A two-compartment modeling and prediction method for sodium kinetics during hemodialysis

Abstract

The application discloses a two-compartment modeling and prediction method for sodium kinetics in hemodialysis. The method divides the patient's body fluid into two compartments of extracellular fluid and intracellular fluid, and establishes a coupled differential equation set to describe the sodium transfer kinetics in the dialysis process. The application corrects the physical error of the existing model in the dispersion equilibrium concentration formula, proposes C_eq=[Na]d / σ (σ=0.97 is the Gibbs-Donnan factor) to replace the traditional Donnan formula and the old recommended formula, eliminates the false dispersion gradient under the condition of isonatric dialysis based on the physical fact that electrolytes are only distributed in the plasma water phase, and removes the error solvent drag term by clearly defining the biophysical constraints of the cell membrane aquaporin not transporting sodium. The application adopts a perturbation reference model to replace the traditional Fick diffusion law to describe the cell membrane sodium exchange, and more accurately reflects the intracellular and extracellular sodium kinetics. The model can accurately predict the serum sodium change and sodium removal under different dialysis prescriptions, and can generate a sodium removal contour map for clinical prescription optimization.

Description

Technical Field

[0001] This invention relates to the fields of biomedical engineering and computational medicine, and in particular to a dual-chamber modeling and prediction method for sodium dynamics during hemodialysis. This method can accurately predict the dynamic changes in serum sodium concentration and the cumulative sodium clearance at any time during dialysis, providing quantitative evidence for the formulation of clinical prescriptions for hemodialysis and the prevention and control of dialysis-related complications. Background Technology

[0002] Sodium transport kinetics during hemodialysis significantly impact patients' serum sodium concentration, volume status, and hemodynamic stability. Accurately predicting sodium clearance and serum sodium changes during dialysis is fundamental to achieving precise dialysis prescriptions.

[0003] Traditional single-compartment sodium kinetic models treat all of a patient's body fluids as homogeneous chambers, severely overestimating diffuse sodium excretion. For example, for a standard patient (65 kg, serum Na = 140 mmol / L, dialysate Na = 140 mmol / L, 4-hour dialysis), the single-compartment model predicts a postdialysis serum sodium drop to 127.6 mmol / L, which is clinically impossible. This model neglects the buffering effect of intracellular fluid on changes in extracellular sodium concentration.

[0004] While existing two-compartment models incorporate an intracellular fluid compartment, they contain two key physical errors. First, the diffusion equilibrium concentration formula C_eq = σ × [Na]d (σ being the Donnan factor ≈ 0.97) incorrectly applies the Donnan factor to the dialysate side. When the dialysate sodium concentration [Na]d = 140 mmol / L (equal to serum sodium), C_eq = 0.97 × 140 = 135.8 mmol / L, while the plasma sodium concentration is 140 / 0.93 = 150.5 mmol / L, resulting in a diffusion gradient of 14.7 mmol / L, severely overestimating diffusion-induced sodium excretion. Another older suggested formula, C_eq = [Na]d / 0.93, also contains errors—the dialysate is 100% aqueous and protein-free, and should not be divided by 0.93; this formula incorrectly reduces the diffusion gradient to zero under isosodium conditions.

[0005] Second, some models include a solvent-dragging sodium transport term (q_refill ×Ci) in the cell membrane water redistribution term, implying that water carries sodium ions when crossing the cell membrane. However, aquaporins on the cell membrane are highly selective water channels and do not transport sodium ions. Therefore, water transmembrane transport should not result in sodium solvent drag.

[0006] The root cause of the two errors mentioned above lies in a failure to correctly understand the following physical facts: plasma consists of an aqueous phase (approximately 93% by volume) and a protein / lipid phase (approximately 7%), and electrolytes are dissolved and distributed only in the aqueous phase, not in the entire plasma volume. Therefore, any calculation involving transmembrane diffusion equilibrium must use the aqueous phase concentration, not the total plasma concentration, as an equivalent benchmark. 0.93 (the volume fraction of aqueous plasma) is an unavoidable physical constraint in the diffusion equilibrium equation, not an optional empirical correction factor.

