Transcript Volume Shifts in Hemodialysis

Volume Shifts in
Hemodialysis
Matlab Introductory Exercise
Hypothesis:
Extravascular water in limbs (arm & leg) and trunk
are measured during dialysis – while water is being
removed by ultrafiltration at prescribed rate, ufr.
 Trunk extravascular fluid is in volume equilibrium
with blood; exchange with limbs and blood is
worse. Effect rises with rising ufr.
 Rapid water removal by ultrafiltration from blood
decreases trunk volume more than limb volume.
Refilling of trunk volume occurs only after dialysis
Difference of end-dialysis and re-equilibrated trunk
volume measures disequilibrium.
The
Model
VA
VT
ufr
VL
dVA
 kTAVT  k AVA
dt
dVL
 kTLVT  kLVL
dt
dVT
   kTAVT  k AVA    kTLVT  kLVL   ufr
dt
Refined Model
dVA
 k A  AVT  VA 
dt
dVL
 k L  LVT  VL 
dt
t
VT  VT (0)   ufr  VA  VT
0
Proposed Initial Conditions
VT(0) = 35 L
VL(0) = 10 L
 VA(0) = 5 L
 ufr = 1 L/hr
 TDIALYSIS= 3 hr
The question:
How do values of k
affect disequilibration?
Simulink Model
Simulink Results (Scope Outputs) k’s=0.5 hr-1
Leg Volume
Trunk Volume
Arm Volume
Disequilibration, Liters
Notes
 Results are show for one set of k’s, kA=kL=0.5.
’s are determined as ratios of initial volumes.
 Note that the leg and arm volume integrators
must be set for initial values of 10 and 5 liters.
The initial trunk volume is 35 liters.
 Disequilibration is the difference between VT
and 0.7total volume at any time. End-dialysis
disequilibration for this example has risen to
about 0.37 Liter.
Addendum
 To show results more graphically, the model can
be augmented to stop ultrafiltration at t =3 hr and
then to run longer without further change in total
volume. This is done by introducing positive
ultrafiltration after 3 hr, using a transport (time)
delay element. The positive ultrafiltration then
cancels the negative filtration and the volumes
balance among themselves without further
change in total volume.
Modified flowsheet. Note transport delay in red.
Addendum results:
Disequilibrium rises during dialysis and then falls in the post-dialysis period
Volume ‘trading’ occurs between arms and legs and trunk after dialysis.