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Transvascular and interstitial
transport
Tissue Engineering & Drug Delivery
BBI 4203
LECTURE #12
Vascular permeability
• Capacity of a blood vessel wall to allow for the flow of
small molecules (ions, water, nutrients) or even whole
cells (lymphocytes on their way to the site of
inflammation) in and out of the vessel.
• Flux across membrane J=P*S*∆C
– J= rate of mass flow kg/s (not kg/m2*s)
– S= vessel wall surface area in m2
– ∆C= pressure difference across vessel wall in kg m-3
• Permeability coefficient P=J/(S*∆C) (m s-1)
– units of distance per unit time
Vascular permeability varies
• Blood vessel walls are lined by a single layer of
endothelial cells.
• The gaps between endothelial cells (cell junctions)
are strictly regulated depending on the type and
physiological state of the tissue.
• Blood-brain barrier has tight endothelial cell
junctions
• Arteries and veins are intended for blood transport,
have thicker walls, and are less permeable
• Capillaries or microvessels are the most permeable
Microvessels is a tube comprised of 1-3
endothelial cells and basement membrane
Cross-section of microvessel
I. Structure of the microvessel wall:
* Glycocalyx: fibrous chains of the membrane glycoproteins
with negative charge. Thickness is 100 ~ 400 nm.
* Basement membrane: An electrodense fiber matrix layer,
containing type IV collagen, proteoglycan (e.g., perlecan),
laminin, fibronectin, and glycoproteins.
BM
Extravasation of D20 in the rabbit granulation tissue
Extravasation of D20 in the rabbit granulation tissue
1 min
5 min
20 min
10 min
40 min
• What are the major barriers
for transvascular transport?
• Endothelial layer
• Glycocalyx
• What are paths available for transport across the
microvessel wall?
• What are cutoff sizes of pores for drug and gene
delivery across microvessel wall?
Endothelial cell junctions:
• tight junction:
- claudins, occludin,
- junctional adhesion molecule (JAM) family,
- nectin,
- endothelial cell selective adhesion molecule
(ESAM).
Dejana, J., NATURE REV | MOL CELL BIOL, 5: 263, 2004.
• adhesion junctions:
- vascular endothelial cadherin (VE-cadherin)
- vascular endothelial protein tyrosine phosphatase (VEPTP) modulates cadherin phosphorylation
- Adhesion junction is enhanced
by platelet endothelial cell
adhesion molecule (PE-CAM).
- Adhesion to pericytes and
smooth muscle cells is mediated
by neuronal cadherin (Ncadherin)
1. Pathways for transendothelial transport
(i) Continuous capillary
(i) Direct diffusion through cells
https://www.stu.qmul.ac.uk/SMD/
kb/microanatomy/cardiovascular/
index.htm
Molecule
EC
Cellular Junction
EC
(ii) Vesicular pathways
(a) Transendothelial vesicles (shuttles)
(b) Fusion-fission of vesicles
(c) Transendothelial vesicular channels
(iii) Diffusion along the cell membrane
2. Fenestrated capillary (e.g., in
the kidney, pancreas, adrenal
cortex, and choroid in the eye)
In addition to the pathways in
continuous capillaries, molecules can
cross endothelial cells through
diaphragmed or open fenestrae (~100
nm) within the EC.
Diaphragmed fenestrae
EC
Open fenestrae
Basement membrane
Peritubular capillary in renal tube
A
Thin sections of the
peritubular capillary
shows single and double
diaphragms bridging the
fenestral pores.
Fenestral diaphragms on the
luminal surface of peritubular
capillary in the rat kidney
cortex
B
BEARER, E.L. AND ORCI, L., J CELL BIOL 100:418-428, 1985.
3. Discontinuous capillary (e.g.,
in the liver, spleen, bone
marrow, and solid tumors)
In addition to the pathways in
continuous capillaries, molecules
can cross endothelial cells through
open gaps.
Liver
https://www.stu.qmul.ac.uk/SMD/kb/microanato
my/cardiovascular/index.htm
Open intercellular gaps
Basement membrane (partial or total absence)
II. Quantitative analysis of transvascular transport
(1) Phenomenological approach
(a) Flux of fluid
JV  LP S (p   s  ) Starling's law of filtration
spaces)
where:
Jv - rate of fluid flow,
LP - hydraulic conductivity (ease with which fluid flows thru interstitial
S - surface area of the endothelium
p - hydrostatic pressure difference
 π - osmotic pressure difference
s - osmotic reflection coefficient
(A) Starling's law presented in physiology textbooks
JV  LP S (p   s  )
In the arterial end
pv = 35 mmHg, pi = - 2 mmHg;
v = 28 mmHg, i = 0.1 mmHg
Assume LpS same
for both arterial
and venous sides
and that s = 1.0
 pnet = (pv - pi) - s(v - i) = 9.1 mmHg => Filtration
In the venous end
pv = 15 mmHg, pi = - 2 mmHg;
v = 28 mmHg, i = 3 mmHg

