A method for constructing a model for calculating inert gas tension in human tissue

Abstract

The present application is a method for constructing an inert gas tension calculation model in human tissue: a pressure change rate function of a certain tissue in a human body is established and is transformed to obtain a first-order non-homogeneous linear differential equation; a standard form and a general solution form of the first-order non-homogeneous linear differential equation are constructed; the first-order non-homogeneous linear differential equation and the general solution form are correspondingly assigned and substituted into the general solution form to obtain a general pressure function of a certain tissue in a human body; the general pressure function of a certain tissue in a human body is used to construct a pressure function g1(x) of a certain tissue in a human body under an exponential pressurization scenario of respiratory gas, a pressure function g2(x) of a certain tissue in a human body under a linear depressurization scenario, and a pressure function g3(x) of a certain tissue in a human body under a linear pressurization scenario; and the g1(x), g2(x) and g3(x) are used together with an inert gas percentage content d to construct inert gas tension calculation models G1(x), G2(x) and G3(x) of a certain tissue in a human body under the exponential pressurization, linear depressurization and linear pressurization scenarios.

Description

Technical Field

[0001] This invention relates to the field of model building technology, and in particular to a method for constructing a calculation model of inert gas tension in human tissue. Background Technology

[0002] Diving (the process of a person submerging below the surface to a certain depth, staying there for a period of time, and then rising to the surface) has been a means for humans to struggle against nature since the primitive era. With the needs of production struggles, class struggles, scientific experiments, and the continuous improvement of industrial technology, diving technology has been increasingly widely used and developed accordingly, and has now become a specialized technology.

[0003] Diving has become an indispensable technology in economic development, national defense, scientific research, and military operations, undertaking many important tasks in both military and civilian fields. These include: submarine rescue, salvage of sunken ships (objects), maritime rescue, underwater exploration, underwater construction (laying pipelines and cables, building naval ports and wharves, underwater special engineering and facilities), channel clearing, underwater reconnaissance and blasting, underwater supply, bridge construction, aquaculture, reservoir maintenance, underwater resource exploration and development (oil, natural gas, mineral deposits), and marine scientific research—all of which require extensive diving operations.

[0004] At normal atmospheric pressure, a human experiences 1 ata. At a depth of 10 meters underwater (referring to seawater; freshwater corresponds to 10.3 meters), the human body experiences 1 ata of atmospheric pressure and 1 ata of hydrostatic pressure, resulting in a total environmental pressure of 2 ata. At a depth of 20 meters, the human body experiences 1 ata of atmospheric pressure and 2 ata of hydrostatic pressure, resulting in a total environmental pressure of 3 ata, and so on. Therefore, during diving operations, a person simultaneously experiences atmospheric pressure and the corresponding depth's hydrostatic pressure, requiring them to breathe compressed air to balance the internal and external pressures, thus placing them in a high-pressure environment.

[0005] In terms of breathing air, its main components are oxygen, carbon dioxide, and nitrogen. When breathing compressed air under high pressure, the levels of oxygen and carbon dioxide usually do not change significantly due to the body's special regulatory functions (except for "oxygen poisoning" caused by excessively high oxygen partial pressure or "carbon dioxide poisoning" due to special accidents). Nitrogen, as the most abundant component of air, is the most commonly encountered inert gas in conventional air diving (it has low chemical reactivity, does not participate in the body's metabolism, is not utilized by the body, and exists in the body only in a purely physical dissolved state; such gases are called "inert gases" in diving medicine, such as nitrogen, helium, neon, argon, krypton, and xenon). However, the human body cannot utilize nitrogen, nor does it have a mechanism to regulate nitrogen levels. The amount of nitrogen dissolved in the body increases with increasing nitrogen partial pressure in inhaled air and decreases with decreasing nitrogen partial pressure. This characteristic creates unique challenges in diving medicine.

[0006] When the body is in a high-pressure environment, inert gases continuously dissolve into various tissues. Over time, the total amount of inert gas dissolved in the tissues gradually increases until it reaches an equilibrium state, where the amount of gas entering and leaving the tissues is equal. This state, where a certain inert gas reaches a point under a certain pressure where it can no longer dissolve in tissues, is called "saturation" of that gas within the tissue at that pressure.

