System for analyzing vascular refill during short-pulse ultrafiltration in hemodialysis

1. A method, comprising:

receiving, by a processing system, measurements of a blood-related parameter corresponding to a patient undergoing hemodialysis treatment;

estimating, by the processing system, values of hemodialysis treatment-related parameters by applying a vascular refill model based on the received measurements of the blood-related parameter, wherein the hemodialysis treatment-related parameters are indicative of an effect of vascular refill on the patient caused by the hemodialysis treatment and include a filtration coefficient (L p ) and a hydrostatic capillary pressure (P c );

determining, by the processing system, based on the estimated values of the hemodialysis treatment-related parameters, a hemodialysis treatment-related operation; and

facilitating, by the processing system, performance of the hemodialysis treatment-related operation;

wherein the vascular refill model is a two-compartment model based on a first compartment corresponding to blood plasma in the patient's body, a second compartment based on interstitial fluid in the patient's body, and a semi-permeable membrane separating the first compartment and the second compartment;

wherein the dynamics of the two-compartment model are described by the following system of equations:

{

dV

p

dt

=

J

v

+

κ

-

J

UF

d

⁢

⁢

c

p

dt

=

J

s

-

c

p

⁡

(

J

v

+

κ

-

J

UF

)

V

p

,

dV

i

dt

=

-

J

v

-

κ

,

d

⁢

⁢

c

i

dt

=

-

J

s

+

c

i

⁡

(

J

v

+

κ

)

V

i

,

⁢

⁢

where

⁢

⁢

J

v

=

L

p

⁡

(

σ

⁡

(

(

a

p

1

⁢

c

p

+

a

p

2

⁢

c

p

2

)

-

(

a

i

1

⁢

c

i

+

a

i

2

⁢

c

i

2

)

)

-

(

P

c

-

P

i

)

)

,

⁢

J

s

=

{

J

v

⁡

(

1

-

σ

)

⁢

(

c

i

-

c

p

-

c

i

e

x

-

1

)

+

α

⁢

⁢

κ

if

⁢

⁢

J

v

>

0

,

α

⁢

⁢

κ

if

⁢

⁢

J

v

=

0

,

J

v

⁡

(

1

-

σ

)

⁢

(

c

p

-

c

p

-

c

i

e

x

-

1

)

+

ακ

if

⁢

⁢

J

v

<

0

,

⁢

⁢

and

⁢

⁢

x

=

J

v

⁡

(

1

-

σ

)

PS

,

wherein V p corresponds to the first compartment, J v corresponds to the amount of fluid crossing the membrane at a certain time, κ corresponds to a constant lymph flow from interstitum to plasma, J UF corresponds to ultrafiltration rate, J s corresponds to net protein flux, c p corresponds to a protein concentration in plasma, c i corresponds to a protein concentration in interstitum, V i corresponds to the second compartment, σ corresponds to the osmotic reflection coefficient, P i corresponds to hydrostatic interstitial pressure, α corresponds to a constant protein concentration of the constant lymph flow, x corresponds to a Peclet number describing convective flux relative to diffusive capacity of the membrane, and PS corresponds to a permeability-surface area product.

2. The method according to claim 1 , wherein the hemodialysis treatment-related operation comprises adjustment of a rate of ultrafiltration for the patient undergoing hemodialysis treatment.

3. The method according to claim 1 , wherein the hemodialysis treatment-related operation comprises stoppage of the hemodialysis treatment for the patient.

4. The method according to claim 1 , wherein the hemodialysis treatment-related operation comprises generating an alert.

5. The method according to claim 1 , wherein the hemodialysis treatment-related operation comprises providing a notification indicating the estimated values of the hemodialysis treatment-related parameters.

6. The method according to claim 5 , wherein the notification is displayed on a screen.

7. The method according to claim 1 , wherein the measurements of the blood-related parameter are hematocrit measurements or relative blood volume measurements.

8. The method according to claim 1 , wherein the hemodialysis treatment-related parameters further include one or more of the group consisting of:

hydrostatic interstitial pressure (P i );

a systemic capillary reflection coefficient (σ);

constant protein concentration (α); and

constant lymph flow rate (κ).