[0007] Furthermore, existing two-compartment models generally employ an instantaneous concentration gradient model based on Fick's diffusion law to describe intracellular and extracellular sodium exchange. This model assumes the exchange flux j_ic = K_ic × (Ce - Ci), which is proportional to the instantaneous concentration difference between the extracellular and intracellular fluids. However, a significant concentration difference of approximately 140 mmol / L exists between the pre-dialysis extracellular sodium concentration (approximately 150 mmol / L) and the intracellular sodium concentration (approximately 10 mmol / L). This concentration difference is a steady-state gradient maintained by the active transport of Na⁺-K⁺-ATPase. The Fick diffusion model cannot distinguish between this steady-state background gradient and the perturbation gradient caused by dialysis, predicting a large amount of sodium transport from ICF to ECF at the moment dialysis begins, which deviates significantly from physiological reality. The correct modeling approach should be to use the pre-dialysis steady-state state as a reference baseline and establish kinetic equations only for the perturbation portion that deviates from the steady-state.

[0008] It should be noted that this invention does not deny the diffuse transport of sodium ions under conditions of a real concentration gradient, but rather points out that both the traditional Donnan formula and the old proposed formula contain physical errors. The correct diffusion equilibrium concentration is C_eq = [Na]d / σ (σ = 0.97 is the Gibbs-Donnan factor), and the diffusion gradient under isosodium conditions is 6.0 mmol / L (reflecting the real Donnan effect), while the direction and magnitude of diffuse transport under non-isosodium conditions can be accurately predicted. Summary of the Invention

[0009] The technical problem to be solved by this invention is to provide a physically self-consistent two-chamber sodium kinetic model for hemodialysis, correct the physical errors in the diffusion equilibrium concentration formula and solvent drag assumption in the existing model, and accurately predict the changes in serum sodium concentration and cumulative sodium clearance at any time during dialysis.

[0010] Therefore, this invention proposes a dual-chamber modeling and prediction method for sodium dynamics during hemodialysis, comprising the following: I. Model Structure. The patient's body fluids are divided into two chambers: an extracellular fluid (ECF) chamber with volume Ve and sodium concentration Ce (initial value is plasma sodium concentration, approximately [Na]s / 0.93 ≈ 150.5 mmol / L); and an intracellular fluid (ICF) chamber with volume Vi and sodium concentration Ci (initial approximately 10-12 mmol / L). The dialyzer acts directly on the ECF chamber, removing sodium through both convection and diffusion mechanisms.

[0011] II. Core Formula – Diffusion Equilibrium Concentration. C_eq = [Na]d / σ (σ = 0.97 is the Gibbs-Donnan factor). The physical meaning of this formula: The Gibbs-Donnan effect reduces the mobile sodium concentration on the plasma side to σ × Ce (Ce is the plasma water-sodium concentration = [Na]s / 0.93 ≈ 150.5 mmol / L), and the effective diffused sodium concentration on the plasma side = σ × Ce = 0.97 × 150.5 = 146.0 mmol / L (note the difference from the diffusion equilibrium concentration C_eq = [Na]d / σ); the dialysate side is 100% aqueous, so [Na]d is the actual concentration and requires no correction. When [Na]d = [Na]s = 140, the diffusion gradient = 146.0 - 140 = 6.0 mmol / L (reflecting the true Donnan effect). Zero diffusion point: [Na]d = σ×[Na]s / 0.93 ≈ 146 mmol / L. When [Na]d < 146, the diffusion direction is from the patient to the dialysate (sodium excretion). When [Na]d > 146, the diffusion direction is from the dialysate to the patient (sodium infusion).

[0012] III. System of Differential Equations. ECF Sodium Mass Balance Equation: d(Ve×Ce) / dt = -Quf×Ce - K_Na×(Ce - C_eq) - j_ic The first term is convective sodium clearance, the second is diffuse sodium clearance, and the third is intracellular and extracellular sodium exchange. After expansion, the convection term and the volume change term approximately cancel each other out (ignoring the Ce×q_refill residual term, since q_refill is much smaller than Q_uf), simplifying to: Ve × dCe / dt = -K_Na × (Ce - C_eq) - j_ic ICF sodium mass balance equation: d(Vi×Ci) / dt = j_ic.