[0007] When the pressure drops from high to low, the amount of inert gas that had dissolved into the tissue at high pressure exceeds the maximum amount that the gas should dissolve in the tissue at lower pressure. However, the excess gas still dissolves in the tissue. This state is called "supersaturation".

[0008] When the surface tension of an inert gas dissolved in a tissue is higher than the external air pressure, the inert gas will be released from the tissue to gradually balance the surface tension of the inert gas in the tissue with the external air pressure. This process is called "desaturation".

[0009] The saturation and desaturation of inert gases in tissues are accomplished through the respiratory and circulatory systems.

[0010] When compressed air is inhaled, the partial pressure of nitrogen in the alveoli increases accordingly. As blood flows through the alveoli, nitrogen dissolves into the blood due to the pressure difference between nitrogen and nitrogen tension within the blood, thus increasing the nitrogen tension in the blood. Blood saturated with a certain amount of nitrogen flows to the tissues, where the nitrogen tension is higher than that in the tissues, causing nitrogen to diffuse from the blood into the tissues. When blood flows back from the tissues to the alveoli, nitrogen dissolves into the blood again. This cycle repeats continuously. Finally, the partial pressure of nitrogen in the alveoli and the nitrogen tension in the blood and tissues tend to reach equilibrium, achieving complete saturation. This process is called nitrogen saturation.

[0011] When the external air pressure decreases to a certain level, the partial pressure of nitrogen in the alveoli decreases accordingly. The surface tension of dissolved nitrogen in the blood is higher than the partial pressure of nitrogen in the alveoli (supersaturation of nitrogen in the blood), so nitrogen leaves the blood and diffuses into the alveoli (desaturation of nitrogen in the blood). When this blood flows back to the tissues, the surface tension of nitrogen previously dissolved in the tissues is higher than that in the blood, so nitrogen continues to leave the tissues and diffuse into the blood (desaturation of nitrogen in the tissues). The blood circulates back to the alveoli, and the nitrogen brought from the tissues diffuses into the alveoli again. This process is called nitrogen desaturation. This process repeats until the surface tension of nitrogen in the tissues and the partial pressure of nitrogen in the alveoli gradually reach equilibrium, that is, complete desaturation is achieved. It must be pointed out that this is a form of desaturation, in which the gas, in a dissolved state, leaves the tissues through the blood circulation and respiratory system in a gradual diffusion manner, and finally leaves the body through the alveoli. Such desaturation does not have a harmful effect on the body, so it is called "safe desaturation." The decompression that can cause "safe desaturation" of inert gases is called "safe decompression." Another form of desaturation occurs when the external air pressure decreases beyond the safe decompression range, causing the tension of the dissolved inert gas to exceed the external air pressure by too much. The dissolved inert gas in the tissues and blood then escapes "in place" to form bubbles, which can cause "decompression sickness".

[0012] Decompression sickness is a disease caused by the rapid and significant drop in external pressure after the body has been exposed to a certain atmospheric pressure environment for a period of time. This rapid and significant drop in external pressure causes the inert gases that were originally dissolved in the body tissues to become gaseous and form bubbles, leading to a series of pathological reactions.

[0013] It mainly occurs in: (1) diving operations (including simulated diving in dry and wet pressurized chambers); (2) high-pressure (caisson, tunnel) operations; (3) crew members of a wrecked submarine escaping from the seabed and surfacing; (4) flight personnel riding in unpressurized cabin aircraft, or simulating flight in a low-pressure chamber to ascend to high altitude, or when the airtightness of a pressurized cabin at high altitude fails; (5) working in a hyperbaric oxygen therapy chamber, etc.

