Table 3 Definitions and formulas for efficiencies, intensities and efficacies

Efficiency

Target (prescribed)

K _T

ml/kg/h

Assuming that the patient’s clinical condition does not change, K_T 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

\( {K}_{Pr}=\frac{{\displaystyle {\int}_0^{t_1}}{K}_{Cr}dt + \left({t}_{tot}-{t}_1\right) \cdot {K}_{Tm}^{\hbox{'}}}{t_{tot}} \)

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

\( {K}_{Aed}=\frac{1}{t_1}\cdot {\displaystyle \underset{0}{\overset{t_1}{\int }}}{K}_{Cd}dt \)

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

\( {E}_{Aed}=\frac{I_{Ced}}{V}=\frac{K_{Ced}\cdot {t}_1}{V}=\frac{1}{V}\cdot {\int}_0^{t_1}{K}_{Cd}dt \)