Method and apparatus for determining safe and effective prescription interval for hemodialysis

Abstract

The present application relates to hemodialysis prescription optimization technical field, especially in a kind of method and device for determining safe and effective prescription interval of hemodialysis.The method is in two-dimensional parameter space with ultrafiltration volume and dialysate sodium concentration as coordinate axis, using double-chamber sodium dynamics model (diffusion equilibrium concentration C_eq=[Na]d / σ (σ=0.97)) to calculate the sodium removal of each parameter combination and serum sodium after dialysis, superimpose sodium removal target line, ultrafiltration rate safety line and serum sodium safety area three constraint boundaries, the area that meets all constraints simultaneously is determined as safe and effective prescription interval.The safe and effective prescription interval is obtained by mathematical model calculation, not determined directly by preset empirical threshold.The present application first proposes the concept of safe and effective prescription interval, upgrades dialysis prescription from single-point empirical selection to interval optimization selection, and the constraint boundary can be dynamically adjusted according to individualized parameters of patients, to provide intuitive multi-constraint prescription decision support tool for clinicians.

Description

Technical Field

[0001] This invention relates to the field of hemodialysis prescription optimization technology, and in particular to a method and apparatus for determining a safe and effective prescription range for hemodialysis. Background Technology

[0002] The core parameters of a hemodialysis prescription include ultrafiltration volume, dialysate sodium concentration, and dialysis time. A safe and effective dialysis prescription needs to simultaneously meet several constraints: sodium clearance must reach the target value to remove sodium-water accumulation between dialysis sessions; the ultrafiltration rate must not exceed the safe threshold to avoid hypotension and cardiovascular events; and postdialysis serum sodium must be within the normal range to avoid electrolyte disturbances. These constraints are interdependent: for example, reducing the dialysate sodium concentration can increase diffuse sodium excretion, but may lead to excessively low serum sodium; increasing the ultrafiltration volume can increase convective sodium excretion, but may exceed the safe ultrafiltration rate.

[0003] Currently, dialysis prescriptions in clinical practice are set by doctors based on experience before dialysis, lacking systematic multi-constraint analysis tools. Doctors can only consider each constraint one by one based on experience, making it difficult to simultaneously consider sodium clearance targets, ultrafiltration rate safety, and serum sodium stability, easily leading to overlooking some aspects. Existing dialysis information systems only provide data recording and statistical functions and do not have the ability to optimize prescriptions based on multiple constraints.

[0004] Some literature proposes prescription recommendations based on empirical thresholds, such as "ultrafiltration rate not exceeding 10 ml / h / kg" and "dialysis fluid sodium concentration set at 138 mmol / L." However, these recommendations are isolated, single constraints that do not consider the interactions between constraints or are calculated based on the patient's individual sodium kinetic parameters. More importantly, these empirical thresholds cannot tell physicians which combinations of prescription parameters are feasible, or what the optimal combination is, while satisfying all constraints.

[0005] It is important to note that the determination of the safe and effective prescription range must be based on quantitative calculations using mathematical models, rather than simple lookups of pre-set empirical thresholds. Empirical thresholds can only provide a rough range for a single parameter and cannot reflect the coupling relationship between multiple parameters; while mathematical models can accurately calculate sodium clearance and serum sodium changes under each parameter combination, thereby delineating the boundary of the region that truly satisfies all constraints in the continuous parameter space. Summary of the Invention

[0006] The purpose of this invention is to provide a method for determining the safe and effective prescription range for hemodialysis. By superimposing multiple clinical constraint boundaries in a two-dimensional parameter space (ultrafiltration volume × dialysate sodium concentration), the method automatically identifies the prescription parameter combination region that simultaneously meets all safety and effectiveness requirements, providing clinicians with a visual prescription decision support tool.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a method for determining the safe and effective prescription range for hemodialysis, comprising the following steps: Step 1: Define the two-dimensional parameter space A two-dimensional prescription parameter space was constructed with ultrafiltration volume V_UF as the horizontal axis and dialysate sodium concentration [Na]_d as the vertical axis. The ultrafiltration volume range was set to 0.5–4.0 L, and the dialysate sodium concentration range was set to 134–146 mmol / L.