9. The method according to claim 1 , wherein the vascular refill model defines short-term dynamics of vascular refill with respect to a time period of about an hour.

10. The method according to claim 1 , further comprising:

receiving, by the processing system, an ultrafiltration rate set by a dialysis machine providing the hemodialysis treatment to the patient;

wherein estimating the values of the hemodialysis treatment-related parameters by applying the vascular refill model is further based on the received ultrafiltration rate.

11. The method according to claim 1 , wherein estimating the values of the hemodialysis treatment-related parameters by applying the vascular refill model is further based on previously estimated values of the hemodialysis treatment-related parameters corresponding to the patient obtained from a database.

12. The method according to claim 1 , wherein estimating the values of the hemodialysis treatment-related parameters by applying the vascular refill model is further based on initial default values for the hemodialysis treatment-related parameters.

13. The method according to claim 1 , wherein applying the vascular refill model includes iteratively solving an inverse problem to compute the estimated values of the hemodialysis treatment-related parameters.

14. The method according to claim 1 , further comprising:

determining a quality level of the received measurements; and

selecting one or more types of hemodialysis treatment-related parameters to estimate based on the determined quality level.

15. A non-transitory processor-readable medium having processor-executable instructions stored thereon, the processor-executable instructions, when executed by a processor, being configured to facilitate performance of the following steps:

receiving, by a processing system, measurements of a blood-related parameter corresponding to a patient undergoing hemodialysis treatment;

estimating, by the processing system, values of hemodialysis treatment-related parameters by applying a vascular refill model based on the received measurements of the blood-related parameter, wherein the hemodialysis treatment-related parameters are indicative of an effect of vascular refill on the patient caused by the hemodialysis treatment and include a filtration coefficient (L p ) and a hydrostatic capillary pressure (P c );

determining, by the processing system, based on the estimated values of the hemodialysis treatment-related parameters, a hemodialysis treatment-related operation; and

facilitating, by the processing system, performance of the hemodialysis treatment-related operation;

wherein the vascular refill model is a two-compartment model based on a first compartment corresponding to blood plasma in the patient's body, a second compartment based on interstitial fluid in the patient's body, and a semi-permeable membrane separating the first compartment and the second compartment;

wherein the dynamics of the two-compartment model are described by the following system of equations:

{

dV

p

dt

=

J

v

+

κ

-

J

UF

d

⁢

⁢

c

p

dt

=

J

s

-

c

p

⁡

(

J

v

+

κ

-

J

UF

)

V

p

,

dV

i

dt

=

-

J

v

-

κ

,

d

⁢

⁢

c

i

dt

=

-

J

s

+

c

i

⁡

(

J

v

+

κ

)

V

i

,

⁢

⁢

where

⁢

⁢

J

v

=

L

p

⁡

(

σ

⁡

(

(

a

p

1

⁢

c

p

+

a

p

2

⁢

c

p

2

)

-

(

a

i

1

⁢

c

i

+

a

i

2

⁢

c

i

2

)

)

-

(

P

c

-

P

i

)

)

,

⁢

J

s

=

{

J

v

⁡

(

1

-

σ

)

⁢

(

c

i

-

c

p

-

c

i

e

x

-

1

)

+

α

⁢

⁢

κ

if

⁢

⁢

J

v

>

0

,

α

⁢

⁢

κ

if

⁢

⁢

J

v

=

0

,

J

v

⁡

(

1

-

σ

)

⁢

(

c

p

-

c

p

-

c

i

e

x

-

1

)

+

ακ

if

⁢

⁢

J

v

<

0

,

⁢

⁢

and

⁢

⁢

x

=

J

v

⁡

(

1

-

σ

)

PS

,

wherein V p corresponds to the first compartment, J v corresponds to the amount of fluid crossing the membrane at a certain time, κ corresponds to a constant lymph flow from interstitum to plasma, J UF corresponds to ultrafiltration rate, J s corresponds to net protein flux, c p corresponds to a protein concentration in plasma, c i corresponds to a protein concentration in interstitum, V i corresponds to the second compartment, σ corresponds to the osmotic reflection coefficient, P i corresponds to hydrostatic interstitial pressure, α corresponds to a constant protein concentration of the constant lymph flow, x corresponds to a Peclet number describing convective flux relative to diffusive capacity of the membrane, and PS corresponds to a permeability-surface area product.

