# Patent

## Title
Method of controlling diffusive sodium transport in dialysis

## Abstract

A method of controlling diffusive sodium transport from the dialysate solution to the blood of a patient undergoing hemodialysis treatment or from the blood to the dialysate solution includes calculating SNa+average, an average of the patient's historic serum sodium concentrations, and estimating SNa+estimated, the patient's pre-dialysis serum sodium concentration, based on the average of the patient's measured historic pre-dialysis serum sodium concentrations, SNa+measured. The method enables adjusting DNa+, the sodium concentration of the dialysate solution, based on the average of the patient's historic serum sodium concentrations, SNa+average, if needed, and performing the dialysis treatment of the patient using a dialysate solution containing a sodium concentration DNa+.

## Background
RELATED APPLICATION
This application claims the benefit of U.S. Provisional Application No. 61/277,957, filed on Oct. 1, 2009. The entire teachings of the above application are incorporated herein by reference.


BACKGROUND OF THE INVENTION
The pre-dialysis serum sodium (Na+) concentration is relatively constant in hemodialysis patients, but varies with each patient's individual osmolar set point. See F. M. De Paula, et al., Clinical consequences of an individualized dialysate sodium prescription in hemodialysis patients, Kidney International, Vol. 66 (2004) pp. 1232-1238; A. S. Peixoto, et al., Long-Term Stability of Serum Sodium in Hemodialysis Patients, Blood Purification, Vol. 29 (2010) pp. 264-267, and M. L. Keen, and F. A. Gatch, The association of the sodium “setpoint” to interdialytic weight gain and blood pressure in hemodialysis patients, The International Journal of Artificial Organs, Vol. (11) pp. 971-979 (2007). The gradient (GNa+) between the serum sodium (SNa+) concentration and the dialysate sodium (DNa+) concentration is a major determinant of post-dialytic SNa+ concentration. A positive gradient (DNa+>SNa+) can result in a higher post-dialytic SNa+, and consequent thirst, excess interdialytic weight gain, volume overload, and increased blood pressure. A negative gradient (DNa+<SNa<+) is also undesirable because it can result in the patient becoming hypotensive. Basing DNa+ on SNa+ (e.g., gradient GNa+=0) would minimize diffusive sodium transport, and thus reduce the aforementioned problems. However, the measurement of the serum sodium concentration, SNa+measured, of each patient before each dialysis treatment is costly and time consuming using existing technology.
Therefore, there is a need for a method of controlling diffusive sodium transport from the dialysate solution to the blood of a patient undergoing dialysis treatment that minimizes or eliminates the aforementioned problems.
SUMMARY OF THE INVENTION
The invention is generally related to a method of controlling diffusive sodium transport from the dialysate solution to the blood of a patient undergoing hemodialysis treatment or from the blood to the dialysate solution. The method includes calculating SNa+average, an average of the patient's historic serum sodium concentrations, and estimating SNa+estimated, the patient's pre-dialysis serum sodium concentration, based on the average of the patient's historic pre-dialysis serum sodium concentrations, SNa+measured. The method enables adjusting DNa+, the sodium concentration of the dialysate solution, based on the average of the patient's historic serum sodium concentrations, SNa+average, if needed, and performing the dialysis treatment of the patient using a dialysate solution containing a sodium concentration DNa+.
In some embodiments, the patient's present pre-dialysis serum sodium concentration is estimated as equal to the average of the patient's historic serum sodium concentrations measured pre-dialysis treatment over a historic time interval. The patient's measured historic serum sodium concentrations can be corrected for void volume and/or the Gibbs-Donnan effect. In certain embodiments, the sodium concentration of the dialysate solution, DNa+, is equal to the estimated pre-dialysis serum sodium concentration, SNa+estimated. In some embodiments, the historic time interval is at least 2 months. In other embodiments, the historic time interval is at least 4 months.
This invention provides a method of accurately predicting a dialysis patient's pre-dialysis serum sodium concentration, SNa+estimated, which in turn, allows a dialysis solution to be used for dialysis of the patient with a dialysate sodium concentration, DNa+, based upon the patient's SNa+estimated. Use of such a dialysate solution reduces the health consequences of a positive or negative sodium gradient, GNa+, during dialysis.
This invention has many advantages, including the ability to eliminate the measurement of the serum sodium concentration, SNa+measured, of each patient before each dialysis treatment.



BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing will be apparent from the following more particular description of example embodiments of the invention, as illustrated in the accompanying drawings illustrating embodiments of the present invention.
FIG. 1 is a graph of the number of patients for a large group of hemodialysis patients studied, where SNa+measured as well as DNa+ were available (n=3,114), versus the distribution of the dialysate to serum sodium gradient GNa+ (GNa+=DNa+−SNa+measured). A normal distribution curve approximation, based on the average and the standard deviation of the data, is indicated by a solid line.
FIG. 2 is a graph showing the standard deviation of the difference between the average serum sodium over a certain period of time, SNa+average, of different tested models, and measured serum sodium concentrations, SNa+measured, versus the number of months used for the calculation of the average serum sodium concentration, SNa+average.
FIG. 3 is a graph of the serum sodium concentration measured in the current month SNa+measured Month(i=0) versus the average serum sodium concentration SNa+average averaged over the previous 4 months (SNa+measured(Month(i=−1) to Month(i=4)). A line of indentity is indicated by a dashed line.
FIG. 4 is a graph of the number of patients for a large group of hemodialysis patients studied, where SNa+measured as well as DNa+ were available (n=3,114), versus the distribution of the dialysate to serum sodium gradient GNa+ (GNa+=DNa+−SNa+average) after calculation of an average serum sodium concentration the SNa+average over a historic time interval (SNa+measured of Month(i=−1) to Month(i=−4)). A normal distribution curve approximation, based on the average and the standard deviation of the data, is indicated by a solid line.
FIG. 5 is a graph of the number of patients for a large group of hemodialysis patients studied, where SNa+measured, DNa+, and total protein concentrations (TP) were available (n=2,788), versus the distribution of the dialysate to serum sodium gradient, G′Na+ (G′Na+=DNa+−S′Na+measured), after adjustment for the Gibbs-Donnan effect and the void volume correction. A normal distribution curve approximation, based on the average and the standard deviation of the data, is indicated by a solid line.
FIG. 6 is a graph of the number of patients for a large group of hemodialysis patients studied, where SNa+measured, DNa+, and total protein concentrations (TP) were available (n=2,788), versus the distribution of the dialysate to serum sodium gradient, G′Na+ (G′Na+=DNa+−S′Na+average), after adjustment for the Gibbs-Donnan effect and the void volume correction in the calculation of the average serum sodium concentration, S′Na+average, over a historic time interval (S′Na+measured of Month(i=1) to Month(i=−4)). A normal distribution curve approximation, based on the average and the standard deviation of the data, is indicated by a solid line.
FIG. 7 is a graph of the post-dialysis minus pre-dialysis serum sodium concentration (PPSD) as a function of the nominal dialysate sodium minus serum sodium gradient.
FIG. 8 is a graph of the post-dialysis minus pre-dialysis serum sodium concentration (PPSD) as a function of the dialysate sodium minus serum sodium gradient after adjustment for the void volume and the Gibbs-Donnan effect.