pnet = (pv - pi) - s(v - i) = -8.0 mmHg => Reabsorption
Microvessel filtration and resorption
Arterial side
Net fluid
outflow
Hydrostatic pressure dominates
Venous side
Net fluid
inflow
Osmotic pressure dominates
(b) Flux of solute
Factors that affect solute motion in
addition to fluid flux
_
J S  JV (1   f ) CS  PSC
(Kedem and Katchalsky equation 1958)
where:
JS - rate of solute transport,
f - filtration reflection coefficient
(Note: in general f  s)
_
C S - average molar concentration within the membrane
P - microvascular permeability coefficient
S – surface area
C - concentration difference
(c) Phenomenological constants in transvascular transport
Hydraulic
permeability
J /S


fluid flux


LP   V
 
 p  CS 0  hydrostati c pressure difference  CS 0
Permeability
coefficient
solute flux
J /S


P S



 C  JV 0  concentrat ion difference  JV 0
Osmotic
reflection
coefficient
S  
Filtration
reflection
coefficient
 hydrostati c pressure difference
 p 
 

   JV 0  osmotic pressure difference



 JV 0
JS / S 
 solute flux across vessel wall 

 1 

(
J
C
)
/
S
solute
flux
in
the
solution

 C 0
 V 0
 C 0
 f  1  
(IV) Measurement of microvascular permeability
inject fluorescent dye into vessel and then flush it out
Fluorescent
intensity in tissue
Saline
Fluorescence
dye
Measure time it
takes for
maximum
fluorescence to be
reached. Shorter
time means more
permeable
Vessel permeability
v
a
c
LS174T tumor
tissue
Normal mouse
s.c. tissue
Microvascular Permeability
-8
10 cm/sec
1000
Normal Tissue
Tumor Tissue
100
10
1
0.1
Dextran 150
~ 10 nm
BSA
~ 7 nm
Liposome
~ 90 nm
Molecular size cutoff of pores in different
tumor vessels (sieving effect)
2000
1500
1000
MCa IV
ST- 12
LS174T
HCa I
0
ST-8
500
Shionogi
Liposome Size (nm)
2500
Hobbs, et al, PNAS, 1998
Factors that affect the transvascular transport
 Size, charge, configuration (shape), polarity of molecules
 Size and density of pores in the vascular endothelium
 Density of the extracellular matrix (e.g., glycocalyx, BM)
 Concentration and pressure differences across the vessel wall
 Concentration of drugs in the blood
Example modeling representations
Glycocalyx
EC cell junctions
Microvessel
w/ outlined
EC border
Basement membrane
(connective tissue)
Interstitial Transport
(Transport of the interstitial fluid)
Lymph and interstitial fluid (ISF)
• Lymph is formed when fluid that lies in the interstices of
tissues (ISF) is collected and transported through lymph
vessels.
• Lymph vessels empty into the right or the left subclavian
vein, where it mixes back with blood and is recirculated.
• Composition of ISF continually changes as the blood and
the surrounding cells exchange substances with the
interstitial fluid.
• ISF is essentially serum w/ WBCs
Lymph emptied into tissue space
collected by lymph vessels
Fluid exits microvessels bc hydrostatic pressure
of vessel exceeds osmotic pressure of tissue
Starling
Forces
Drugs entering the ISF is a major step of circulating drugs reaching
tissue
Once in ISF drug must move around – Interstitial Transport
Molecules move in tissue space by a
combination of diffusion and
convection
• Diffusion is the net movement of a
substance (e.g., an atom, ion or molecule)
from a region of high concentration to a
region of low concentration.
• Convection is the concerted, collective
movement of groups or aggregates of
molecules within fluids
Analogy of a sailing ship
• In the absence of wind the ship drifts in the
direction of the currents
– Analogous to the motion of molecules from
high to low concentration away from vessel
• In the presence of wind the ship moves
faster that the current and can even sail
opposite to the current
– Analogous to molecules moving (convecting)
across vessel wall against the osmotic gradient
L is the characteristic length
n is the local flow velocity
D is the diffusion coefficient
Convection Lv
Peclet Number =
~
Diffusion
D
Mol.
MW
D (cm2/s)
tD(min) tC(min)
Oxygen
Glucose
Fab’
Antibody
DNA
32
180
50,000
150,000
4 ´106
2 ´10-5
2 ´10-6
3 ´10-7
1 ´10-8
1 ´10-9
0.1
0.8
5.6
166.7
1666.7
3.3
3.3
3.3
3.3
3.3
tD/tC= Pe
0.03
0.25
1.67
50
500
tDiffusion = L2/D,
tConvection = L/v
Assuming:
v = 0.5 µm/sec,
L = 100 mm
Convection is important for macromolecular
transport while diffusion is the major mechanism of
the transport of small molecules.
Interstitial fluid transport
(Baxter, et al., Microvasc Res, 37: 77-104, 1989; Netti, et al., Cancer Res, 55:
5451-5458, 1995; Truskey et al., Transport Phenomena in Biological Systems, 2nd
Ed., 2009)
General approach:
mass balance and momentum balance.
Curl is a measure of field rotation using the
right hand rule
W rotation (curl>0) No rotation (curl=0) CW rotation (curl<0)
Cyclone in Northern hemisphere
Waterfall
Cyclone in Southern hemisphere
Divergence – 3D vector change in quantity wrt
distance Source (viv>0)
Sink (div<0)
Steady state (div=0)
Gradient – scalar change in quantity wrt
distance
Concentration Gradient
Pressure Gradient
Gradient of light on wall
Rate of drug accumulation in ISF is equal to
difference between the rate of drug that
extravasates into tissue FV minus the rate of
drug that is drained by the lymph FL