[0014] To minimize the risk of decompression sickness, it is necessary to study the saturation and desaturation patterns of inert gases in human tissues. When the body is exposed to high pressure, the initial nitrogen tension difference between the alveoli and tissues is the largest, and the nitrogen saturation rate is also the fastest. Subsequently, as the tissues gradually become nitrogen-saturated, the nitrogen tension increases, causing the nitrogen partial pressure difference between the alveoli and tissues to gradually decrease. Furthermore, after the body is saturated under high pressure, the nitrogen partial pressure difference between the tissues and alveoli is largest at the moment of decompression, and the desaturation rate is also the fastest. Subsequently, as decompression occurs and nitrogen desaturates in the tissues, the nitrogen tension decreases, causing the nitrogen partial pressure difference between the tissues and alveoli to gradually decrease. Therefore, it can be seen that the rates of nitrogen saturation and desaturation in the body are not the same at different stages, but decrease as the nitrogen partial pressure difference between the alveoli and tissues decreases.

[0015] The composition of various tissues in the human body differs, and blood distribution also varies significantly. Therefore, the saturation rate of inert gases differs among different tissues. For ease of application, Haldane, based on the air diving depth (shallower than 60m) and underwater exposure time studied at the time, as well as relevant experimental data, roughly divided all tissues into five categories according to the concept of the time required to reach half-saturation. This classification of tissues is hypothetical and is therefore called "theoretical tissue." The half-saturation times for the five theoretical tissue categories are 5 min, 10 min, 20 min, 40 min, and 75 min, respectively. The mathematical model is: S = (1 - 0.5) / ( ... t The mathematical model is 100% × 100%, where S is the saturation level and t is the assumed time unit. This model is best suited for calculating underwater dwell time, i.e., when a person remains at a certain depth underwater while maintaining constant environmental pressure. The problem is that environmental pressure changes continuously; a person cannot be directly immersed in water pressure at a certain depth or instantly emerge from the water at a certain depth.

[0016] Current mathematical models cannot calculate the manner in which environmental pressure increases (uniform or exponentially). They merely approximate the descent and dwell times as working time and directly substitute them into the mathematical model, resulting in an approximate calculation with an overestimation of nitrogen tension. Humans also experience this problem during ascent. To address this issue, this invention establishes a mathematical model for calculating tissue inert gas tension based on the physics and medicine-recognized theory that "gas diffusion rate is proportional to pressure difference." This model can accurately calculate the theoretical inert gas tension of a tissue at any given moment during linear pressurization, linear depressurization, and exponential pressurization. Summary of the Invention

[0017] This invention addresses the problems and shortcomings of existing technologies by providing a method for constructing a calculation model of inert gas tension in human tissues.

[0018] The present invention solves the above-mentioned technical problems through the following technical solution:

[0019] This invention provides a method for constructing a calculation model of inert gas tension in human tissue, characterized by comprising the following steps:

[0020] S1. Based on the theory that the diffusion rate of gas is proportional to the pressure difference, establish a pressure change rate function for a certain tissue in the human body;

[0021] S2. Transform the function of the rate of change of pressure in a certain tissue of the human body to obtain the corresponding first-order non-homogeneous linear differential equation.

[0022] S3. Construct the standard form and general solution form of the first-order nonhomogeneous linear differential equation;

[0023] S4. Assign corresponding values ​​to the first-order non-homogeneous linear differential equation and its general solution form, and substitute them into the general solution form to obtain the general pressure function of a certain human tissue.

[0024] S5. Using a general human tissue pressure function, construct the human tissue pressure function g1(x) under the exponential pressurization scenario of respiratory gas, the human tissue pressure function g2(x) under the linear depressurization scenario of respiratory gas, and the human tissue pressure function g3(x) under the linear pressurization scenario of respiratory gas respectively.

[0025] S6. Construct a calculation model G1(x) for the tension of an inert gas in a human tissue under the respiratory gas index pressurization scenario using the pressure function g1(x) of a certain human tissue and the percentage content of the inert gas.

[0026] A calculation model G2(x) for the tension of an inert gas in a human tissue under a linear decompression scenario of respiratory gas is constructed using the pressure function g2(x) of a certain human tissue and the percentage content of the inert gas.

[0027] A calculation model G3(x) for the tension of an inert gas in a human tissue under a linear pressurization scenario of respiratory gas is constructed using the pressure function g3(x) of a certain human tissue and the percentage content of the inert gas.

