation system will be activated, causing a series of complications such as thrombosis, sepsis, and multiple organ failure. Coating heparin on the surface of artificial materials can effectively improve the blood compatibility of the materials and reduce the postoperative inflammatory response at the same time. Therefore, heparin coating technology has received extensive attention and application. Heparin coatings are formed by chemical preparation, usually in two forms: ionic bonds and covalent bonds. Regardless of the form in which heparin binds to the material surface, its release kinetics are relatively complex, there is a lack of numerical theoretical research on the release process, and there are problems such as a long experimental period and a complicated process for heparin-coated pipelines. Therefore, numerical prediction can be achieved by performing numerical modeling on the release process Summary of the Invention

[0003] In order to solve the technical problems of the long experimental period and complicated process of the heparin-coated pipeline experimental method, the present invention provides a numerical prediction model that can quickly and effectively conduct theoretical numerical research on the release process, thereby shortening the R & D cycle and cost

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for establishing a numerical model for the release of heparin anticoagulant coating pipelines, including the following steps

[0005] S1. Calculate the heparin release amount in the next unit time according to the initial release rate and initial coating area required in the design task book

[0006] S2. Calculate the effective coating area consumed per unit time according to the heparin release amount, coating concentration, and heparin release amount

[0007] S3. Calculate the effective coating area in the next unit time according to the coating area consumed per unit time

[0008] S4. Calculate the coating area influence coefficient according to the ratio of the coating area consumed per unit time to the effective coating area

[0009] S5. Calculate the wall shear rate of the pipeline wall according to the pipeline radius and flow rate by the Poiseuille formula

[0010] S6. Calculate the thrombus growth rate per unit time according to the mathematical model of the wall shear rate and thrombus growth rate

[0011] S7. Calculate the thrombus growth thickness per unit time based on the thrombus growth rate and the initial wall thickness;

[0012] S8. Obtain the number of platelets generated by the thrombus per unit time according to the relationship between the thrombus growth thickness and platelets, and calculate the amount of heparin consumed per unit time, x, according to the relationship between the number of platelets and the number of heparin molecules consumed;

[0013] S9. Calculate the amount of free heparin per unit time and the total amount of free heparin according to the heparin release amount and the amount of heparin consumed;

[0014] S10. Calculate the free heparin influence coefficient M(i) according to the relationship between the total amount of free heparin and the coating concentration n;

[0015] S11. Calculate the release rate V(i + 1) for the next unit time according to the initial release rate, the coating area influence coefficient, and the free heparin influence coefficient.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0017] 1. The present invention proposes to establish a numerical model for the release of a heparin anticoagulant coating pipeline, and analyzes the influencing factors of the heparin coating release rate through this numerical model.

[0018] 2. By calculating the characteristics of the release amount and release rate changing with time in the heparin coating pipeline through this model, the present invention utilizes an iterative numerical model, making the model more time-dependent and coherent.

[0019] 3. It reduces more costs for the research of heparin coating pipelines, improves the research speed, and provides a theoretical basis for studying the release process of heparin coating pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flowchart of the present invention;

[0021] Figure 2 is a model result diagram of the present invention, where (a) is a diagram of the release amount result. (b) is a diagram of the release rate and the amount of free heparin result;

[0022] Figure 3 is a comparison diagram of the model simulation release amount result of the present invention and the release amount results of other experimental models; DETAILED DESCRIPTION OF THE INVENTION

[0023] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0024] A method for establishing a numerical model for the release of a heparin anticoagulant coating pipeline is as Figure 1 shown, and includes the following steps: First, establish an expression for the heparin release amount per unit time and an expression for the consumed coating area:

[0025] H R (i) = V(i) × S(i) (1)

[0026] where V(i) is the initial heparin release rate and S(i) is the initial coating area.

[0027]

[0028] where n is the coating concentration.

[0029] From formula (1), the effective area of the coating in the next unit time can be obtained:

[0030]

[0031] According to the consumed coating area, an expression for the influence coefficient of the coating area can be obtained:

[0032]

[0033] The thickness of the thrombus represents the number of platelets. The free heparin is mainly produced by the unconsumed heparin. Therefore, to calculate the amount of free heparin, the growth rate of the thrombus thickness needs to be calculated. The expression for the growth rate of the thrombus thickness is:

[0034]

[0035] where Sr is the wall shear rate, Q is the pipeline flow rate, and r is the pipeline radius.

[0036]

[0037] where J is the thrombus growth rate, and a, b, c, d, e are empirical values, which are -28.3, -1, 27.4, -10, 2.718 respectively.

[0038]

[0039] where r(i) is the thickness of the thrombus growth, dt is the change amount per unit time, and r(0) is the initial thrombus thickness.

