CAPILLARY DYNAMICS, TISSUE FLUID, AND TISSUE PROTEIN
This portion of the model calculates the movement of fluid and protein through the
capillary membrane. It also calculates the volumes of fluid in the free fluid space
of the interstitium and in the gel fluid space. It calculates the pressures in both
of these fluids as well as the so-called solid tissue pressure caused by the compression
of solid elements against other portions of the interstitium. In addition, the quantities
of proteins and their concentrations in both the free fluid and the gel fluid are calculated.
And, finally, the flow of both fluid and proteins in the lymph system are computed, as well
as the overall body protein balance.
Encapsulation grouping component containing all the components in the Capillary Dynamics Model. The inputs and
outputs of the Capillary Dynamics Model must be passed by this component.
Containment grouping component for "capillary_pressure" and
"rate_of_fluid_out_of_capillaries".
CP1 and CP2:
The capillary pressure (PC) is equal to the resistance to blood flow in the
small veins (RVS) times the blood flow in the small veins (BFN), times a constant
to represent the additional normal flow through the muscles and kidneys, plus
the pressure in the large vein circulation. The value of the capillary pressure (PC)
is assumed to be the same in all tissues of the body.
CP1 and CP2:
The capillary pressure (PC) is equal to the resistance to blood flow in the
small veins (RVS) times the blood flow in the small veins (BFN), times a constant
to represent the additional normal flow through the muscles and kidneys, plus
the pressure in the large vein circulation. The value of the capillary pressure (PC)
is assumed to be the same in all tissues of the body.
$\mathrm{PC}=\mathrm{RVS}\times 1.7\mathrm{BFN}+\mathrm{PVS}$
CP3:
The pressure gradient for filtration of fluid across the capillary membranes (PCGR)
is equal to the capillary pressure (PC), plus the colloid osmotic pressure of the
tissue gel (PTC), minus the plasma colloid osmotic pressure (PPC), minus the hydrostatic
pressure of the gel (PGH).
CP4:
The rate of filtration of fluid out of the capillaries of the systemic circulation (CFILTR)
is equal to the pressure gradient across the capillary membranes (PCGR) times the capillary
filtration coefficient (CFC).
CP5:
The total rate of movement of fluid out of all the systemic capillaries of the body (VTC) is
equal to the rate of filtration from the systemic capillaries (CFILTR) plus the rate of
leakage of whole plasma though leaky capillaries (VTCPL).
CP3:
The pressure gradient for filtration of fluid across the capillary membranes (PCGR)
is equal to the capillary pressure (PC), plus the colloid osmotic pressure of the
tissue gel (PTC), minus the plasma colloid osmotic pressure (PPC), minus the hydrostatic
pressure of the gel (PGH).
CP4:
The rate of filtration of fluid out of the capillaries of the systemic circulation (CFILTR)
is equal to the pressure gradient across the capillary membranes (PCGR) times the capillary
filtration coefficient (CFC).
CP5:
The total rate of movement of fluid out of all the systemic capillaries of the body (VTC) is
equal to the rate of filtration from the systemic capillaries (CFILTR) plus the rate of
leakage of whole plasma though leaky capillaries (VTCPL).
$\mathrm{VTC}=(\mathrm{PC}-\mathrm{PPC}-\mathrm{PGH}+\mathrm{PTC})\mathrm{CFC}+\mathrm{VTCPL}$
Containment grouping component for "plasma_volume", "plasma_protein_concentration",
"protein_destruction_and_formation", "plasma_leakage", "protein_influx_into_interstitium",
"total_plasma_protein" and "plasma_colloid_osmotic_pressure".
CP10:
The rate of change of plasma volume (VPD) is equal to the rate of inflow of
fluid into the plasma by way of the lymph (VTL) minus the rate of loss of
fluid from the systemic tissue capillaries (VTC), minus the rate of loss of
fluid from the pulmonary capillaries (DFP), and plus any rate of transfusion
of plasma into the circulation.
CP11:
The plasma volume (VP) is determined by integrating the rate of change of the
plasma volume (VPD) with respect to time.
CP10:
The rate of change of plasma volume (VPD) is equal to the rate of inflow of
fluid into the plasma by way of the lymph (VTL) minus the rate of loss of
fluid from the systemic tissue capillaries (VTC), minus the rate of loss of
fluid from the pulmonary capillaries (DFP), and plus any rate of transfusion
of plasma into the circulation.
CP11:
The plasma volume (VP) is determined by integrating the rate of change of the
plasma volume (VPD) with respect to time.