[0008] Step 2: Calculate the sodium kinetics at each point in the parameter space. For each (V_UF, \[Na\]_d) combination in the two-dimensional parameter space, the following two key indices are calculated using a two-chamber sodium kinetic model: - Total sodium removal (Na_total, including convective and diffuse removal); - Predicting serum sodium concentration [Na]_post after dialysis.

[0009] The diffusion equilibrium concentration was calculated using C_eq = [Na]d / σ (σ = 0.97, the Gibbs-Donnan factor), and intracellular and extracellular sodium exchange was performed using a perturbation model with the initial steady state as a reference. Two two-dimensional matrices were generated: a sodium clearance matrix M_Na and a serum sodium matrix M_post. The safe and effective prescription range was calculated using the above mathematical model, rather than being directly determined by a preset empirical threshold.

[0010] Step 3: Overlay constraint boundaries Plot the following three types of clinical constraint boundaries in parameter space: - Sodium clearance target line: Extract the contour line where Na_total = Na_target from the sodium clearance matrix M_Na, where Na_target = (W_pre - W_dry) × [Na]s / 0.93 (0.93 is the plasma water fraction, used to convert serum sodium concentration to plasma water-sodium concentration) is the target sodium clearance. This contour line divides the parameter space into two regions: one side corresponding to parameter combinations with higher V_UF or lower [Na]d is the region of sufficient sodium clearance, and the other side is the region of insufficient sodium clearance; - Ultrafiltration rate safety line: V_UF_max = UFR_max × W_pre × t / 1000, where UFR_max is the upper limit of the safe ultrafiltration rate (default 10 ml / h / kg), W_pre is the patient's weight (kg), and t is the dialysis time (hours). This vertical line divides the parameter space into a safe zone on the left and a dangerous zone on the right. - Serum sodium safe zone: Extract two contour lines [Na]post = [Na]post_min and [Na]post = [Na]post_max from the serum sodium matrix M_post (default values ​​are 136 and 143 mmol / L). The area between these two lines is the serum sodium safe zone.

[0011] Step 4: Determine the safe and effective prescription range The parameter region that simultaneously satisfies the above three constraints (i.e., above the sodium clearance target line ∩ to the left of the ultrafiltration rate safety line ∩ within the serum sodium safety zone) is defined as the safe and effective prescription interval. Any combination of (V_UF, [Na]d) within this interval can achieve adequate and safe dialysis.

[0012] Step 5: Recommend the optimal prescription Within the safe and effective prescription range, the parameter combination that best approximates the sodium clearance level to the target value Na_target is selected as the optimal prescription recommendation. This recommendation balances adequacy (achieving the target sodium clearance) and conservatism (avoiding excessive clearance).

[0013] Step Six (Optional): Visualization Output The safe and effective prescription range is displayed in the form of a contour map. The map includes: the background color represents the amount of sodium clearance, the green dashed line represents the sodium clearance target line, the red dashed line represents the ultrafiltration rate safety line, and the blue solid line represents the serum sodium safety boundary. The area enclosed by the three lines is the safe and effective prescription range, and the optimal prescription point is displayed with a special mark. Attached Figure Description

[0014] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 A schematic diagram of the safe and effective prescription range (the safe and effective prescription range enclosed by the superposition of three constraints). Where, - Horizontal axis: Ultrafiltration volume V_UF (L); - Vertical axis: Sodium concentration in dialysate [Na]_d (mmol / L); - Background color: Sodium removal contour lines (warm tone); - Green dashed line: Target sodium clearance contour (301 mmol); - Red dashed line: Upper limit of ultrafiltration rate safety (2.60L @10ml / h / kg, 65kg, 4h); - Blue solid line: The safe boundary of serum sodium after dialysis (136-143 mmol / L).