[0013] IV. Perturbation Model – ICF Buffer (distinct from the Fick diffusion model). The intracellular and extracellular sodium exchange flux is modeled using a perturbation model with reference to the initial steady state: j_ic = K_ic × [(Ce - Ci) - (Ce0 - Ci0)] Where K_ic is the intracellular and extracellular sodium transport coefficient (typical value 0.03 L / min), and Ce0 and Ci0 are the initial concentrations before dialysis. The core modeling idea of ​​this model is that the huge concentration difference between intracellular and extracellular fluids before dialysis (about 140 mmol / L) is maintained by active transport of Na⁺-K⁺-ATPase, which is a steady-state background gradient and should not produce net passive exchange; only when dialysis causes a change in extracellular fluid concentration, causing (Ce-Ci) to deviate from the initial value (Ce0-Ci0), will net sodium transport occur. This is fundamentally different from the Fick diffusion model used in existing models (j = K_ic×(Ce-Ci)): the Fick diffusion model conflates the steady-state background gradient with the dialysis perturbation gradient, generating a spurious driving force of about 140 mmol / L at the moment dialysis begins, predicting a large amount of ICF→ECF sodium transport; while the perturbation model has j_ic = 0 at the beginning of dialysis (because Ce-Ci = Ce0-Ci0), and as dialysis progresses, Ce decreases, (Ce-Ci) decreases, and j_ic becomes negative (in the ECF→ICF direction), correctly reflecting the buffering effect of ICF on the decrease in ECF sodium concentration.

[0014] V. Water redistribution model. The osmotic pressure-driven water redistribution rate is: q_refill = Lp × 2 × (Ce - Ce0) (The coefficient 2 originates from the fact that Na⁺ and its associated anion Cl⁻ each contribute 1 unit to the osmotic pressure change, and the total effective osmotic pressure change is twice the sodium concentration gradient) + Quf × α Where Lp is the permeability coefficient of the osmotic water (typical value 0.0003), and α is the basic refill ratio coefficient (typical value 0.25). Key physical constraint: Cell membrane aquaporins only transport water and not sodium ions; therefore, the sodium mass conservation equation does not include a solvent drag term of q_refill×Ci. Water redistribution only changes the volume of the ECF and ICF, and does not directly result in the transmembrane transport of sodium.

[0015] VI. Numerical Solution. The Euler method was used for numerical integration with a step size of 1 minute. At each step, the following were updated: sodium concentrations of ECF and ICF (mass conservation), volumes of ECF and ICF (water balance), and cumulative convective and diffuse sodium removal.

[0016] VII. Model Input and Output Parameters. Input parameters: Patient's predialysis weight W_pre (kg), dry weight W_dry (kg), predialysis serum sodium [Na]s (mmol / L), dialysate sodium concentration [Na]d (mmol / L), blood flow rate Q_b (mL / min), dialysate flow rate Q_d (mL / min), ultrafiltration volume V_UF (L), dialysis time T (h), sodium diffusion clearance rate K_Na (mL / min), cell membrane sodium exchange coefficient K_ic (mL / min), and permeability coefficient Lp. Output parameters: Postdialysis serum sodium concentration [Na]s_post (mmol / L), total sodium clearance Na_total (mmol), diffuse sodium clearance Na_diff (mmol), convective sodium clearance Na_conv (mmol), ECF volume change trajectory, and serum sodium concentration time series.

[0017] The beneficial effects of this invention compared to the prior art are: (1) The diffusion equilibrium concentration formula (C_eq = [Na]d / σ, σ=0.97, replacing the traditional σ×[Na]d and the old suggestion [Na]d / 0.93) was revised, reducing the diffusion gradient under isosodium dialysis conditions from 14.7 mmol / L to 6.0 mmol / L, making the model prediction consistent with clinical observations. This revision is based on the physical fact that electrolytes are distributed only in the aqueous phase of plasma, elevating 0.93 from an empirical correction factor to an indispensable physical constraint.

[0018] (2) The biophysical constraint that cell membrane aquaporins do not transport sodium was clarified, the erroneous solvent drag term was removed, and the physical self-consistency of the model was improved.

[0019] (3) The perturbation model with the initial steady state as a reference is used to replace the instantaneous concentration gradient model based on Fick's diffusion law in the existing technology. It correctly distinguishes the steady-state background gradient maintained by Na⁺-K⁺-ATPase from the perturbation gradient caused by dialysis, avoids false sodium transport in the initial state, and enables the model to give reasonable predictions under various dialysate sodium concentration conditions.

[0020] (4) The model prediction results were highly consistent with clinical experience: when [Na]d=134, serum Na after dialysis was approximately 137.2 mmol / L, and total sodium clearance was 324 mmol (significant diffusion sodium excretion); when [Na]d=140, serum Na after dialysis was approximately 138.2 mmol / L, and total sodium clearance was 290 mmol (close to pure convection); when [Na]d=145, serum Na after dialysis was approximately 139.0 mmol / L, and total sodium clearance was 263 mmol (reversal of diffusion direction).