$\mathrm{VPD}=\mathrm{VTL}-\mathrm{VTC}-\mathrm{DFP}+\mathrm{TRPL}\frac{d \mathrm{VP}}{d \mathrm{time}}=\mathrm{VPD}$
CP35:
The concentration of protein in the plasma (CPP) is equal to the total quantity
of protein in the plasma (RPR) divided by the plasma volume (VP).
CP35:
The concentration of protein in the plasma (CPP) is equal to the total quantity
of protein in the plasma (RPR) divided by the plasma volume (VP).
$\mathrm{CPP}=\frac{\mathrm{PRP}}{\mathrm{VP}}$
CP37 and CP38:
A factor related to the rate of destruction of protein by the liver (CPPD) is
equal to plasma protein concentration CPP) minus a critical protein limiting value (CPR).
Block CP38 limits the rate of destruction of protein by the liver to a lower limit of zero.
CP39 and CP40:
Curve-fitting blocks to calculate the rate of destruction of protein by the
liver (LPPRDS) from the factor (CPPD) calculated in Block 37. The curve-fitting
constants are LPDE and LPK.
CP41:
Net rate of protein exchange between the liver and the plasma (DLP) is equal to the
rate of production of protein by the liver (LPPR) minus the rate of destruction of
protein by the liver (LPPRDS).
CP37 and CP38:
A factor related to the rate of destruction of protein by the liver (CPPD) is
equal to plasma protein concentration CPP) minus a critical protein limiting value (CPR).
Block CP38 limits the rate of destruction of protein by the liver to a lower limit of zero.
CP39 and CP40:
Curve-fitting blocks to calculate the rate of destruction of protein by the
liver (LPPRDS) from the factor (CPPD) calculated in Block 37. The curve-fitting
constants are LPDE and LPK.
CP41:
Net rate of protein exchange between the liver and the plasma (DLP) is equal to the
rate of production of protein by the liver (LPPR) minus the rate of destruction of
protein by the liver (LPPRDS).
$\mathrm{CPPD}=\begin{cases}0 & \text{if $\mathrm{CPP}-\mathrm{CPR}< 0$}\\ \mathrm{CPP}-\mathrm{CPR} & \text{otherwise}\end{cases}\mathrm{DLP}=\mathrm{LPPR}-\mathrm{CPPD}^{\mathrm{LPDE}}\mathrm{LPK}$
CP25 and CP26:
Calculation of a pressure gradient to cause whole plasma leakage through the
capillary membranes (PRCD), calculated by adding the capillary pressure (PC) and
subtracting a critical capillary pressure (PCR) below which no whole plasma will leak.
Block CP26 limits the rate of plasma leakage (PRCD) to a lower level of zero.
CP27 and CP28:
The rate of leakage of whole plasma through the capillary membrane (VTCPL) is equal
to the pressure gradient for leakage of plasma (PRCD) times a constant (CPK) and this
product raised to a power (PCE).
CP25 and CP26:
Calculation of a pressure gradient to cause whole plasma leakage through the
capillary membranes (PRCD), calculated by adding the capillary pressure (PC) and
subtracting a critical capillary pressure (PCR) below which no whole plasma will leak.
Block CP26 limits the rate of plasma leakage (PRCD) to a lower level of zero.
CP27 and CP28:
The rate of leakage of whole plasma through the capillary membrane (VTCPL) is equal
to the pressure gradient for leakage of plasma (PRCD) times a constant (CPK) and this
product raised to a power (PCE).
$\mathrm{PRCD}=\begin{cases}0 & \text{if $\mathrm{PC}-\mathrm{PCR}< 0$}\\ \mathrm{PC}-\mathrm{PCR} & \text{otherwise}\end{cases}\mathrm{VTCPL}=(\mathrm{PRCD}\mathrm{CPK})^{\mathrm{PCE}}$
CP29:
Rate of leakage of plasma protein in the leaking whole plasma into the interstitium
from the circulating plasma (TVCPL) equals the volume of plasma leaking (VTCPL)
times the concentration of protein in the plasma (CPP).
CP30 and CP31:
The rate of diffusion of protein through the capillary pores (PLPRDF) is equal
to the difference between plasma concentration of protein (CPP) minus the concentration
of protein in the interstitial free fluid (CPI) times a constant in Block CP31.
CP32:
Rate of influx of protein into the interstitium from the plasma in the capillaries (DPC)
is equal to the rate of protein leaking in the whole plasma (VTCPL) plus the rate of
diffusion of protein through the capillary pores (PLPRDF).