 


u


    v  (1   )
 v   L

t 



where
v: rate of fluid extravasation from blood vessels per
unit volume,
L: rate of lymphatic drainage per unit volume,
: fractional volume of fluid in tissues,

v

: velocity of the interstitial fluid,
u : solid tissue displacement.
Transport across microvessels
v 
J v LPv S v

[ pv  pi  v ]
V
V
J L LPL S L
L 

[ pi  pL  L ]
V
V
(blood vessel)
(lymph vessel)
Osmotic pressure difference terms 
v   v ( v   i )
L   L ( i   L )
Note: It may not be valid for continuous capillary at steady state
but still be useful for transient delivery or for transport
across leaky vessels (i.e., no osmotic pressure difference)
The rate that ISF moves through tissue is a
function of the tissue permeability (k), fluid
viscosity (m), and the pressure gradient ( p)
(Generalized Biot's law, 1856)



u 
k

 v
  pi   Kpi

t 
m



where:
µ: viscosity of the fluid,
k = K µ, specific permeability of porous medium,
K: hydraulic conductivity of tissues,
pi: gradient of IFP.
®
ev =-
k
m
Ñpi
Darcy’s law
Fluid transport in solid tumors at steady state
(no sources or sinks)

  v  v   L

v 
K

p
 K p  v   L
2
(mass balance)
(fluid momentum balance, Darcy’s law)
(governing equation)
K=hydraulic permeability of tissue, p is pressure, F rate of
fluid extravisation and lymph drainage
Simplified version of ISF pressure in 1D
Ñ p = ¶ p / ¶x
2
2
2
(div squared in 1D)
Governing Equation reduces to
-Kd2p/dx2=FV-FL
K=hydraulic permeability of tissue, d2p/dx2 is the second
derivative ISF pressure p wrt x, FV-FL is the difference in the
rate of fluid extravisation and lymph drainage
Blood
vessel FV
ISF pressure
x
Lymph
FL vessel
Parameters That Govern Drug Transport In Tissues
(P, LP, p, )
Drugs
Cells
Uptake
(Nr, Vmax, Km)
Microvessel
Diffusion (c, D)
Binding (kf, kr , Nr)
Convection (p, K, )
Available volume fraction (KAV, )
Vessel wall
(v, p, R)
Consider example of bolus IV
injection of drug
Residence time of drug in ISF. How do these
factors affect the shape of this curve?
Tissue Concentration
Residence
Clearance
Convection v. diffusion?
Vessel permeability?
Fluid viscosity?
Hydraulic conductivity?
Hydrostatic pressure gradient?
Percent porosity of tissue?
Osmotic pressure gradient?
Filtration rate?
Clearance rate (lymph uptake)?
Molecular size?
Molecular solubility in water?
Cellular uptake?
Accumulation
Time