DETAILED DESCRIPTION OF THE INVENTION
The method of controlling diffusive sodium transport from the dialysate solution to the blood of a patient undergoing hemodialysis treatment or from the blood to the dialysate solution includes calculating SNa+average, an average of the patient's historic serum sodium concentrations, and estimating SNa+estimated, the patient's pre-dialysis serum sodium concentration, based on the average of the patient's historic pre-dialysis serum sodium concentrations, SNa+measured, measured pre-dialysis treatment over a historic time interval. The pre-dialysis serum sodium concentration of a patient can either be measured with flame photometry, or with an ion selective electrode using either direct (undiluted specimens) or indirect (diluted specimens) potentiometry. The results obtained by indirect potentiometry can be corrected for void volume and the Gibbs-Donnan effect, as discussed below. Alignment was shown to reduce consequences of positive or negative gradients. See F. M. De Paula, et al., Clinical consequences of an individualized dialysate sodium prescription in hemodialysis patients, Kidney International, Vol. 66 (2004) pp. 1232-1238. In clinical routine of the treatment of chronic hemodialysis patients, the measurement of serum sodium, SNa+measured, is taken pre-dialysis, typically once a month, preferably in the first week of every month, more preferably mid-week during the first week of every month of a thrice weekly dialysis treatment regimen. The data is accumulated over a historic time interval that is preferably at least 2 months, more preferably at least 4 months. A particularly preferred historic time interval is at least 4 months, but not more than 12 months.
The estimate of the patient's pre-dialysis serum sodium concentration, SNa+estimated, is based on the arithmetic average of the patient's historic pre-dialysis serum sodium concentrations, SNa+measured. In some embodiments, the patient's pre-dialysis serum sodium concentration is estimated as equal to the average of the patient's historic serum sodium concentrations measured pre-dialysis treatment over the historic time interval. The patient's measured historic serum sodium concentrations can include corrections for void volume and the Gibbs-Donnan effect discussed below. A patient's normal pre-dialysis serum sodium concentration typically varies from about 135 mmol/liter to about 145 mmol/liter, depending on each patient's individual osmolar set point. See M. L. Keen, and F. A. Gotch, The association of the sodium “setpoint” to interdialytic weight gain and blood pressure in hemodialysis patients, The International Journal of Artificial Organs, Vol. 30 (11) pp. 971-979 (2007).
It was found that the correlation of the measured serum sodium SNa+measured of Month(i=0) with the measured serum sodium SNa+measured of the preceding month (Month(i=−1), was poor (R2=0.29). The model employing the average over the preceding 12 months resulted in a better correlation than a model over the preceding 4 months, which was in turn better than a model employing an average over the preceding 2 months. It is expected that a model employing an average over a historic time interval larger than 12 months would show a worse correlation, due to, for example, possible significantly increased deterioration of the patient's health during a period closer to the dialysis treatment.
The method enables adjusting DNa+, the sodium concentration of the dialysate solution, if needed, based on either SNa+average or S′Na+average, the average of the patient's historic measured serum sodium concentrations, SNa+measured or S′Na+measured (the ′ refers to SNa+ estimates taking the void volume correction and the Gibbs-Donnan effect into account, as discussed below). By contrast, in a typical dialysis treatment using a dialysate with an unadjusted sodium concentration, that concentration is typically set at about 138 to 142 mmol/liter. Controlling diffusive sodium transport from the dialysate solution to the blood of a patient undergoing dialysis treatment or from the blood to the dialysate solution can include adjusting DNa+ to be slightly smaller than the serum sodium concentration, such that a physician-prescribed slight diffusive loss of sodium from the patient's blood is accomplished, for example, for treatment of hypertensive patients. Additionally, controlling diffusive sodium transport from dialysate solution to blood of a patient undergoing dialysis treatment or from the blood to the dialysate solution can include adjusting DNa+ to be slightly larger than the serum sodium concentration, such that a physician-prescribed slight diffusive gain of sodium by the patient's blood is accomplished, for example, for treatment of hypotensive patients. See A. Murisasco, G. France, G. Leblond, C. Durand, M. El Mehdi, A. Crevat, R. Elsen, Y. Boobes, and M. Baz, Sequential sodium therapy allows correction of sodium-volume balance and reduces morbidity, Clinical Nephrology, Vol. 24 (4) pp. 201-208 (1985).
In certain embodiments, the sodium concentration of the dialysate solution, DNa+, is set equal to the estimated pre-dialysis serum sodium concentration, either SNa+estimated or S′Na+estimated, which is based on either SNa+average or S′Na+average the average of the measured historic serum sodium concentrations, SNa+measured and S′Na+measured, respectively. Additionally, the sodium concentration of the dialysate solution, DNa+, should be adjusted to account for two additional factors: firstly, the void volume correction and secondly, the Gibbs-Donnan effect. The former requires the distinction between plasma (containing plasma water, lipid and proteins) and plasma water. Void volume correction is only required for measurements by indirect potentiometry (measuring the serum sodium concentration in a defined amount of plasma and thus creating the need for void volume correction); indirect potentiometry can produce lower results, as compared to direct potentiometry and flame photometry (the former directly measuring conductivity and thus electrically active sodium in plasma water and the latter measuring the total amount of sodium in a defined volume). This distinction is necessary because the sodium concentration in the plasma water is the concentration determining the diffusive processes at the dialysis membrane. Secondly, the Gibbs-Donnan effect, which is caused by negative protein charges (on the blood side), impacts the transmembrane flux of (positively charged) sodium ions, and therefore also has to be taken into account for alignment.
The following empirical equation was proposed by Gotch et al. (1980) to calculate plasma water sodium concentration (PWNa+) by accounting for the void volume:




  
    
      
        
          
            PW
            ⁢
            
              
            
            ⁢
            
              Na
              +
            
          
          =
          
            
              S
              ⁢
              
                
              
              ⁢
              
                Na
                +
              
            
            
              0.989
              -
              
                0.0047
                ×
                TP
              
            
          
        
        ,
      
    
    
      
        (
        1
        )
      
    
  




where SNa+ is the serum sodium concentration determined by indirect potentiometry and TP is the total protein concentration in the plasma.
The following empirical equation was proposed by Gotch et al. (1980) to account for the Gibbs-Donnan effect:

Donnan−coefficient=1.007−0.009×TP  (2)

where TP is the total protein concentration.
The equation accounting for both effects is




  
    
      
        
          
            
              S
              ′
            
            ⁢
            
              Na
              +
            
          
          =
          
            S
            ⁢
            
              
            
            ⁢
            
              Na
              +
            
            ×
            
              
                1.007
                -
                
                  0.009
                  ×
                  TP
                
              
              
                0.989
                -
                
                  0.0047
                  ×
                  TP
                
              
            
          
        
        ,
      
    
    
      
        (
        3
        )
      
    
  




where S′Na+ is the sodium concentration which results in a dialysate to serum sodium gradient of zero (GNa+=0) taking the void volume and the Gibbs-Donnan effect into account, SNa+ is the serum sodium concentration (either estimated or measured, but measured with indirect potentiometry) and TP is the total protein concentration in the plasma.
See F. A. Gotch, M. A. Lam, M. Prowitt, and M. L. Keen, Preliminary Clinical Results with Sodium-Volume Modeling of Hemodialysis Therapy, Proceedings Clinical Dialysis Transplant Forum, Vol, 10 (1980) pp. 12-17.
Exemplification
The predictability of the next month's serum sodium concentration, SNa+estimated and S′Na+estimated, respectively, on the basis of the patient's historic serum sodium concentrations, SNa+measured and S′Na+measured, measured pre-dialysis treatment over a historic time interval was investigated. In this retrospective analysis, monthly serum sodium concentrations, SNa+measured and S′Na+measured, were analyzed over one year (12 months) in a large group of chronic maintenance hemodialysis patients receiving dialysis at Renal Research Institute clinics. Linear regression analysis was employed to investigate the relationship between SNa+measured in Month(i=0) and SNa+average, the arithmetic average of Months (i=−4) to (i=−1).
Monthly SNa+measured as well as DNa+ values of 3,114 hemodialysis patients were available (1,763 males, 1,755 blacks, mean age 60 years). The SNa+measured Month(i=0) was 140.4±3.4 mmol/liter. As illustrated in FIG. 1, GNa+ in Month(i=0) was −0.83±3.95 mmol/liter (95% confidence interval (CI)-0.97 to −0.70). SNa+measured Month(i=0) and SNa+measured Month(i=−1) were poorly correlated (R2=0.29). As illustrated in FIG. 2, various models were tested, including an increasing amount of monthly SNa+measured values, and the arithmetic average SNa+measured of Months(i=−1) to (i=−4) was preferred. After 4 months the slope decreases below −0.05 and flattens consecutively, which indicates no substantial gain for the estimation of SNa+estimated. The correlation of the average serum sodium concentration of this preferable observation period (i.e., historic time interval) SNa+average Months(i=−1 to −4) to SNa+measured Month(i=0) is illustrated in FIG. 3 (SNa+measured Month(i=0)=22.79+0.845*SNa+average Months(i=−1 to −4); R2=0.40), and listed in Table 1 below. Other models using different historic time intervals are not shown.