[0016] Figure 2 A comparison chart showing the changes in safe and effective prescription ranges under different patient parameters; Among them, (A) standard patient (65kg, dW=2kg); (B) Patients with significant weight gain (65kg, dW=3.5kg); (C) Low body weight patients (50kg, dW=2kg). Detailed Implementation

[0017] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the specific embodiments. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this patent, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this patent.

[0018] Example 1: Determination of the safe and effective prescription range for standard patients This embodiment details how to determine the safe and effective prescription range for hemodialysis for a patient with standard parameters using the method of the present invention.

[0019] Step 1: Define the two-dimensional prescription parameter space A two-dimensional parameter space was constructed with ultrafiltration volume (V_UF) as the horizontal axis and dialysate sodium concentration ([Na]_d) as the vertical axis. Based on commonly used clinical ranges, the value range of V_UF was set to 0.5 L to 4.0 L, and the value range of [Na]_d was set to 130 mmol / L to 148 mmol / L (appropriately expanded from the 134-146 mmol / L range in the invention description to fully represent all constraint boundaries). This space covers the vast majority of prescription combinations that may be used in clinical practice.

[0020] Step 2: Calculation of indices based on the two-chamber sodium kinetic model Patient's basic parameters: predialysis weight W_pre = 67 kg, dry weight W_dry = 65 kg, interdialysis weight gain ΔW = W_pre – W_dry = 2 kg, predialysis serum sodium concentration [Na]_s = 140 mmol / L, and dialysis time set at t = 4 hours.

[0021] For each grid point in the parameter space, i.e., each combination of (V_UF, \[Na\]_d), simulation calculations are performed using a pre-built and validated two-chamber sodium kinetic model. The core computational logic of the model is as follows: Total sodium removal (Na_total): This includes the sum of convective and diffuse removal. The driving force for diffuse removal is based on a modified concentration gradient, where the equilibrium concentration on the dialysate side is determined by the formula \( C_{eq} = \frac{[Na]_d}{\sigma} \), where σ is the Gibbs-Donnan factor, taken as an empirical value of 0.97.

[0022] Predicted serum sodium concentration after dialysis ([Na]_post): The model comprehensively considers sodium ion exchange and changes in body fluid volume during dialysis, and performs perturbation calculations based on the patient's initial homeostasis.

[0023] By traversing the entire parameter space, two key two-dimensional matrices were generated: the sodium clearance matrix (M_{Na}) and the post-dialysis serum sodium concentration matrix (M_{post}).

[0024] Step 3: Overlay clinical constraint boundaries In the aforementioned two-dimensional parameter space, three key clinical constraint boundaries are plotted: Sodium clearance target line: Calculate the target sodium clearance (Na_{target} = \frac{\Delta W\times [Na]_s}{0.93} = \frac{2 \times 140}{0.93} \approx 301 \text{mmol} \) based on patient data. Extract the contour line of (Na_{total} = 301 \text{mmol} \) from the matrix \( M_{Na} \) as the target sodium clearance. Figure 1 The green dashed line in the diagram. The area above this line (typically corresponding to higher V_UF or lower \[Na\]_d) is the "sodium clearance adequate region".

[0025] Ultrafiltration Rate Safety Line: Set the upper limit of the safe ultrafiltration rate (UFR_{max} = 10 ml / h / kg). Calculate the maximum safe ultrafiltration capacity (V_{UF_max} = UFR_{max} × W_{pre} × t = 1000 = 10 × 67 × 4 = 2.68 L). Plot a vertical line of (V_{UF} = 2.68 L) in parameter space as... Figure 1 The red dashed line in the image. The area to the left of this line is the "ultrafiltration rate safety zone".