[0028] The positive and progressive effects of this invention are as follows:

[0029] This invention establishes a mathematical model for calculating the inert gas tension of tissues based on the theory that the diffusion rate of gas is proportional to the pressure difference. It can accurately calculate the theoretical inert gas tension, such as nitrogen tension, of a tissue at any moment during linear pressurization, linear depressurization, and exponential pressurization of the ambient pressure. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating a preferred embodiment of the present invention for constructing a calculation model of inert gas tension in human tissue. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] like Figure 1 As shown, this embodiment of the invention provides a method for constructing a calculation model for inert gas tension in human tissue, which includes the following steps:

[0033] Step 101: Based on the theory that the diffusion rate of gas is proportional to the pressure difference, establish the pressure change rate function of a certain tissue in the human body, denoted as Equation (1):

[0034] g′(x)=k[f(x)-g(x)] (1)

[0035] In the formula, f(x) is the pressure of the respiratory gas (environmental gas), in meters; g(x) is the pressure of a certain tissue in the body, in meters; g′(x) is the rate of change of pressure of a certain tissue in the body, in meters / s; k is defined as the saturation coefficient, which is dimensionless and defined as greater than 0. When f(x) is greater than g(x), g′(x) is greater than 0, and when f(x) is less than g(x), g′(x) is less than 0. It is calculated that k = ln2 / t, where t is the half-saturation time of a certain tissue in the body, in seconds.

[0036] Step 102: Transform the function (1) representing the rate of change of pressure in a certain tissue of the human body to obtain the corresponding first-order non-homogeneous linear differential equation, denoted as equation (2):

[0037] g′(x) + k·g(x) = k·f(x) (2)

[0038] Step 103: Construct the standard form of the first-order nonhomogeneous linear differential equation (2), denoted as equation (3), and its general solution form, denoted as equation (4):

[0039]

[0040] Step 104: Assign corresponding values ​​to the first-order non-homogeneous linear differential equation (2) and its general solution form (4), then P(x) = k, Q(x) = kf(x), substitute into equation (4) to obtain the general human tissue pressure function, denoted as equation (5):

[0041] g(x) = e -kx (∫kf(x)e kx dx+C) (5)

[0042] In the formula, C is an arbitrary constant that needs to be determined through initial conditions.

[0043] Step 105: Using the general human tissue pressure function (5), construct the human tissue pressure function g1(x) under the exponential pressurization scenario of respiratory gas, the human tissue pressure function g2(x) under the linear depressurization scenario of respiratory gas, and the human tissue pressure function g3(x) under the linear pressurization scenario of respiratory gas.

[0044] 1) Increased respiratory gas (ambient gas) pressure index

[0045] Use case: When a diver is in a pressurized chamber, the pressure index is increased to control the chamber pressure.

[0046] Take an exponential pressurization function, where the pressure doubles every n seconds, and assume... Where P0 is the initial pressure of the breathing gas.

[0047] Will Substituting into equation (5), we get

[0048]

[0049] The value of g(0) is generally known. Substituting x = 0s into equation (6) yields...

[0050]

[0051] Substituting C into equation (6), we construct the pressure function g1(x) of a certain tissue in the human body under the exponential pressurization scenario of respiratory gases:

[0052]

[0053] If the pressure of human tissue is already fully balanced with the environmental pressure at the start of pressurization, then g(0) = P0; if the test personnel are repeatedly diving / depressurizing at the start of pressurization, then the value of g(0) should fully consider the actual situation.

[0054] Substituting g(0) = P0 into equation (7) yields

[0055]

[0056] Substituting equation (9) into equation (6), we get

[0057]

[0058] 2) Linear decompression of respiratory gases (ambient gases)

[0059] Use case A: A diver ascends at a constant speed from a great depth to a certain shallow depth;

[0060] Use Case B: A diver is in a pressurized chamber, and the chamber pressure is controlled to decrease at a constant rate.

[0061] The mathematical model corresponding to the linear decompression of respiratory gas is f(x) = P1 - ax, where P1 is the initial pressure of the respiratory gas, a represents a constant, and a represents the decrease of ambient pressure by a meters per second.