[0021] (5) The model can generate sodium clearance contour maps, with ultrafiltration volume and dialysate sodium concentration as coordinate axes, to intuitively show the effects of different prescription parameter combinations, providing quantitative basis for clinical decision-making. Attached Figure Description

[0022] Figure 1 This is a four-panel plot of simulation results under different dialysate sodium concentrations (134-145 mmol / L), including: (A) a curve showing the change of serum sodium over time, with the horizontal axis representing dialysis time (in min) and the vertical axis representing serum sodium concentration (in mmol / L), displaying 134, 136, 138, 140, 142, and 145 mmol / L. (A) Dynamic changes in serum sodium at six different dialysate sodium concentrations; (B) Curve showing cumulative sodium clearance over time, with the horizontal axis representing dialysis time (min) and the vertical axis representing cumulative sodium clearance (mmol), simultaneously displaying the dynamic changes in sodium clearance at the six different dialysate sodium concentrations, and indicating the clinical total sodium clearance target of 301 mmol; (C) Bar chart comparing convective and diffuse sodium clearance, with the horizontal axis representing dialysate sodium concentration (mmol / L) and the vertical axis representing sodium clearance (mmol), visually comparing the proportion and quantitative differences of convective and diffuse sodium clearance at different dialysate sodium concentrations; (D) Curve showing ECF volume over time, with the horizontal axis representing dialysis time (min) and the vertical axis representing ECF volume (L), displaying the dynamic changes in extracellular fluid volume during dialysis, and indicating the baseline ECF volume corresponding to the patient's dry weight.

[0023] Figure 2 The simulation results are shown for different dialysis times (3-8 hours). Figure 2(A) shows the curve of serum sodium concentration versus dialysis time, with the horizontal axis representing dialysis time (min) and the vertical axis representing serum sodium concentration (mmol / L), illustrating the dynamic changes in serum sodium at five dialysis times: 180, 240, 300, 360, and 480 minutes. Figure 2(B) shows the curve of cumulative sodium clearance versus dialysis time, with the horizontal axis representing dialysis time (min) and the vertical axis representing cumulative sodium clearance (mmol), simultaneously illustrating the dynamic changes in sodium clearance at the five dialysis times. Figure 2(C) is a comparison of sodium clearance and ultrafiltration rate safety, with the horizontal axis representing dialysis time (min) and the vertical axes representing sodium clearance (mmol) and ultrafiltration rate (ml / h / kg), respectively, demonstrating the quantitative matching relationship between sodium clearance and ultrafiltration rate at different dialysis times, and indicating the clinical ultrafiltration rate safety limits. Figure 3(A) is a contour plot of sodium removal. The total sodium removal is plotted with ultrafiltration volume (unit: L) on the x-axis and dialysate sodium concentration (unit: mmol / L) on the y-axis. Contour lines of total sodium removal are plotted for different combinations of ultrafiltration volume and dialysate sodium concentration, and the sodium removal values ​​corresponding to each contour line are marked. Figure 3 (B) is a contour plot of serum sodium concentration after dialysis. The horizontal and vertical axes are the same as those in Figure 3 (A). Contour lines of serum sodium concentration after dialysis were drawn under different combinations of ultrafiltration volume and dialysate sodium concentration, and the corresponding serum sodium concentration values ​​of each contour line were labeled.

[0024] Figure 4 It is a safe and effective prescription interval chart, with ultrafiltration volume (unit: L) as the x-axis and dialysate sodium concentration (unit: mmol / L) as the y-axis. The two-dimensional coordinate chart is superimposed with three major clinical constraint lines: sodium clearance target line (301 mmol), ultrafiltration rate safety line (2.6L@10ml / h / kg), and serum sodium safety zone. This chart determines and marks the safe and effective prescription interval for hemodialysis, providing a direct and visual reference for the quantitative formulation of clinical dialysis prescriptions. Detailed Implementation

[0025] The following detailed implementation of the technical solution of the present invention, combined with actual clinical parameters, enables those skilled in the art to fully and accurately implement the modeling and prediction method of the present invention; all clinical parameters are conventionally obtainable parameters in the field of hemodialysis, and the model parameters are typical clinical values ​​that can be fine-tuned according to individual patient differences.