[0026] Serum sodium safety zone: The safe range for serum sodium after dialysis is defined as \(136 \text{ mmol / L} \leq[Na]_{post} \leq 143 \text{ mmol / L} \). Two isopleths corresponding to 136 mmol / L and 143 mmol / L are extracted from the matrix \( M_{post} \) as... Figure 1 The solid blue line in the middle. The area between the two lines is the "serum sodium safe zone".

[0027] Step 4: Determine the safe and effective prescription range The intersection of the three constraint regions mentioned above—that is, the area above the sodium clearance target line, to the left of the ultrafiltration rate safety line, and within the serum sodium safety zone—is defined as the "safe and effective prescription interval." Figure 1 The closed region enclosed by the three lines is shown. Any point within this region (V_UF, \[Na\]_d) represents a dialysis prescription that simultaneously meets the three core requirements of adequate sodium removal, safe ultrafiltration rate, and normal serum sodium levels after dialysis.

[0028] Step 5: Recommend the optimal prescription Within the defined safe and effective prescription range, an optimization algorithm is used to find the point where the total sodium clearance (Na_total) is closest to the target value (Na_target = 301 mmol). For example... Figure 1 As shown, the optimal prescription point (e.g., V_UF = 2.0 L, [Na_d] = 138 mmol / L) can be highlighted in the graph by special markings (such as asterisks). This prescription maximizes the sodium removal target while ensuring safety.

[0029] Step 6: Visualize the output pass Figure 1The contour map shown presents the results visually to clinicians. In the map, the background color (warm tone) represents the amount of sodium clearance; the green dashed line, red dashed line, and blue solid line represent the three constraint boundaries mentioned above; the area they enclose is the desired result; the optimal prescription point is clearly marked.

[0030] Example 2: Application and Variation in Different Clinical Scenarios This embodiment demonstrates the adaptability and dynamic adjustment capability of the method of the present invention under different patient characteristics, corresponding to Figure 2 The three subgraphs in the diagram.

[0031] Scenario A: Patients with significant weight gain (high sodium load) Patient parameters: W_pre = 68.5 kg, W_dry = 65 kg, ΔW = 3.5 kg, t = 4 h.

[0032] The calculated values ​​are: Na_{target} \approx 527 \text{ mmol} \) and V_{UF\_max} =2.74 \text{ L \).

[0033] like Figure 2 As shown in (B), due to the significant increase in target sodium clearance, the sodium clearance target line (green line) shifts sharply to the upper right. During the 4-hour dialysis period, the three constraint boundaries cannot form an effective region (i.e., the safe and effective prescription interval is an empty set). At this point, the system will automatically issue a prompt: "Unable to find a prescription that simultaneously satisfies all constraints under the current conditions; it is recommended to extend the dialysis time."

[0034] If the dialysis time is extended to 5 hours, then \( V_{UF\_max} = \frac{10 \times 68.5 \times 5}{1000} = 3.43 \text{ L} \), the ultrafiltration rate safety line (red line) shifts to the right, and the safe and effective prescription range reappears, providing a clear direction for clinical adjustment of the treatment plan.

[0035] Scenario B: Low-weight patients Patient parameters: W_pre = 52 kg, W_dry = 50 kg, ΔW = 2 kg, t = 4 h.

[0036] The calculated values ​​are: Na_{target} \approx 301 \text{ mmol} \), V_{UF\_max} = \frac{10 \times 52 \times 4}{1000} = 2.08 \text{ L} \).

[0037] like Figure 2 As shown in (C), due to the patient's lighter weight, the ultrafiltration rate safety line (red line) shifted significantly to the left, resulting in a lower safe and effective prescription range compared to standard patients. Figure 2 (A) shows a clear leftward contraction. The optimal formulation may be adjusted to V_UF = 2.0 L, \[Na\]_d ​​= 136 mmol / L to accommodate stricter ultrafiltration rate restrictions.