[0062] Substituting f(x) = P1 - ax into equation (5), we get

[0063]

[0064] The value of g(0) is generally known. Substituting x = 0s into equation (11) yields...

[0065]

[0066] At this point, g(0) is the tissue pressure value before decompression. Substituting equation (12) into equation (11), we construct the tissue pressure function g2(x) of the human body under the linear decompression scenario of respiratory gas:

[0067]

[0068] 3) Linear pressurization of respiratory gases (ambient gases)

[0069] Use case A: A diver descends from a shallow depth to a certain greater depth at a constant speed;

[0070] Use Case B: A diver is in a pressurized chamber, and the chamber pressure is increased at a constant rate.

[0071] The mathematical model corresponding to the linear pressurization of the breathing gas is f(x) = P0 + bx, where P0 is the initial pressure of the breathing gas, b represents a constant, and b represents the increase of the ambient pressure by b meters per second.

[0072] Substituting f(x) = P0 + bx into equation (5), we get

[0073]

[0074] The value of g(0) is generally known. Substituting x = 0s into equation (14) yields...

[0075]

[0076] Substituting equation (15) into equation (14) yields

[0077]

[0078] If the pressure of human tissue is already fully balanced with the environmental pressure at the start of pressurization, then g(0) = P0. If, at the start of pressurization, the test personnel are subject to repeated diving / decompression, the value of g(0) should fully consider the actual situation.

[0079] When g(0) = P0, at this time

[0080] Step 106: Construct a calculation model for the tension of an inert gas in a human tissue under the exponential pressurization scenario of respiratory gases, using the pressure function g1(x) of a certain human tissue and the percentage content d of the inert gas. The model is G1(x) = d * g1(x).

[0081] A calculation model for the tension of an inert gas in a human tissue under a linear decompression scenario is constructed using the pressure function g2(x) of a certain human tissue and the percentage content d of the inert gas. The model is G2(x) = d * g2(x).

[0082] A calculation model for the tension of an inert gas in a human tissue under a linear pressurization scenario is constructed using the pressure function g3(x) of a certain human tissue and the percentage content d of the inert gas. The model is G3(x) = d * g3(x).

[0083] When calculating the nitrogen tension of a certain tissue in the human body, d is 0.79.

[0084] This invention establishes a mathematical model for calculating the inert gas tension of tissues based on the theory that the diffusion rate of gas is proportional to the pressure difference. It can accurately calculate the theoretical inert gas tension, such as nitrogen tension, of a tissue at any moment during linear pressurization, linear depressurization, and exponential pressurization of the ambient pressure.

[0085] The final mathematical model is shown in Table 1. When calculating tissue nitrogen tension, simply multiply by 0.79.

[0086] Table 1 Mathematical Model

[0087]

[0088] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A method for constructing a calculation model for inert gas tension in human tissue, characterized in that, It includes the following steps: S1. Based on the theory that the diffusion rate of a gas is proportional to the pressure difference, the pressure change rate function of a certain tissue in the human body is established as equation (1): （1） In the formula, The pressure of breathable gases, i.e., ambient gases, is measured in meters (m). The pressure in a certain tissue within the body is expressed in meters (m). The rate of change of pressure in a tissue within the body is expressed in m / s; k is defined as the saturation coefficient, dimensionless, and defined as greater than 0 when... Greater than hour, Greater than 0, when Less than hour, If less than 0, k is calculated as ln2 / t, where t is the half-saturation time of a certain tissue in the body, in seconds. S2. Transform the function of the rate of change of pressure in a certain tissue of the human body to obtain the corresponding first-order non-homogeneous linear differential equation. S3. Construct the standard form and general solution form of the first-order nonhomogeneous linear differential equation; S4. Assign corresponding values ​​to the first-order non-homogeneous linear differential equation and its general solution form, and substitute them into the general solution form to obtain the general pressure function of a certain human tissue. S5. Using a general human tissue pressure function, construct the human tissue pressure function under the exponential pressurization scenario of respiratory gases. Pressure function of a certain tissue in the human body under linear decompression scenario of respiratory gas. The pressure function of a certain tissue in the human body under the scenario of linear pressurization of respiratory gas. ; S6. Utilizing the pressure function of a certain human tissue A calculation model for inert gas tension in a human tissue under a respiration gas index pressurization scenario was constructed based on the percentage content of the inert gas. ; Using the pressure function of a certain human tissue A calculation model for inert gas tension in a human tissue under a linear decompression scenario of respiratory gas was constructed based on the percentage content of the inert gas. ; Using the pressure function of a certain human tissue A calculation model for inert gas tension in a human tissue under a linear pressurization scenario of respiratory gas was constructed based on the percentage content of the inert gas. .