CP29:
Rate of leakage of plasma protein in the leaking whole plasma into the interstitium
from the circulating plasma (TVCPL) equals the volume of plasma leaking (VTCPL)
times the concentration of protein in the plasma (CPP).
CP30 and CP31:
The rate of diffusion of protein through the capillary pores (PLPRDF) is equal
to the difference between plasma concentration of protein (CPP) minus the concentration
of protein in the interstitial free fluid (CPI) times a constant in Block CP31.
CP32:
Rate of influx of protein into the interstitium from the plasma in the capillaries (DPC)
is equal to the rate of protein leaking in the whole plasma (VTCPL) plus the rate of
diffusion of protein through the capillary pores (PLPRDF).
$\mathrm{DPC}=\mathrm{VTCPL}\mathrm{CPP}-\mathrm{CPP}\times 0.00104$
CP33: The rate of change of the quantity of protein in the plasma (DPP)
is equal to the net rate of formation of protein by the liver (DLP), plus
the rate of return of protein to the circulation in the lymph (DPL), minus
the loss of protein from the circulation into the systemic interstitium (DPC),
minus the rate of loss of protein through the pulmonary capillary membranes (PPD).
CP34:
The total quantity of protein in the plasma (PRP) is determined by integrating
the rate of change of the protein in the plasma (DPP) with respect to time.
CP33: The rate of change of the quantity of protein in the plasma (DPP)
is equal to the net rate of formation of protein by the liver (DLP), plus
the rate of return of protein to the circulation in the lymph (DPL), minus
the loss of protein from the circulation into the systemic interstitium (DPC),
minus the rate of loss of protein through the pulmonary capillary membranes (PPD).
CP34:
The total quantity of protein in the plasma (PRP) is determined by integrating
the rate of change of the protein in the plasma (DPP) with respect to time.
$\mathrm{DPP}=\mathrm{DLP}+\mathrm{DPL}-\mathrm{DPC}-\mathrm{PPD}+\mathrm{TRPL}\times 72\frac{d \mathrm{PRP}}{d \mathrm{time}}=\mathrm{DPP}$
CP36:
The plasma colloid osmotic pressure (PPC) is calculated in this block from
the concentration of protein in the plasma (CPP).
CP36:
The plasma colloid osmotic pressure (PPC) is calculated in this block from
the concentration of protein in the plasma (CPP).
$\mathrm{PPC}=0.28\mathrm{CPP}+0.0019\mathrm{CPP}^{2}$
Containment grouping component for "total_systemic_fluid_volume",
"interstitial_fluid_volume", "total_interstitial_protein",
"interstitial_protein_concentration", "interstitial_colloid_osmotic_pressure"
and "lymph_protein_flow".
CP6:
The total fluid volume in the systemic circulation portion of the body (VTS)
is equal to the total extracellular fluid volume (VEC) minus plasma volume (VP)
and minus pulmonary extracellular fluid volume (VPF).
CP6:
The total fluid volume in the systemic circulation portion of the body (VTS)
is equal to the total extracellular fluid volume (VEC) minus plasma volume (VP)
and minus pulmonary extracellular fluid volume (VPF).
$\mathrm{VTS}=\mathrm{VEC}-\mathrm{VP}-\mathrm{VPF}$
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
$\frac{d \mathrm{VTS2}}{d \mathrm{time}}=((\mathrm{VTS}-12)\mathrm{TSSLML}-\mathrm{VTS2})\mathrm{TSSLTC}\mathrm{VTS1}=\mathrm{VTS}-\mathrm{VTS2}$
CP42:
The rate of change of protein in the systemic interstitium (DPI) is equal to
the rate of leakage from the plasma of protein through the systemic capillary
membranes (DPC) minus the rate of return of the protein from the systemic
interstitium by way of the lymphatics (DPL).
CP43:
The total tissue protein (TSP) is calculated by integrating the rate of
change of protein in the interstitium (DPI) with respect to time.
CP42:
The rate of change of protein in the systemic interstitium (DPI) is equal to
the rate of leakage from the plasma of protein through the systemic capillary
membranes (DPC) minus the rate of return of the protein from the systemic
interstitium by way of the lymphatics (DPL).
CP43:
The total tissue protein (TSP) is calculated by integrating the rate of
change of protein in the interstitium (DPI) with respect to time.