[0038] Example 3: Personalized Dynamic Adjustment of Constraint Boundaries This embodiment illustrates how to individually adjust the constraint boundaries according to the patient's specific condition, demonstrating the flexibility of the present invention.

[0039] Adjusting the ultrafiltration rate safety threshold: For a patient with heart failure, to avoid inducing heart failure, clinicians can tighten the ultrafiltration rate safety threshold (UFR_{max} \) from the default 10 ml / h / kg to 8 ml / h / kg or even lower. The system will then recalculate (V_{UF_max} \) accordingly, generating a more left-leaning red dashed line, thus obtaining a more conservative and safe prescription range.

[0040] Adjusting the serum sodium safe zone: For a patient at risk of hypernatremia, the safe upper limit of serum sodium ([Na]_{post_max}) can be lowered from the default 143 mmol / L to 140 mmol / L.

[0041] For a patient at risk of hyponatremia, the safe lower limit of serum sodium ([Na]_{post_min}) can be increased from the default 136 mmol / L to 138 mmol / L.

[0042] These adjustments will change the position of the blue solid line, making the final prescription range more aligned with the individualized safety needs of patients.

[0043] Example 4: Integration of Hemodynamic Stability Constraints To further enhance prescription safety, another embodiment of the present invention integrates a fourth constraint—hemodynamic stability—in step 3. Based on the patient's historical dialysis data, a model is established relating ultrafiltration rate, dialysate sodium concentration, and the reduction in blood pressure during dialysis. By plotting contour lines in the parameter space indicating that "the reduction in blood pressure does not exceed a preset threshold (e.g., a decrease in systolic blood pressure of no more than 20 mmHg)," prescription regions more conducive to maintaining hemodynamic stability can be further screened.

[0044] Example 5: Application and Integration of the Device The device of this invention can be integrated as a functional module into various clinical systems. For example, in a dialysis information management system, the doctor's workstation can automatically obtain the patient's weight and recent blood sodium data before dialysis that day, call the calculation unit of this device, and generate data such as... within seconds. Figure 1 The diagram shows the safe and effective prescription range. Physicians can use this range, combined with their clinical experience, to make a final decision, or directly adopt the optimal prescription recommended by the system. This device can also be integrated into intelligent dialysis machines or AI-assisted decision-making systems to automate and intelligently generate prescriptions.

[0045] Okay, as per your request, the technical solutions corresponding to claims 6 and 9, along with the supplementary description you provided, have been integrated into the "Detailed Embodiments" section of the original specification document "100002 Specification-4.docx", forming two new embodiments.

[0046] Example 6: Expansion and Analysis of Three-Dimensional Parameter Space This embodiment demonstrates the extension of the method of the present invention from a two-dimensional plane to a three-dimensional space, using dialysis time as the third dimension to provide a more comprehensive perspective for clinical decision-making, corresponding to the technical solution described in claim 6.

[0047] In the aforementioned embodiments, we fixed the dialysis time at t = 4 hours and sought a safe and effective prescription range on a two-dimensional plane comprising ultrafiltration volume (V_UF) and dialysate sodium concentration ([Na]d). However, dialysis time itself is a key modulatory variable. Extending the dialysis time can increase the total ultrafiltration volume without increasing the ultrafiltration rate, or achieve the same sodium clearance target at a lower ultrafiltration rate, especially suitable for patients with high sodium load or cardiovascular instability.

[0048] This embodiment extends the two-dimensional parameter space to a three-dimensional parameter space, and the coordinate axes are defined as follows: - X-axis: Ultrafiltration volume V_UF (L) - Y-axis: Sodium concentration in dialysate [Na]d (mmol / L) - Z-axis: Dialysis time t (h) In this three-dimensional space, the dual-chamber sodium kinetic model of step S2 will calculate for each (V_UF, [Na]d, t) combination to generate a three-dimensional sodium clearance data volume and a post-dialysis serum sodium concentration data volume.