16. The non-transitory processor-readable medium according to claim 15 , wherein the hemodialysis treatment-related parameters further include one or more of the group consisting of:

hydrostatic interstitial pressure (P i );

a systemic capillary reflection coefficient (σ);

constant protein concentration (α); and

constant lymph flow rate (κ).

17. A system, comprising:

a monitoring device configured to obtain measurements of a blood-related parameter corresponding to a patient undergoing hemodialysis treatment; and

a processing system configured to:

receive the measurements of the blood-related parameter corresponding to the patient undergoing hemodialysis treatment from the monitoring device;

estimate values of hemodialysis treatment-related parameters by applying a vascular refill model based on the received measurements of the blood-related parameter, wherein the hemodialysis treatment-related parameters are indicative of an effect of vascular refill on the patient caused by the hemodialysis treatment and include a filtration coefficient (L p ) and a hydrostatic capillary pressure (P c );

determine, based on the estimated values of the hemodialysis treatment-related parameters, a hemodialysis treatment-related operation; and

facilitate performance of the hemodialysis treatment-related operation;

wherein the vascular refill model is a two-compartment model based on a first compartment corresponding to blood plasma in the patient's body, a second compartment based on interstitial fluid in the patient's body, and a semi-permeable membrane separating the first compartment and the second compartment;

wherein the dynamics of the two-compartment model are described by the following system of equations:

{

dV

p

dt

=

J

v

+

κ

-

J

UF

d

⁢

⁢

c

p

dt

=

J

s

-

c

p

⁡

(

J

v

+

κ

-

J

UF

)

V

p

,

dV

i

dt

=

-

J

v

-

κ

,

d

⁢

⁢

c

i

dt

=

-

J

s

+

c

i

⁡

(

J

v

+

κ

)

V

i

,

⁢

⁢

where

⁢

⁢

J

v

=

L

p

⁡

(

σ

⁡

(

(

a

p

1

⁢

c

p

+

a

p

2

⁢

c

p

2

)

-

(

a

i

1

⁢

c

i

+

a

i

2

⁢

c

i

2

)

)

-

(

P

c

-

P

i

)

)

,

⁢

J

s

=

{

J

v

⁡

(

1

-

σ

)

⁢

(

c

i

-

c

p

-

c

i

e

x

-

1

)

+

α

⁢

⁢

κ

if

⁢

⁢

J

v

>

0

,

α

⁢

⁢

κ

if

⁢

⁢

J

v

=

0

,

J

v

⁡

(

1

-

σ

)

⁢

(

c

p

-

c

p

-

c

i

e

x

-

1

)

+

ακ

if

⁢

⁢

J

v

<

0

,

⁢

⁢

and

⁢

⁢

x

=

J

v

⁡

(

1

-

σ

)

PS

,

wherein V p corresponds to the first compartment, J v corresponds to the amount of fluid crossing the membrane at a certain time, K corresponds to a constant lymph flow from interstitum to plasma, J UF corresponds to ultrafiltration rate, J s corresponds to net protein flux, c p corresponds to a protein concentration in plasma, c i corresponds to a protein concentration in interstitum, V i corresponds to the second compartment, σ corresponds to the osmotic reflection coefficient, P i corresponds to hydrostatic interstitial pressure, α corresponds to a constant protein concentration of the constant lymph flow, x corresponds to a Peclet number describing convective flux relative to diffusive capacity of the membrane, and PS corresponds to a permeability-surface area product.

18. The system according to claim 17 , further comprising:

a data storage configured to communicate with the processing system and to receive and store the estimated values of the hemodialysis treatment-related parameters.

19. The system according to claim 17 , wherein the hemodialysis treatment-related parameters further include one or more of the group consisting of:

hydrostatic interstitial pressure (P i );

a systemic capillary reflection coefficient (σ);

constant protein concentration (α); and

constant lymph flow rate (κ).