[0026] Example 1: Simulation prediction of sodium concentration in different dialysate Patient baseline parameters: dry weight 65 kg, predialysis weight 67 kg (ΔW = 2 kg), predialysis serum sodium [Na]s = 140 mmol / L, dialysis time 4 hours, ultrafiltration volume 2.0 L. Model parameters: K_Na = 0.025 L / min, K_ic = 0.03 L / min, Lp = 0.0003, α = 0.25.

[0027] Simulations were conducted with dialysate sodium concentrations set at 134, 136, 138, 140, 142, and 145 mmol / L, respectively. Figure 1As shown, the results indicate that: (1) the lower the sodium concentration in the dialysate, the more sodium is diffusely excreted, and the greater the total sodium clearance; (2) when [Na]d = 140 mmol / L (isosodium dialysis), there is still a diffusion gradient of 6.0 mmol / L (Gibbs-Donnan effect), which verifies the correctness of the formula C_eq = [Na]d / σ (σ=0.97); (3) when [Na]d > 146 mmol / L (zero diffusion point = σ×[Na]s / 0.93), the diffusion direction is reversed, and sodium is infused into the patient's body from the dialysate.

[0028] Example 2: Simulation Prediction of Different Dialysis Times With a fixed ultrafiltration volume of 2.0 L and a dialysate sodium concentration of 138 mmol / L, dialysis times were set to 3, 4, 5, 6, and 8 hours. Figure 2 As shown, extending the dialysis time can reduce the ultrafiltration rate (improving safety) while increasing the diffusion sodium excretion time and thus increasing total sodium removal. When the dialysis time was extended from 3 hours to 5 hours, the ultrafiltration rate decreased from approximately 10.0 ml / h / kg to approximately 6.0 ml / h / kg (below the safety threshold of 10 ml / h / kg), while sodium removal increased by approximately 15%.

[0029] Example 3: Generation of Sodium Removal Contour Maps like Figure 3 As shown, in a two-dimensional parameter space of ultrafiltration volume (1.0-3.5 L) × dialysate sodium concentration (130-148 mmol / L), a two-chamber model was run for each parameter combination to calculate total sodium clearance and post-dialysis serum sodium, generating a contour plot. This plot visually demonstrates that the combination of low dialysate sodium and high ultrafiltration volume produces maximum sodium clearance, while the combination of high dialysate sodium and low ultrafiltration volume produces minimum sodium clearance or even sodium infusion.

[0030] Example 4: Determination of the safe and effective prescription range like Figure 4 As shown, three constraints are superimposed on the contour map: (1) the contour line where sodium clearance reaches the target value Na_target = ΔW × [Na]s / 0.93; (2) the vertical boundary where the ultrafiltration rate does not exceed 10 ml / h / kg; and (3) the region where serum sodium after dialysis is in the range of 136-143 mmol / L. The region enclosed by the three constraints is the safe and effective prescription interval.

[0031] Example 5: Example of a sodium kinetics prediction system.

[0032] This invention also provides a sodium kinetics prediction system, comprising: a parameter input module for receiving patient parameters (weight, serum sodium concentration, dialysis prescription, etc.) and dialysis machine parameters (dialysis fluid sodium concentration, blood flow rate, dialysate flow rate, etc.); a calculation engine module, which incorporates the aforementioned dual-chamber sodium kinetics model and uses the Euler method to solve the coupled differential equation system with a 1-minute step size for numerical integration, thereby calculating the serum sodium change trajectory and cumulative sodium clearance in real time; a result output module for outputting the model prediction results, including post-dialysis serum sodium concentration, total sodium clearance, convective and diffuse sodium clearance components, and R_Na predicted value; and a visualization module for generating simulation curves (such as...). Figure 1 , Figure 2 The following are examples: serum sodium dynamic change curves, sodium clearance curves, and sodium clearance contour maps (e.g., [examples of curves showing these curves]). Figure 3 (As shown). The above modules can be implemented as standalone software systems or embedded device firmware.

