*3.1.1 Kt/V estimation from UV absorbance*

Assuming that urea is distributed in a single pool volume in the body, that urea generation rate and ultrafiltration are negligible during the session and that the ratio K/V remains constant over the dialysis, the following equation holds [57, 58] (Eq. (7)):

$$\text{Kt/V} = -\ln \frac{\mathbf{C\_t}}{\mathbf{C\_0}} \tag{7}$$

where Ct is the post and C0 is the pre-dialysis urea blood concentration, respectively.

#### **Figure 3.**

*The schematic set up during the studies. All spent dialysate was also collected in a collection tank to be able to calculate total removal of solutes. [Reprinted from [6]].*

From the differential equation, describing urea mass balance during a dialysis session, it can be determined that the average value of the urea clearance (K) in mL/min divided with urea distribution volume in the body (V) in mL (K/V) during a session may be approximated as the slope from the natural logarithm (ln) plot of the urea blood concentration in the blood versus time, S*B*. Similarly, but instead of blood urea concentrations, the concentrations of urea in dialysate (S*D*) can be used (Eq. (8)). Hence:

$$\mathbf{Kt}/\mathbf{V} \approx -\mathbf{S}\_{\mathbf{B}}\mathbf{T} \approx -\mathbf{S}\_{\mathbf{D}}\mathbf{T} \tag{8}$$

where T is the dialysis session length in minutes. According to Eq. (8), we obtain Eq. (9):

$$\frac{\mathbf{C\_t}}{\mathbf{C\_0}} \approx \exp(-\mathbf{Kt}/\mathbf{V}) \approx \exp(\mathbf{S\_B T}) \approx \exp(\mathbf{S\_D T}) \approx \exp(\mathbf{S\_t T})\tag{9}$$

If the slopes are used instead of the blood urea concentrations. This approximation is equivalent to the equation when two measuring points are used, and the previously mentioned assumptions are fulfilled. This equation would hold strictly if urea obeys fixed volume and single pool kinetics and no urea is generated during the session [59]. In order to calculate Kt/V from the online UV absorbance, the slope of blood or dialysate urea concentration was replaced by the ln slope of the UV absorbance, Sa, see Eq. (9) versus time (Kt/V ≈ � Sa\*t, **Figure 4**), [7].

Using the UV absorbance slope values (Sa), **Figure 4**, according to Eq. (9), the Daugirdas-based mono compartmental (single pool, sp) Equation (Eq. (10)) [60]:

$$\mathrm{sp}(\mathrm{Kt/V}) = -\ln\left(\frac{\mathrm{C\_t}}{\mathrm{C\_0}} - 0.008\frac{\mathrm{T}}{60}\right) + \left(4 - 3.5\frac{\mathrm{C\_t}}{\mathrm{C\_0}}\right)\frac{\mathrm{UF}}{\mathrm{BW}}\tag{10}$$

**Figure 4.**

*Online absorbance curve during a single 4 hours HD treatment, where UV absorbance is plotted against time. The corresponding natural logarithmic (ln) fitting line is also shown and used for Kt/V calculation [Reprinted from [7]].*

can be written as [7] Eq. (11):

$$\mathrm{sp}(\mathrm{Kt/Va}) = -\ln\left(\exp(\mathrm{S\_4T}) - 0.008\frac{\mathrm{T}}{60}\right) + (4 - 3.5\exp(\mathrm{S\_4T})) \frac{\mathrm{UF}}{\mathrm{BW}} \tag{11}$$

where UF and BW are the ultrafiltration volume in liters (L) and the patient's dry body weight in kg. The equilibrated Kt/V from UV absorbance, eKt/Va, according to the rate adjustment method [60], is predicted from the rate of dialysis (K/V) and the sp(Kt/Va) as Eq. (12):

$$\mathbf{e}\mathbf{Kt}/\mathbf{V}\mathbf{a} = \mathbf{s}\mathbf{p}(\mathbf{Kt}/\mathbf{V}\mathbf{a}) - \frac{\mathbf{0.6}}{\left(\frac{\mathbf{T}}{60}\right)}\mathbf{s}\mathbf{p}(\mathbf{Kt}/\mathbf{V}\mathbf{a}) + \mathbf{0.03} \tag{12}$$

The rate adjustment method predicts that the urea rebound is related to the rate of dialysis or dialysis efficiency [61].

