SME
Biotransport
Mass transfer
Use this for “Blood at 300 mL/min enters a dialyzer with 100 mg/dL urea and leaves with 40 mg/dL. What is the clearance, and Kt/V after 240 min for 40 L of body water?”
Diagram
K
=
Qb(Cᵢₙ − Cₒᵤₜ)
Cᵢₙ
=
300
×
100 − 40
100
=
180
mL/min:
60%
of
the
blood
flow
is
cleared
of
urea.
Kt/V
=
180
×
240
40 × 1000
=
1.08;
URR
=
1
−
e
−Kt/V
=
66%.
This is an example. Type your own values to start a new problem.
K (mL/min)
=
Qb (mL/min)
×
(
−
)
Cᵢₙ
Kt/V
=
K (mL/min)
×
t (min)
V (L)
URR
Urea reduction ratio
calculated · %
Formulas
K
=
Qb
×
Cᵢₙ − Cₒᵤₜ
Cᵢₙ
180
=
300
×
100 − 40
100
Kt
/
V
=
K
×
t
1,000 ×
V
1.08
=
180
×
240
1,000 × 40
URR
=
100
×
(1
−
1
e
Kt
/
V
)
66
=
100
×
(1
−
1
e
1.08
)
Assumptions
•
Clearance K is the blood flow freed of urea completely: Qb times the share of urea the dialyzer takes out.
•
The body’s urea sits in one well-mixed pool, its total body water V, so the share left falls exponentially with Kt/V.
•
Urea the body makes during the session is ignored.
Step-by-step
WE KNOW
Qb = 300 mL/min, Cᵢₙ = 100 mg/dL, Cₒᵤₜ = 40 mg/dL, t = 240 min, V = 40 L
FIND
clearance (K), dose of dialysis (Kt/V), urea reduction ratio (URR)
Step 1 · Find clearance (K)
Use K = Qb × (Cᵢₙ − Cₒᵤₜ) ÷ Cᵢₙ
The
blood
loses
the
share
Cᵢₙ − Cₒᵤₜ
Cᵢₙ
of
its
urea;
that
share
of
the
blood
flow
is
cleared.
K
=
300
×
100 − 40
100
K
=
300
×
60
100
K
=
18,000
100
K
=
180
mL/min
Step 2 · Find dose of dialysis (Kt/V)
Use Kt/V = K × t ÷ (1,000 × V)
The
blood
cleared
in
the
session,
K
×
t
in
mL,
over
the
body
water
(1
L
is
1000
mL).
Kt
/
V
=
180
×
240
1,000 × 40
Kt
/
V
=
180
×
240
40,000
Kt
/
V
=
43,200
40,000
Kt
/
V
=
1.08
Step 3 · Find urea reduction ratio (URR)
Use URR = 100 × (1 − 1 ÷ eKt/V)
In
one
well-mixed
pool
the
urea
left
is
e
−
Kt
/
V
of
the
start;
the
rest
is
the
share
removed.
URR
=
100
×
(1
−
1
e
1.08
)
URR
=
100
×
(1
−
1
2.945
)
URR = 100 × (1 − 0.3396)
URR = 100 × 0.6604
URR = 66%
Check
Put the numbers back in. Both sides should match.
180
=
300
×
100 − 40
100
✓
1.08
=
180
×
240
1,000 × 40
✓
66
=
100
×
(1
−
1
e
1.08
)
✓
Topic check
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