[0033] 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 scope of the technology 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 for modeling and predicting sodium dynamics in a two-compartment system during hemodialysis, characterized in that, Includes the following steps: Step A: Divide the patient's body fluid into extracellular fluid chambers and intracellular fluid chambers, characterized by volumes Ve and Vi and sodium concentrations Ce and Ci, respectively. The dialyzer acts directly on the extracellular fluid chambers. Step B: Establish the formula for calculating the diffusion equilibrium concentration C_eq: C_eq = [Na]d / σ (σ=0.97 is the Gibbs-Donnan factor) Where [Na]d is the set value of dialysate sodium concentration, and σ=0.97 is the Gibbs-Donnan factor; this formula is based on the following physical facts: plasma-side proteins carry a negative charge, and through the Gibbs-Donnan effect, the mobile sodium concentration is reduced to σ×Ce (Ce is the plasma water-sodium concentration), while the dialysate side is 100% aqueous and requires no correction; under isosodium conditions, the diffusion gradient is 6.0 mmol / L, which correctly reflects the true physical contribution of the Gibbs-Donnan effect; Step C: Establish the sodium mass balance equation for the extracellular fluid chamber: d(Ve×Ce) / dt = -Quf×Ce - K_Na×(Ce - C_eq) - j_ic Where Quf is the ultrafiltration rate, K_Na is the sodium dialyzer clearance rate, and j_ic is the intracellular and extracellular sodium exchange flux; Step D: Establish the sodium mass balance equation for the intracellular fluid chamber: d(Vi×Ci) / dt = j_ic Step E: Establish an osmotic pressure-driven water redistribution model, in which cell membrane aquaporins transport only water and do not carry sodium ions, that is, water transmembrane transport does not produce solvent-drafted sodium transport. Step F: Solve the above coupled equations by numerical integration to predict the serum sodium concentration and cumulative sodium clearance at any time during dialysis.

2. The method as described in claim 1, characterized in that, In step B, the diffusion equilibrium concentration formula C_eq = [Na]d / σ (σ=0.97) replaces both the traditional Donnan formula C_eq = σ×[Na]d and the old suggested formula C_eq = [Na]d / 0.93; the σ=0.97 only applies to the diffusion equilibrium calculation on the plasma side, while the dialysate side is 100% aqueous and requires no correction.

3. The method as described in claim 1, characterized in that, The intracellular and extracellular sodium exchange fluxes in steps C and D are calculated using a perturbation model with reference to the initial steady state: j_ic = K_ic × [(Ce - Ci) - (Ce0 - Ci0)] Where K_ic is the intracellular and extracellular sodium transport coefficient, and Ce0 and Ci0 are the initial concentrations before dialysis; the perturbation model uses the steady-state concentration difference before dialysis (Ce0-Ci0) as the reference baseline and only calculates the net exchange flux generated after the system deviates from the steady state.

4. The method as described in claim 1, characterized in that, The method for calculating the water redistribution rate in step E is as follows: q_refill = Lp × 2 × (Ce - Ce0) + Quf × α Where Lp is the permeability coefficient of the permeate water, and α is the basic refill ratio coefficient; the water redistribution only changes the volume of the extracellular fluid and intracellular fluid, and does not produce sodium transmembrane transport.

5. The method as described in claim 1, characterized in that, In step C, the extracellular fluid sodium mass balance equation, after expansion, shows that the convection term and the volume change term cancel each other out, simplifying to: Ve × dCe / dt = -K_Na × (Ce - C_eq) - j_ic This means that changes in extracellular sodium concentration are determined solely by diffusion clearance and intracellular / extracellular exchange.

6. The method as described in claim 1, characterized in that, The input parameters of the method include: patient dry weight, predialysis weight, predialysis serum sodium concentration, dialysate sodium concentration, ultrafiltration volume, and dialysis time; the outputs include: predicted postdialysis serum sodium concentration, convective sodium clearance, diffuse sodium clearance, total sodium clearance, and serum sodium change curve over time.

7. The method as described in claim 1, characterized in that, It also includes the step of generating a sodium clearance contour map, with ultrafiltration volume and dialysate sodium concentration as the coordinate axes and total sodium clearance or post-dialysis serum sodium as the contour values, to visually demonstrate the effect of different prescription parameter combinations on sodium clearance.

8. A hemodialysis sodium kinetic prediction system, characterized in that, include: The parameter input module is used to receive patient parameters and dialysis prescription parameters; A dual-chamber model computation engine implements the modeling and prediction method described in claim 1, and solves the coupled differential equation system in real time; The results output module is used to output the predicted serum sodium concentration change curve, cumulative sodium clearance, and sodium clearance components. A visualization module is used to generate sodium clearance contour maps and safe prescription interval maps.

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