2. The method for constructing a calculation model for inert gas tension in human tissue as described in claim 1, characterized in that, S2. By performing a formal transformation on the rate of change function of pressure in a certain human tissue, the corresponding first-order non-homogeneous linear differential equation is obtained, denoted as equation (2): （2） S3. Construct the standard form of the first-order nonhomogeneous linear differential equation, denoted as equation (3), and its general solution form, denoted as equation (4): （3） （4） S4. Assign corresponding values ​​to equation (4) and equation (2), then , Substituting into equation (4), we obtain the general human body pressure function, denoted as equation (5): （5） In the formula, C is an arbitrary constant that needs to be determined through initial conditions; In S5, we take an exponential pressurization function, where the pressure doubles every n seconds. Where P0 is the initial pressure of the breathing gas, Substituting into equation (5), we get （6） The value of g(0) is generally known. Substituting x=0 s into equation (6) yields... （7） Substituting C into equation (6), we construct the pressure function of a certain tissue in the human body under the exponential pressurization scenario of respiratory gases. : （8） If the pressure in human tissues is already fully balanced with the environmental pressure when pressurization begins, then If, at the start of pressurization, the test personnel are subject to repeated diving / depressurization, the value of g(0) should fully consider the actual situation. In S6, a calculation model for the inert gas tension of a certain human tissue under the respiratory gas exponential pressurization scenario is constructed. , This represents the percentage content of inert gases.

3. The method for constructing a calculation model for inert gas tension in human tissue as described in claim 2, characterized in that, In S5, the mathematical model for linear decompression of respiratory gases is: Where P1 is the initial pressure of the breathing gas, Substituting into equation (5), we get （11） The value of g(0) is generally known. Substituting x=0 s into equation (11) yields... （12） At this point, g(0) is the tissue pressure value before decompression. Substituting equation (12) into equation (11), we construct the tissue pressure function of the human body under the linear decompression scenario of respiratory gas. : （13） In S6, a calculation model for the inert gas tension of a certain human tissue under a linear decompression scenario of respiratory gas is constructed. .

4. The method for constructing a calculation model for inert gas tension in human tissue as described in claim 3, characterized in that, Linear decompression scenarios for breathing gases include: Use case A: A diver ascends at a constant speed from a great depth to a certain shallow depth; Use Case B: A diver is in a pressurized chamber, and the chamber pressure is controlled to decrease at a constant rate.

5. The method for constructing a calculation model for inert gas tension in human tissue as described in claim 2, characterized in that, In S5, the mathematical model for linear pressurization of respiratory gases is: Where P0 is the initial pressure of the breathing gas, Substituting into equation (5), we get （14） The value of g(0) is generally known. Substituting x=0 s into equation (14) yields... （15） Substituting equation (15) into equation (14) yields （16） If the pressure in human tissues is already fully balanced with the environmental pressure when pressurization begins, then If, at the start of pressurization, the test personnel are subject to repeated diving / depressurization, the value of g(0) should fully consider the actual situation. In S6, a calculation model for the inert gas tension of a certain human tissue under a linear pressurization scenario of respiratory gas is constructed. .

6. The method for constructing a calculation model for inert gas tension in human tissue as described in claim 5, characterized in that, Linear pressurization scenarios for respiratory gases include: Use case A: A diver descends from a shallow depth to a certain greater depth at a constant speed; Use Case B: A diver is in a pressurized chamber, and the chamber pressure is increased at a constant rate.

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