[0049] Correspondingly, the three constraint boundaries in step S3 are also expanded from two-dimensional "lines" and "regions" to three-dimensional "surfaces" and "volumes": - Sodium removal target surface: In the three-dimensional data volume, all points that satisfy Na_total(V_UF, [Na]d, t) = Na_target form a surface.

[0050] - Ultrafiltration rate safety surface: Constraint V_UF ≤ (UFR_max × W_pre × t) / 1000 Defines a half-space in three-dimensional space, whose boundary surface is an inclined plane passing through the origin.

[0051] - Serum sodium safety body: The constraint [Na]post_min ≤ [Na]post(V_UF, [Na]d, t) ≤ [Na]post_max defines an irregular "pipeline" region in three-dimensional space.

[0052] The intersection of these three surfaces (or the area enclosed by the surfaces) in three-dimensional space constitutes the safe and effective prescription volume. Any point within this volume (V_UF, [Na]d, t) represents a prescription that is safe and effective.

[0053] To visually represent three-dimensional information on a two-dimensional plane, the system can generate a series of two-dimensional cross-sectional plots at different dialysis times (t), similar to playing an animation. For example, it can generate multiple safe and effective prescription interval plots for t = 3.0h, 3.5h, 4.0h, 4.5h, and 5.0h. Doctors can visually see how the safe and effective interval on the two-dimensional plane gradually expands as dialysis time increases by sliding the time axis. For the patient mentioned in Example 2 who gained excessive weight (ΔW = 3.5 kg), the safe and effective interval is empty at t = 4h; however, when the plot is switched to t = 5h, a clear safe and effective interval reappears due to the rightward shift of the ultrafiltration rate safety line. This provides clinicians with precise quantitative evidence between "extending dialysis time" and "adjusting other parameters."

[0054] Example 7: Real-time dynamic prescription updates during dialysis This embodiment illustrates how the device of the present invention dynamically updates prescriptions based on real-time monitoring data during dialysis to achieve precise prescription adjustments, corresponding to the technical solution in claim 9 of "dynamically updating the prescription range based on real-time data during dialysis".

[0055] In actual dialysis, the patient's physiological parameters and actual clearance may deviate from the pre-dialysis predictions. For example, the pre-dialysis serum sodium concentration measurement may differ from the preset value, or the actual sodium clearance in the first half of dialysis may be lower than the model prediction. The device of this invention can be integrated into a dialysis machine or AI system with real-time monitoring capabilities to achieve dynamic updates of the prescription interval.

[0056] Scenario: A patient is scheduled for 4 hours of dialysis. The initial prescription is based on their pre-dialysis serum sodium [Na]s,pre = 140 mmol / L. Two hours into dialysis (i.e., remaining time t_remaining = 2h), the online monitoring device displays the patient's current actual serum sodium concentration [Na]s,current = 138 mmol / L. Simultaneously, the system calculates the completed sodium removal, Na_removed = 150 mmol, based on the real-time ultrafiltration volume and dialysate sodium concentration.

[0057] Dynamic update process: 1. Parameter Reset: The system uses the current time (2 hours after dialysis begins) as the new starting point. The patient's current weight W_current can be calculated from the real-time ultrafiltration volume, and the current serum sodium concentration [Na]s,current = 138 mmol / L is the new initial condition. The remaining dialysis time t_remaining = 2h. The target dry weight W_dry remains unchanged, therefore the remaining fluid volume to be removed ΔW_remaining = W_current - W_dry. The remaining sodium volume to be removed Na_target_remaining = Na_target (total) - Na_removed.

[0058] 2. Reconstruct the parameter space: Construct a two-dimensional parameter space for the second half of dialysis with the remaining ultrafiltration volume V_UF,remaining (i.e. ΔW_remaining) as the horizontal axis and the adjustable dialysate sodium concentration [Na]d,remaining as the vertical axis.