$\mathrm{DPI}=\mathrm{DPC}-\mathrm{DPL}\frac{d \mathrm{TSP}}{d \mathrm{time}}=\mathrm{DPI}$
CP44:
The concentration of protein in the interstitium (CPI) is equal to the total
quantity of protein in the interstitium (TSP) divided by the total volume of
fluid in the systemic interstitium (VTS).
CP44:
The concentration of protein in the interstitium (CPI) is equal to the total
quantity of protein in the interstitium (TSP) divided by the total volume of
fluid in the systemic interstitium (VTS).
$\mathrm{CPI}=\frac{\mathrm{TSP}}{\mathrm{VTS}}$
CP45:
The colloid osmotic pressure of the free fluid in the interstitium (PTCPR) is
calculated in this block from the concentration of protein in the interstitium (CPI).
CP45:
The colloid osmotic pressure of the free fluid in the interstitium (PTCPR) is
calculated in this block from the concentration of protein in the interstitium (CPI).
$\mathrm{PTCPR}=0.28\mathrm{CPI}+0.0019\mathrm{CPI}^{2}$
CP46:
The rate of return of protein to the circulation by way of the lymph (DPL) is
equal to the concentration of protein in the systemic interstitium (CPI) times
the rate of lymph flow from the interstitium (VTL).
CP46:
The rate of return of protein to the circulation by way of the lymph (DPL) is
equal to the concentration of protein in the systemic interstitium (CPI) times
the rate of lymph flow from the interstitium (VTL).
$\mathrm{DPL}=\mathrm{CPI}\mathrm{VTL}$
Containment grouping component for "hydrostatic_pressure_of_tissue_gel",
"total_osmotic_pressure_of_tissue_gel", "total_tissue_pressure",
"interstial_free_fluid_pressure", "interstitial_solid_tissue_pressure",
"lymph_flow", "interstitial_gel_volume" and "interstitial_free_fluid_volume".
CP13 and CP14:
Calculation of the concentration of hyaluronic acid in the interstitium (CHY)
from the total quantity of hyaluronic acid in the interstitium (HYL) and the
total volume of fluid in the interstitium (VTS). The exponent CMPTSS describes
the non-linearity of this effect.
CP15 and CP16:
Calculation of the hydrostatic pressure in the tissue gel (PGH) from the
concentration of hyaluronic acid in the interstitium (CHY) and the total
tissue pressure (PTT). (The hyaluronic acid acts as an elastic body that
expands, and, therefore, creates a negative pressure.)
CP13 and CP14:
Calculation of the concentration of hyaluronic acid in the interstitium (CHY)
from the total quantity of hyaluronic acid in the interstitium (HYL) and the
total volume of fluid in the interstitium (VTS). The exponent CMPTSS describes
the non-linearity of this effect.
CP15 and CP16:
Calculation of the hydrostatic pressure in the tissue gel (PGH) from the
concentration of hyaluronic acid in the interstitium (CHY) and the total
tissue pressure (PTT). (The hyaluronic acid acts as an elastic body that
expands, and, therefore, creates a negative pressure.)
$\mathrm{CHY}=\left(\frac{\frac{\mathrm{HYL}}{\mathrm{VTS}}}{5}\right)^{\mathrm{CMPTSS}}\mathrm{PGH}=\mathrm{CHY}\mathrm{PGHF}+\mathrm{PTT}$
CP17:
The osmotic pressure caused by the hyaluronic acid in the gel (POSHYL)
is equal to the concentration of hyaluronic acid in the gel (CHY) times
a constant.
CP18:
The total osmotic pressure of the tissue gel (PTC) is equal to the osmotic
pressure caused by the hyaluronic acid in the gel (POSHYL) times the colloid
osmotic pressure caused by the plasma protein in the free fluid of the
interstitium (PTCPR) times a constant (GCOPF).
CP17:
The osmotic pressure caused by the hyaluronic acid in the gel (POSHYL)
is equal to the concentration of hyaluronic acid in the gel (CHY) times
a constant.
CP18:
The total osmotic pressure of the tissue gel (PTC) is equal to the osmotic
pressure caused by the hyaluronic acid in the gel (POSHYL) times the colloid
osmotic pressure caused by the plasma protein in the free fluid of the
interstitium (PTCPR) times a constant (GCOPF).
$\mathrm{POSHYL}=\mathrm{CHY}\times 2\mathrm{PTC}=\mathrm{POSHYL}\mathrm{PTCPR}\mathrm{GCOPF}$
CP12:
Calculation of the total tissue pressure (PTT) as a function of the total
interstitial fluid volume (VTS1).
CP12:
Calculation of the total tissue pressure (PTT) as a function of the total
interstitial fluid volume (VTS1).
