Hou CdiCa

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Fig. 3. Plasma Ca profiles calculated from the data of Hou et al. [1] with and without fitting values for M Ca.

moval from VCa and recovery in dialysate could be calculated with both sets of measurement and directly compared for validity to predict mass balance. Analysis of their CCaT data with the Ca kinetic model is shown in figure 6 combined with the Hou data. Excellent agreement between the calculated removal from the body and measured recovery in dialysate can be seen over a total flux range from -1,500 to nearly +1,000 mg and DCa 5-172 ml/ min during these treatments. The Nolph data were also analyzed with the Ca model using the CCa2+ measurements and these results are discussed below.

Analysis of Reported Ionized Ca Mass Balance

Although measurement of ionized Ca by direct po-tentiometry should theoretically be the best measure of diffusible Ca, analysis of reported data with mass balance criteria indicate that is not true. This was evaluated in data reported by Argiles et al. [4] and the Nolph data with results shown in figure 7. Note that mass balance could not be closed with the CCa2+ data. We interpret this to reflect the greater inherent variability in ISE measurements compared to colorimetric-based measurements of total Ca and simple estimation that 50% is ionized.

Ca Buffer Pool

The plots in figures 3 and 4 quantify the powerful effects of sequestration (M-Ca) and mobilization (M+Ca) on resisting increases and decreases in Cp Ca2+ with positive and negative dialysate to blood concentration gradients,

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Fig. 5. Comparison of measured dialysate Ca removed to that calculated from the kinetic model (ACp*VCa + MCa2+). There is nearly perfect correlation over a wide range. Certainly this is in part due to linkage of clearance calculated from the plasma and dialysate Ca values but the amount removed by ACp*VCa + MCa2+ is calculated from the kinetic model. As shown below similar analyses with ionized Ca data do not result in closure of mass balance.

respectively. This relationship might be a useful tool for physiologic studies. What controls MCa? Can PTH operate that rapidly? Can the MCa response to dialysis provide some estimate of Ca depletion or overload? These are interesting considerations that might be pursued with the model but the first question is what the properties of this pool are.

The magnitudes of MCa observed in the Hou data over time are shown in figure 8. Note that MCa was constant

Fig. 7. Comparison of mass balance calculated from the data of Hou et al [1] and Nolph et al. [2] using estimated Ca2+ with the data of Argiles et al. [4] and Nolph et al. [2] using measured Ca2+ values. Mass balance is much more reliably determined with estimated Ca2+ values compared to measured Ca2+ values.

throughout the course of these 240-min dialyses which would be expected if MCa represents a response which maintains the CpiCa constant when exposed to a dialyzer concentration gradient.

It is also important to note that the magnitude of MCa is inversely proportional to the gradient and the sign of MCa is opposite the sign of the gradient reflecting mobilization of Ca from the buffer pool with a negative gradient and sequestration of Ca with a positive gradient. The magnitude of MCa compared to the change in Ca content of VCa is depicted in figure 9 for the Hou data with CdiCa 3.50. Sequestration (M-Ca) accounted for 98% of the total accumulation of Ca with a concentration gradient of +1.25 mEq/l and there was virtually no change in CpiCa. These relationships lead directly to the hypothesis shown in figure 10 where MCa is postulated to be a linear function of the driving force.

Miscible Ca Pool

The relationships in figures 4,5 and 8-10 clearly show a powerful mechanism operating to stabilize CpiCa during dialysis with a Ca concentration gradient across the dialyzer. Figure 11 is a diagram of Ca distribution in the body derived from isotope dilution [5]. What is striking, and may be highly relevant to the mechanism underlying MCa, is that VCa has been found to be in rapid diffusion equilibrium with a much larger pool of Ca in the periosteum and exchangeable bone surface Ca. This pool would

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Fig. 5. Comparison of measured dialysate Ca removed to that calculated from the kinetic model (ACp*VCa + MCa2+). There is nearly perfect correlation over a wide range. Certainly this is in part due to linkage of clearance calculated from the plasma and dialysate Ca values but the amount removed by ACp*VCa + MCa2+ is calculated from the kinetic model. As shown below similar analyses with ionized Ca data do not result in closure of mass balance.

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-1,500 -1,000 -500 0 500 1,000 Measured JdCa, mg

Fig. 6. Mass balance calculated from the CAPD data of Nolph et al. [2] also agrees well with that measured in dialysate. Thus mass balance agreement was shown with the model over a range of DCa 6-172 ml/min and Ca flux +700 to -1,400 mg.

Fig. 8. Mobilization (M+Ca) and Sequestration of Ca (M-Ca) in the buffer pool. (1) The rate of MCa is constant during dialysis. (2) It is directly proportional to dia-lyzer flux, Jd, but opposite in sign. (3) The total net flux of Ca may be predictable from Cpi and prescribed DCa, CdiCa and td. (4) It is important to note that these relationships predicting mass balance will be linearly dependent on DCa(CdiCa -Cpi Ca) and treatment time rather than the usual exponential relationship.