[0059] 3. Recalculate and superimpose constraints: Using the two-chamber sodium kinetic model, calculate each parameter combination (V_UF,remaining, [Na]d,remaining) within the remaining time t_remaining, and redraw the three constraint boundaries: - Updated sodium removal target line: contour lines of Na_total,remaining = Na_target_remaining.

[0060] - Updated ultrafiltration rate safety line: V_UF,remaining_max = UFR_max × W_current ×t_remaining / 1000.

[0061] - Updated serum sodium safety zone: Based on the current [Na]s,current, the model predicts the serum sodium concentration [Na]post,new at the end of dialysis and ensures it is within the safe range.

[0062] 4. Generate and recommend a dynamic prescription interval: The system overlays the three new constraints to generate a "dynamic safe and effective prescription interval" for the second half of dialysis. If the system detects insufficient sodium removal in the first half (low Na_removed, resulting in high Na_target_remaining), the new sodium removal target line may shift to the upper right. Based on this, the system will recommend using a lower dialysate sodium concentration [Na]d,remaining in the second half to increase the diffusion of sodium removal and ensure that the total sodium removal target is "caught up" at the end of dialysis.

[0063] This dynamic update mechanism enables the adjustment of dialysis prescriptions to truly move from "empirical prediction" to "closed-loop precision management," effectively addressing various variables in the dialysis process and ensuring that each dialysis treatment can safely and effectively achieve the predetermined goals to the greatest extent possible.

[0064] As can be seen from the above embodiments, the present invention achieves the following beneficial effects: 1. The concept of "safe and effective prescription range" was first proposed, upgrading dialysis prescriptions from "single-point selection" to "range optimization", enabling doctors to see all feasible prescription options intuitively.

[0065] 2. The visualization and overlay of multiple constraints allows doctors to clearly understand the interrelationships between various constraints, avoiding overlooking any aspect.

[0066] 3. The constraint boundaries can be dynamically adjusted according to the patient's individual parameters: for example, the ultrafiltration rate constraint can be tightened for patients with poor cardiac function, and the serum sodium safe range can be adjusted for patients with hypernatremia.

[0067] 4. Contour maps provide a wealth of quantitative information, allowing doctors to flexibly select prescription parameters within a safe range based on clinical judgment.

[0068] 5. This method can be integrated into dialysis information systems or AI Agent systems to achieve automated prescription recommendations.

[0069] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0070] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method of determining a safe and effective prescription interval for hemodialysis, characterized by, The safe and effective prescription range is calculated by a mathematical model, rather than directly determined by a preset empirical threshold, and includes the following steps: Step S1: Define a two-dimensional prescription parameter space with ultrafiltration volume V_UF as the first coordinate axis and dialysate sodium concentration [Na]d as the second coordinate axis; Step S2: For each parameter combination (V_UF, [Na]d) in the two-dimensional parameter space, calculate the total sodium clearance Na_total and the predicted serum sodium concentration [Na]post after dialysis using a two-chamber sodium kinetic model, where the diffusion equilibrium concentration is calculated using C_eq = [Na]d / σ (σ=0.97 is the Gibbs-Donnan factor), and generate the sodium clearance matrix and the serum sodium matrix; Step S3: Superimpose the following constraint boundaries in the two-dimensional parameter space: Constraint 1: Sodium removal target line, i.e., the contour line of Na_total = Na_target, where Na_target = (W_pre - W_dry) × [Na]s / 0.93; Constraint 2: Ultrafiltration rate safety line, i.e., V_UF = UFR_max × W_pre × t / 1000, where UFR_max is the upper limit of safe ultrafiltration rate; Constraint 3: The safe zone for serum sodium, i.e., [Na]post_min ≤ [Na]post ≤ [Na]post_max; Step S4: Determine the parameter range that simultaneously satisfies the above three constraints as the safe and effective prescription range; Step S5: Within the safe and effective prescription range, the parameter combination (V_UF, [Na]d) that makes the sodium clearance closest to the target value is recommended as the optimal prescription.