#### *3.1.2 Estimation of urea removal using UV absorbance*

One way to estimate total removed urea (TRU), assuming that the dialysate flow, Qd(t), is constant and the total UF is known, is to use the following equation (Eq. (13)):

$$\mathbf{TRU(mmolol)} = \overline{\mathbf{Urea}}(\mathbf{Qd} \bullet \mathbf{T} + \mathbf{UF}) \tag{13}$$

where Urea in mmol/L is the mean urea concentration in spent dialysate of a particular HD session [62]. For the TRU calculations, Urea = Dtotal can be utilized as reference, where Dtotal is the urea concentration in the collection tank (all spent dialysate from one session), after the end of dialysis. Qd is the rate of the dialysate flow in L/min, T is the dialysis session length in minutes and UF is the total ultrafiltrated volume in L during the session. Under the condition that a good correlation exists between UV absorbance and concentration of urea, it is possible to utilize this relationship. Therefore, in a similar way, TRU may be calculated from the online UV absorbance curve (**Figure 4**) as Eq. (14) [63]:

$$\text{TRUa}(\text{mmol}) = (\mathbf{a} \cdot \overline{\mathbf{A}} + \mathfrak{P}) \cdot (\mathbf{Qd} \bullet \mathbf{T} + \mathbf{U} \mathbf{F}) \tag{14}$$

where A is the mean of all UV absorbance (A) values from the start to the end of the dialysis. The regression line between the UV absorbance and concentration of urea in spent dialysate from online measurement gives the slope (α) and the intercept (β) inserted in Eq. (14) when determining TRUa from a general model. TRU from the total dialysate collection (TDC), reference, was calculated as Dtotal (mmol/L) multiplied with collected weight (kg), assuming that 1 kg = 1 L of the dialysate [63].

#### *3.1.3 Estimation of nutrition parameters from UV absorbance*

High concentration of urea in blood is not necessarily related to a poor dialysis outcome if urea removal is sufficient [64], but also protein-energy malnutrition is frequently present in HD patients. Several studies have suggested that malnutrition is an important risk factor for morbidity and mortality in HD patients [65]. In order to optimize the diet of patients with renal diseases, dietary protein intake has to be controlled. Protein nitrogen appearance (PNA), formerly protein catabolic rate (PCR) [66], is easily obtainable from UKM and in patients who are not markedly catabolic or anabolic, the normalized PNA (nPNA) correlates closely with dietary protein intake [67, 68]. These parameters can be calculated from TRU. The PCR calculation, from TDC and UV absorbance, was based on a theory by Garred et al. (1995), where a calculation of urea removal is expressed as a fraction of the week's urea generation. The fraction varies with the day of the week and was found to be essentially constant among patients on a given day [69]. The amount of urea could, therefore, be approximated by measuring urea concentration from only one of the three treatments and PCR could be calculated as Eq. (15) [63]:

$$\text{nPCRw} = \text{Factor}\_{\text{1,2 or 3}} \left( \frac{\text{TRU}\_{\text{1,2 or 3}}}{\text{BW}} \right) + \text{0.17} \tag{15}$$

where TRU 1, 2 or 3 (expressed in grams of urea nitrogen) is the TRU from the first (1), midweek (2) or last dialysis in week (3) and Factor one, two or three is the fractional factor for the corresponding days; factor one = 2.45; two = 2.89 and three = 3.10 [69]. Obligatory loss of dietary protein in stools and via skin shedding represents the constant term 0.17 (g protein/kg body weight/day). BW was used for normalization of PCR (nPCRw). Observe that these fractional factors relay to a treatment schedule of three times a week. More frequent dialysis treatments are common today whereas the factors are not appropriate.