TABLE 1







Regression coefficientsa for Average of Serum Sodium Concentration (i = −1 to


i = −4)















95% Confidence



Unstandardized
Standardized

Interval for B













Coefficients
Coefficients

Lower
Upper














Model
B
Std. Error
Beta
T
Sig.
Bound
Bound

















1 (Constant)
22.793
2.511

9.077
.000
17.87
27.716


Average of Serum Na+
.845
.018
.635
46.824
.000
.809
.880


Month(i = −1) to Month (i = −4)





aDependent Variable: Measured Serum Na+ Month (i = 0)






As illustrated in FIG. 4, a prescription of DNa+, based on the predicted SNa+estimated Month(i=0) (DNa+=SNa+estimated) using the average SNa+measured over the preceding 4 months would have resulted in a GNa+ (i=0) of 0.35±3.17 mmol/liter (95% CI 0.24 to 0.46), which is closer to zero than the actually observed GNa+Month(i=0) of −0.83 mmol/liter.
As illustrated in FIG. 5 the dialysate to serum sodium gradient, G′Na+, taking the Gibbs-Donnan effect and the void volume correction into account (G′Na+ mm DNa+-S′Na+estimated) in Month(i=0) was 0.92±3.86 mmol/liter (95% CI 0.77 to 1.06).
As illustrated in FIG. 6, a prescription of DNa+, based on the predicted estimated Month(i=0) (DNa+=S′Na+estimated) using the average S′Na+measured over the preceding 4 months would have resulted in a G′Na+ (i=0) of 2.05+3.08 mmol/liter (95% CI 1.94 to 2.17).
As illustrated in FIG. 7 sodium alignment without adjusting for the void volume and the Gibbs-Donnan effect (DNa+=SNa+) results in an intradialytic increase of serum sodium, SNa+, of approximately 1 mmol/L at a dialysate to serum sodium gradient of zero.
FIG. 8 illustrates that the intradialytic change in serum sodium, SNa+, is much closer to zero (−0.112 mEq/L), following sodium alignment after adjustment for the void volume and the Gibbs-Donnan effect (DNa+=S′Na+).
The relevant teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.
While this invention has been particularly shown and described with references to example embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.

## Claims

1. A method of controlling diffusive sodium transport from dialysate solution to blood of a patient undergoing hemodialysis treatment or from blood into the dialysate solution comprising:
a) calculating SNa+average, an average of the patient's measured historic serum sodium concentrations, SNa+measured;
b) estimating SNa+estimated, the patient's pre-dialysis serum sodium concentration, based on the average, SNa+average, of the patient's pre-dialysis serum sodium concentrations over a historic time interval of at least 4 months;
c) determining GNa+, a desired gradient between SNa+estimated and DNa+, the sodium concentration in a dialysate solution; and
d) performing the dialysis treatment of the patient using the dialysate solution containing the sodium concentration DNa+ based upon SNa+estimated.

2. The method of claim 1, wherein the patient's historic serum sodium concentrations include corrections for void volume and Gibbs-Donnan effect.

3. The method of claim 1, wherein DNa+=SNa+estimated.

4. The method of claim 2, wherein DNa+=SNa+estimated.