# Volume Shifts in Hemodialysis Matlab Introductory Exercise.

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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

Refined Model

Proposed Initial Conditions  V T (0) = 35 L  V L (0) = 10 L  V A (0) = 5 L  ufr = 1 L/hr  T DIALYSIS = 3 hr The question: How do values of k affect disequilibration?

Simulink Results (Scope Outputs) k’s=0.5 hr -1 Leg Volume Arm Volume Trunk VolumeDisequilibration, Liters

Notes  Results are show for one set of k’s, k A =k L =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 V T 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.