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JdCa = -S3 mg/h

M-Ca = +55 mg/h

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Jdo, = + 27 mg/h

M-Ca = -25 mg/h

JdCa = + 258 mg/h

M-Ca = -220 mg/h

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have the effect of greatly increasing the effective VCa by 8-fold and could readily explain the rapid rates of MCa seen in the above analyses. Thus the acute control of Cpi Ca during dialysis may be wholly or in part a passive process of diffusion equilibrium rather than a hormonal response. Further studies are required to clarify this.

Generalized Solution of the Ca Model

As developed above, kinetic estimation of Ca mass balance over the course of a dialysis would require values for VCa, DCa, CdiCa, CpoCa and MCa. A value for VCa can be readily estimated from Vu and, with an appropriate in vivo data base we should be able to reliably calculate D Ca from values for in vivo KoAca, Qb, Qd and Qf. Since the threat to CpiCa2+ during dialysis is the driving force for Ca flux, DCa*(CdiCa - CpiCa2+), it might be anticipated that MCa is a well-defined function of this driving force, i.e., that it is dependent on the combined driving force variables. The relationship of MCa to DCa*(CdiCa - CpiCa2+) was examined using the data developed from the literature. The sequential steps in model formation can be viewed in figures 12 and 13. Figure 12A shows all the serial MCa values calculated from each data set plotted as a function of the inlet concentration gradient and D Ca for each data set indicated for each group. What is missing here is an axis to express the effect of DCa. From the behavior of MCa described in figure 8 MCa would be expected to be a linear function of (Cdi Ca - Cpi Ca) with the slope related directly to DCa and a zero intercept when (CdiCa -CpiCa) = 0 (except for convective flux). Figure 12B shows the linear regression for each data set with the regression coefficients with the curves forced through 0.

The slopes were then regressed on DCa and the modeling equation shown in figure 12 derived and shown to be:

Moa = -0.01 + (-0.0008*DCa -0.001)*(CdiCa - CpiCa) (13)

What is this 'buffer pool' and what controls it?

What is this 'buffer pool' and what controls it?

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Fig. 9. The importance of the Ca buffer pool in sequestration of positive Ca balance with high Cdi Ca. The net change in the Ca content of extracellular fluid was virtually zero. More than 99% of the positive Ca balance was sequestered in the Ca buffer pool.

PTH Bone Cardiovascular system

Ca buffer pool

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Fig. 10. MCa appears to be a linear function of the driving force for Ca flux across the dialyzer.

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Fig. 11. The miscible pool of Ca is very likely the 'Ca buffer pool'.

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i Hou data O Hypercalc Ca • XY (scatter) 3 ▲ CAPD

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Generalized modeling equation

Fig. 12. A The five data sets used to develop the model are shown where serial calculated MCa is plotted as a function of the inlet Ca gradient and DCa for each data set is shown. B Linear regression for each data set forced through zero. These slopes were regressed on DCa and the final generalized modeling equation derived as a function of DCa and CdiCa - CpiCa is shown above.

Figure 13 graphically depicts the generalized modeling equation solved over a range of -1.00 < (CdiCa -CpiCa) < 1.00 and DCa ranging from 6 to 200 ml/min. Note that high rates of sequestration or mobilization of Ca are predicted over this range with highly efficient di-alyzers.

Modeled Estimates of the Distribution of Ca Balance during Dialysis of FMC Patients with Currently Prescribed CdiCa2+

The frequency distribution of Cp CaT observed in the FMC patient population (—65,000 patients) is shown in figure 14A along with distribution in normal subjects and

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Mobilization of Ca Sequestration of Ca

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Or is MCa mediated by miscible buffer pool??

CdiCa - CpiCa, mEq/l

Or is MCa mediated by miscible buffer pool??

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Fig. 13. The rate of mobilization (M) of Ca from the buffer pool modeled as a function of dialyzer inlet Ca gradient and Ca dialysance and expressed as mg/h. Note that substantial mobilization rates are predicted with relatively small gradients. How are mobilization and sequestration internally mediated in the body and how do they relate to vascular calcification?

the typically prescribed CdiCa 2.50 mEq/l. These data are quite striking, and simple inspection of the plot suggests that we must be routinely diffusing a substantial quantity of Ca into nearly all of the FMC patients using a standard dialysate CdiCa 2.50 mEq/l. Net Ca flux was calculated from the Ca distribution assuming DCa 150 ml/min and t = 3.5 h with results shown in figure 14B. These calculations indicate that 80% of the patients are in positive Ca balance up to 400 mg during dialysis. There needs to be further evaluation of the appropriateness of nearly universal positive Ca balance during dialysis based on reliable estimates of interdialytic Ca balance as developed below.

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