$\mathrm{PTT}=\left(\frac{\mathrm{VTS1}-\mathrm{VTSF}}{\mathrm{VTSF}}\right)^{2}\times 1$
CP19:
The pressure in the free interstitial fluid (PIF) is equal to the hydrostatic
pressure in the tissue gel (PGH) minus the colloid osmotic pressure of the
hyaluronic acid in the tissue gel (POSHYL).
CP19:
The pressure in the free interstitial fluid (PIF) is equal to the hydrostatic
pressure in the tissue gel (PGH) minus the colloid osmotic pressure of the
hyaluronic acid in the tissue gel (POSHYL).
$\mathrm{PIF}=\mathrm{PGH}-\mathrm{POSHYL}$
CP20:
The solid tissue pressure of the interstitium (PTS) is equal to the total
tissue pressure (PTT) minus the pressure in the free fluid of the interstitium (PIF).
CP20:
The solid tissue pressure of the interstitium (PTS) is equal to the total
tissue pressure (PTT) minus the pressure in the free fluid of the interstitium (PIF).
$\mathrm{PTS}=\mathrm{PTT}-\mathrm{PIF}$
CP21 and CP22:
The pressure gradient that promotes lymph flow (PLD) is equal to a constant (PLDF)
that is determined by the pumping action of the lymphatics plus the interstitial
free fluid pressure (PIF), minus the total tissue pressure (PTT). Block CP22
limits the upper level of this pressure gradient.
CP23 and CP24:
The rate of lymph flow (VTL) is equal to the pressure gradient that causes
lymph flow (PLD) times a constant representing lymphatic conductance.
Block CP24 limits the lower level of lymph flow to zero.
CP21:
The pressure gradient that promotes lymph flow (PLD) is equal to a constant (PLDF)
that is determined by the pumping action of the lymphatics plus the interstitial
free fluid pressure (PIF), minus the total tissue pressure (PTT).
CP22:
Block CP22 limits the upper level of this pressure gradient.
] CP23 and CP24:
The rate of lymph flow (VTL) is equal to the pressure gradient that causes
lymph flow (PLD) times a constant representing lymphatic conductance.
Block CP24 limits the lower level of lymph flow to zero.
$\mathrm{PLD1}=\mathrm{PIF}+\mathrm{PLDF}-\mathrm{PTT}\mathrm{PLD}=\begin{cases}7 & \text{if $\mathrm{PLD1}> 7$}\\ \mathrm{PLD1} & \text{otherwise}\end{cases}\mathrm{VTL}=\begin{cases}0 & \text{if $\mathrm{PLD}< 0$}\\ \mathrm{PLD}\times 0.02 & \text{otherwise}\end{cases}$
CP8:
This block gives a function curve that relates the volume of the tissue gel (VG)
to the total interstitial fluid volume (VTS).
CP8:
This block gives a function curve that relates the volume of the tissue gel (VG)
to the total interstitial fluid volume (VTS).
$\mathrm{VG}=\begin{cases}0 & \text{if $\mathrm{VTS}\le 0$}\\ 0+\frac{(11.4-0)(\mathrm{VTS}-0)}{12-0} & \text{if $(\mathrm{VTS}> 0)\land (\mathrm{VTS}\le 12)$}\\ 11.4+\frac{(14-11.4)(\mathrm{VTS}-12)}{15-12} & \text{if $(\mathrm{VTS}> 12)\land (\mathrm{VTS}\le 15)$}\\ 14+\frac{(16-14)(\mathrm{VTS}-15)}{18-15} & \text{if $(\mathrm{VTS}> 15)\land (\mathrm{VTS}\le 18)$}\\ 16+\frac{(17.3-16)(\mathrm{VTS}-18)}{21-18} & \text{if $(\mathrm{VTS}> 18)\land (\mathrm{VTS}\le 21)$}\\ 17.3+\frac{(18-17.3)(\mathrm{VTS}-21)}{24-21} & \text{if $(\mathrm{VTS}> 21)\land (\mathrm{VTS}\le 24)$}\\ 18 & \text{otherwise}\end{cases}$
CP9:
The volume of free fluid in the interstitium (VIF) is equal to the total
interstitial fluid volume (VTS) minus the volume of fluid in the tissue gel (VG).
CP9:
The volume of free fluid in the interstitium (VIF) is equal to the total
interstitial fluid volume (VTS) minus the volume of fluid in the tissue gel (VG).
$\mathrm{VIF}=\mathrm{VTS}-\mathrm{VG}$