[0040] After obtaining the thrombus thickness, the number of platelets can be calculated, and the consumed heparin amount can be calculated based on the relationship between platelets and heparin. According to the relationship between the release amount and the consumed heparin amount, the free heparin amount per unit time and the total free heparin amount can be obtained. The expression is as follows:

[0041]

[0042] Where x is the consumed heparin amount, r is the pipe radius, l is the pipe length, Vb is the platelet volume, and Na is Avogadro's constant.

[0043] e(i) = S(i) × V(i) - x (9)

[0044] Where e(i) is the free heparin amount per unit time.

[0045] m(i) = m(i - 1) + e(i - 1) (10)

[0046] Where m(i) is the total free heparin amount.

[0047] According to the influence of free heparin on the release of heparin coating, the expression of the influence coefficient of free heparin is obtained:

[0048]

[0049] Where M(i) is the influence coefficient of free heparin, S(1) is the coating area at the initial moment, and n is the coating concentration.

[0050] Substituting formula (4) and formula (11) into the rate iteration model, the rate expression for the next unit time can be obtained:

[0051] V(i + 1) = V(i) × (1 - (1 + βM(i)) × αc(i)) (12)

[0052] Where V(i + 1) is the rate for the next unit time, V(i) is the rate for the current unit time, α is the coating area influence factor, and β is the free heparin influence factor.

[0053] According to Figure 1 the steps shown for iterative simulation, the numerical change curves of the release amount, release rate, and free heparin amount of the heparin release model over time are obtained, as Figure 2 shown. From Figure 2 it can be seen that the model simulation results have the following characteristics:

[0054] 1. The release amount has a relatively fast growth rate in the initial stage of release. As the release rate slows down, the release amount gradually levels off and then gradually reaches a stable value. The change in the release amount conforms to the release characteristics of the heparin anticoagulant coating.

[0055] 2. The release rate is inversely proportional to the amount of free heparin, indicating that the increase in free heparin inhibits the release of heparin on the coating surface. When the total amount of free heparin increases to a threshold value, the release rate also decreases to a threshold value. The long-term release at a low rate of the release rate can achieve the long-term anticoagulant effect of the heparin coating.

[0056] To further illustrate the feasibility of the model, the simulation results of the model were compared with the experimental results of other models, as Figure 3 shown, in which the time parameter and the release amount parameter were normalized, namely time Tn and release amount Cn. It can be seen from Figure 3 that the results of the release model designed in this paper have a high coincidence with other models and maintain the same release characteristics.

[0057] In summary, the present invention belongs to the technical field of anticoagulant coatings for medical instruments. There is a lack of theoretical research on the release process of heparin coatings. Therefore, the present invention discloses a method for establishing a heparin coating release model. The present invention first proposes two factors affecting the heparin release rate of the model, namely the coating area and free heparin. During the modeling process, the influence mechanisms of the two factors on the model are different, and the two factors are considered separately. When considering the coating area factor, the initial parameters of the coating are used as the initial variables, and the change amount of the subsequent coating area is obtained by an iterative method. When considering the free heparin factor, the shear rate thrombus growth model is used to calculate the heparin consumption. Since there are also differences in the influence degrees of the coating area and free heparin on the model, the influence coefficients of the two factors are defined respectively. The coating area is taken as the main factor and free heparin as the secondary factor. The establishment of the model coefficients can make the model applicable to different types of heparin anticoagulant coatings. Through this model, the time variation laws of the heparin coating release rate and release amount can be analyzed, providing a numerical model basis for the theoretical and applied research of heparin coatings.

[0058] The above only elaborates on the preferred embodiments of the present invention in detail. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those of ordinary skill in the art, various changes can be made without departing from the purpose of the present invention, and all such changes should be included in the protection scope of the present invention.

