# Table 3 Definitions and formulas for efficiencies, intensities and efficacies

Measurement Name Symbol Unit of measure Formula
Efficiency Target (prescribed) K T ml/kg/h Assuming that the patient’s clinical condition does not change, KT is a constant value throughout the treatment
Efficiency Target machine K Tm ml/kg/h Considering the downtime and the reduction in clearance properties of the membranes during treatment, K Tm is usually set at a greater value than K T
Efficiency Current K Cr ml/kg/h $${K}_{Cr}=\frac{\left({Q}_R^{PRE}+{Q}_D+{Q}_{UF}^{NET}+{Q}_R^{POST}\right)}{B.W.}\cdot \frac{Q_B\ }{Q_B + {Q}_R^{PRE}}$$
Efficiency Average K Am ml/kg/h $${K}_{Am}=\frac{1}{t_1}\cdot {\int}_0^{t_1} KCrdt$$
Efficiency Projected K Pr ml/kg/h $${K}_{Pr}=\frac{{\int}_0^{t_1}}{K}_{Cr}dt + \left({t}_{tot}-{t}_1\right) \cdot {K}_{Tm}^{\hbox{'}}}{t_{tot}}$$
where K Tm ' is the new target machine efficiency set
Efficiency Current effective delivered K Cd ml/kg/h $${K}_{Cd}=\left({Q}_B\cdot \frac{C_{Bi}-{C}_{Bo}}{C_{Bi}}+{Q}_{UF}\cdot \frac{C_{Bo}}{C_{Bi}}\right)\cdot \frac{1}{B.W.}$$
Efficiency Average effective delivered K Aed ml/kg/h $${K}_{Aed}=\frac{1}{t_1}\cdot \underset{0}{\overset{t_1}{\int }}}{K}_{Cd}dt$$
Intensity Target (prescribed) I T ml/kg Blood volume that should be cleared applying K T during the total time of treatment
Intensity Target machine I Tm ml/kg Blood volume that should be cleared applying K Tm during the total time of treatment
Intensity Current I Cr ml/kg I Cr  = K Cr t tot
Intensity Average I Am ml/kg $${I}_{Am}\kern0.5em =\kern0.5em {K}_{Cm}\cdot {t}_1\kern0.5em =\kern0.5em {\int}_0^{t_1}{K}_{Cr}dt$$
Intensity Projected I Pr ml/kg $${I}_{Pr}={K}_{Pr}\cdot {t}_{tot}=\kern0.5em {\int}_0^{t_1}{K}_{Cr}dt + \left({t}_{tot}-{t}_1\right) \cdot {K}_{Tm}^{\hbox{'}}$$
Intensity Current effective delivered I Cd ml/kg I Cd  = K Cd t 1
Intensity Average effective delivered I Aed ml/kg $${I}_{Aed}={K}_{Ced}\cdot {t}_1\kern0.5em =\kern0.5em {\int}_0^{t_1}{K}_{Cd}dt$$
Efficacy Target (prescribed) E T Dimensionless Solute removal obtained applying I T to the volume of distribution of the solute
Efficacy Target machine E Tm Dimensionless Solute removal obtained applying I Tm to the volume of distribution of the solute
Efficacy Current E Cr Dimensionless $${E}_{Cr}=\frac{I_{Cr}}{V}=\frac{K_{Cr} \cdot {t}_{tot}}{V}$$
Efficacy Average E Am Dimensionless $${E}_{Am}=\frac{I_{Cm}}{V}=\frac{1}{V}{\int}_0^{t_1}{K}_{Cr}dt$$
Efficacy Projected E Pr Dimensionless $${E}_{Pr}=\frac{I_{Pr}}{V}=\frac{1}{V}\cdot \left[{\int}_0^{t_1}{K}_{Cr}dt + \left({t}_{tot}-{t}_1\right) \cdot {K}_{Tm}^{\hbox{'}}\right]$$
Efficacy Current effective delivered E Cd Dimensionless $${E}_{Cd}=\frac{I_{Cd}}{V}=\frac{K_{Cd}\cdot {t}_1}{V}=\frac{1}{V}\cdot \left({Q}_B\cdot \frac{C_{Bi}-{C}_{Bo}}{C_{Bi}}+{Q}_{UF}\cdot \frac{C_{Bo}}{C_{Bi}}\right)\cdot \frac{1}{B.W.} \cdot {t}_1$$
Efficacy Average effective delivered E Aed Dimensionless $${E}_{Aed}=\frac{I_{Ced}}{V}=\frac{K_{Ced}\cdot {t}_1}{V}=\frac{1}{V}\cdot {\int}_0^{t_1}{K}_{Cd}dt$$
1. B.W. ideal body weight, C Bi pre-filter blood concentration of the reference solute, C BO post-filter blood concentration of the reference solute, dt delta time, Q B blood flow rate, Q D dialysate flow rate, Q R POST post-replacement flow rate, Q R PRE pre-replacement flow rate, Q UF NET net ultrafiltration flow rate, Q UF ultrafiltration flow rate, t tot total time of treatment, V volume of distribution of the reference solute 