2. The method of claim 1, wherein, The physical meaning of constraint one is: the area above the sodium removal target line indicates that the sodium removal amount has reached or exceeded the target value, that is, dialysis is sufficient; the physical meaning of constraint two is: the area to the left of the ultrafiltration rate safety line indicates that the ultrafiltration rate does not exceed the safety threshold, avoiding hypotension and cardiovascular events caused by excessively rapid ultrafiltration; the physical meaning of constraint three is: serum sodium is within the normal range after dialysis, avoiding hyponatremia or hypernatremia.

3. The method of claim 1, wherein, The parameters of the constraint boundaries can be dynamically adjusted according to the individual patient situation: for patients with heart failure, the ultrafiltration rate safety threshold UFR_max is tightened from 10 ml / h / kg to 8 ml / h / kg or lower; for patients with hypernatremia, the upper limit of serum sodium after dialysis [Na]post_max is lowered from 143 mmol / L to 140 mmol / L; for patients with hyponatremia, the lower limit of serum sodium after dialysis [Na]post_min is raised from 136 mmol / L to 138 mmol / L.

4. The method as described in claim 1, characterized in that, It also includes step S6: visually outputting the safe and effective prescription interval in the form of a contour map, wherein the background color intensity indicates the amount of sodium clearance, and the sodium clearance target line, ultrafiltration rate safety line and serum sodium safety boundary are marked with different colors and line types, and the area enclosed by the three lines is the safe and effective prescription interval, and the optimal prescription point is displayed with a special mark.

5. The method as described in claim 1, characterized in that, In step S3, a fourth constraint can also be superimposed: hemodynamic stability constraint, which predicts the parameter range in which the blood pressure drop during dialysis does not exceed a preset threshold based on a model of the relationship between the patient's historical dialysis blood pressure drop and ultrafiltration rate and dialysate sodium concentration.

6. The method as described in claim 1, characterized in that, The two-dimensional parameter space can be expanded into a three-dimensional parameter space, with dialysis time t added as a third coordinate axis. The safe and effective prescription volume is determined in the three-dimensional space and displayed in the form of two-dimensional cross-sections with different dialysis times.

7. The method as described in claim 1, characterized in that, When the three constraints cannot form an effective region, i.e. the safe and effective prescription interval is an empty set, the method automatically prompts that the dialysis time needs to be extended or the dry weight target needs to be adjusted, and recalculates the safe and effective prescription interval after the extended dialysis time.

8. A device for determining the safe and effective prescription range for hemodialysis, characterized in that, include: The parameter input unit is used to receive the patient's predialysis weight, dry weight, serum sodium concentration, and dialysis time. The model calculation unit, which embeds a dual-chamber sodium kinetic model, calculates the total sodium clearance and the predicted serum sodium concentration after dialysis for each parameter combination in the two-dimensional parameter space. The safe and effective prescription range is obtained by the model calculation unit through mathematical model calculation, rather than being directly determined by a preset empirical threshold. The constraint superposition unit superimposes three constraint boundaries—the sodium removal target line, the ultrafiltration rate safety line, and the serum sodium safety zone—in a two-dimensional parameter space to determine the safe and effective prescription range. The prescription recommendation unit selects the optimal combination of prescription parameters within the safe and effective prescription range. The visualization output unit displays safe and effective prescription ranges to clinicians in the form of contour maps.

9. The apparatus as claimed in claim 8, characterized in that, The device is integrated into a dialysis information system, dialysis machine, or AIAgent intelligent dialysis prescription optimization system. It automatically acquires patient parameters and generates a safe and effective prescription interval diagram before dialysis. During dialysis, it dynamically updates the prescription interval based on real-time data.

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