Claims

1. A method for establishing a numerical model of heparin anticoagulant coating release, characterized in that: It includes the following steps: S1. Calculate the heparin release amount in the next unit time according to the initial release rate of the coating and the initial coating area required by the design requirements; S2. Calculate the effective area of the coating consumed per unit time according to the heparin release amount, the coating concentration, and the heparin release amount; S3. Calculate the effective area of the coating in the next unit time according to the area of the coating consumed per unit time; S4. Calculate the coating area influence coefficient according to the ratio of the area of the coating consumed per unit time to the effective coating area; S5. Calculate the wall shear rate of the pipe wall according to the pipe radius and flow rate by the Poiseuille formula; S6. Calculate the thrombus growth rate per unit time according to the mathematical model of the wall shear rate and the thrombus growth rate; S7. Calculate the thrombus growth thickness per unit time according to the thrombus growth rate and the initial wall thickness; S8. Obtain the number of platelets generated by the thrombus per unit time according to the relationship between the thrombus growth thickness and platelets, and calculate the amount of heparin consumed per unit time, x, according to the relationship between the number of platelets and the number of heparin molecules consumed; S9. Calculate the amount of free heparin and the total amount of free heparin per unit time according to the heparin release amount and the amount of heparin consumed; S10. Calculate the free heparin influence coefficient M(i) according to the relationship between the total amount of free heparin and the coating concentration n; S11. Calculate the release rate V(i + 1) in the next unit time according to the initial release rate, the coating area influence coefficient, and the free heparin influence coefficient; The heparin release amount H per unit time in S1 R (i) The calculation formula is as follows: H R (i) = V(i) × S(i) Wherein, V(i) is the initial heparin release rate, and S(i) is the initial coating area; The effective area H of the coating consumed per unit time in S2 S (i) The calculation formula is as follows: The said n is the coating concentration; The calculation formula for the effective area S(i + 1) of the coating in the next unit time in S3 is: Wherein, V(i) is the initial heparin release rate, S(i) is the initial coating area, n is the coating concentration, the coating area is related to the release rate, the more heparin is released, the faster the effective area of the heparin coating decreases. If the coating concentration remains unchanged, the change in the effective area will affect the release rate in the next time period; The calculation formula for the coating area influence coefficient C(i) in S4 is: Wherein, V(i) is the initial heparin release rate, S(i) is the initial coating area, n is the coating concentration, the surface of the coating is affected by the fluid shear force, which will cause the coating area to decrease due to the erosion effect. After the heparin coating releases a certain amount of heparin molecules, the released heparin molecular weight is equivalent to the consumption of the heparin coating area, that is, the released heparin molecular weight corresponds to the consumed coating area amount; The calculation formula for the wall shear rate Sr of the pipe wall is: Wherein, Q is the pipe flow rate, r is the pipe radius. In human blood vessels and pipe equipment, the flow state is relatively stable, and the wall shear force is proportional to the flow velocity and resistance; In S7, the calculation formula for the thrombus growth rate J per unit time is: Wherein, Sr is the wall shear rate of the pipe wall, and a, b, c, d, e are empirical values, which are -28.3, -1, 27.4, -10, 2.718 respectively; The calculation formula for the thrombus growth thickness r(i) per unit time is: Among them, r(0) is the initial thrombus thickness, and dt is the change amount per unit time; there is a corresponding relationship between the thrombus formation speed and the wall shear stress. Under a certain resistance, the greater the flow velocity, the greater the wall shear stress, and the greater the destruction effect of platelets per unit time, resulting in a thicker thrombus thickness; The calculation formula for the amount of heparin consumed x per unit time is: where r(i) is the thickness of thrombus growth per unit time, r is the radius of the pipeline, l is the length of the pipeline, V b is the platelet volume, and N a is the Avogadro constant; according to the thickness r (μm) of the thrombus and the area of the vessel wall surface (cm 2 ), the volume of the thrombus layer (cm 3 ) can be calculated; multiplying the volume of the thrombus layer by the concentration of platelets in the human body can approximately obtain the number of platelets contained in the thrombus layer; after obtaining the number of platelets, the number of thrombin receptors on the platelets is used to obtain the number of heparin molecules required to resist the thrombus. After taking the ratio of the number of heparin molecules to the Avogadro constant and multiplying by the mass of the heparin molecular weight during the preparation of the coating, the total amount of heparin x consumed to eliminate the thrombus with a thickness of r per unit time can be obtained; The calculation formulas for the free heparin amount e(i) and the total free heparin amount m(i) per unit time are: e(i) = S(i)×V(i) - x m(i) = m(i - 1) + e(i - 1) Among them, V(i) is the initial heparin release rate, and S(i) is the initial coating area; The calculation formula for the free heparin influence coefficient M(i) is: The method for obtaining the release rate V(i + 1) in the next unit time in S11 is: Substituting the coating area influence coefficient and the free heparin influence coefficient into the rate iteration relationship, we can get: V(i + 1) = V(i)×(1 - (1 + βM(i))×αc(i)) Among them, α is the coating area influence factor, and β is the free heparin influence factor; since the influence of the free heparin amount on the release rate is essentially a diffusion effect, and the total free heparin amount m(i) and the free heparin influence coefficient M(i) are an accumulative process, so before the free heparin amount reaches a certain threshold, the influence on the release rate is relatively small; considering the coating area, the effective area consumed will directly affect the coating area coefficient c(i), so the coating area is regarded as the main influencing factor α, and the free heparin is regarded as the secondary influencing factor β. Thus, the release rate in the next unit time is defined.

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