Three-dimensional

Numerical

Modeling

and

Computational

Fluid

Dynamics

Simulations

to

Analyze

and

Improve

Oxygen

Availability

in

the

AMC

Bioartificial

Liver

A

numerical

model

to

investigate

fluid

flow

and

oxygen

-LRB-

-RRB-

transport

and

consumption

in

the

AMC-Bioartificial

Liver

-LRB-

AMC-BAL

-RRB-

was

developed

and

applied

to

two

representative

micro

models

of

the

AMC-BAL

with

two

different

gas

capillary

patterns

each

combined

with

two

proposed

hepatocyte

distributions

Parameter

studies

were

performed

on

each

configuration

to

gain

insight

in

fluid

flow

shear

stress

distribution

and

oxygen

availability

in

the

AMC-BAL

We

assessed

the

function

of

the

internal

oxygenator

the

effect

of

changes

in

hepatocyte

oxygen

consumption

parameters

in

time

and

the

effect

of

the

change

from

an

experimental

to

a

clinical

setting

In

addition

different

methodologies

were

studied

to

improve

cellular

oxygen

availability

i.e.

external

oxygenation

of

culture

medium

culture

medium

flow

rate

culture

gas

oxygen

content

-LRB-

-RRB-

and

the

number

of

oxygenation

capillaries

Standard

operating

conditions

did

not

adequately

provide

all

hepatocytes

in

the

AMC-BAL

with

sufficient

oxygen

to

maintain

consumption

at

minimally

of

maximal

uptake

rate

Cellular

oxygen

availability

was

optimized

by

increasing

the

number

of

gas

capillaries

and

of

the

oxygenation

gas

by

a

factor

two

Pressure

drop

over

the

AMC-BAL

and

maximal

shear

stresses

were

low

and

not

considered

to

be

harmful

This

information

can

be

used

to

increase

cellular

efficiency

and

may

ultimately

lead

to

a

more

productive

AMC-BAL

Introduction

Acute

liver

failure

-LRB-

ALF

-RRB-

is

a

severe

disease

with

high

mortality

rates

-LRB-

-RRB-

At

present

the

only

efficient

therapy

is

orthotopic

liver

transplantation

-LRB-

OLT

-RRB-

To

bridge

ALF

patients

to

liver

transplantation

or

to

regeneration

of

the

native

liver

liver

support

systems

are

needed

The

most

promising

bridging

method

for

the

treatment

of

ALF

patients

are

bioartificial

liver

-LRB-

BAL

-RRB-

support

systems

These

systems

are

extracorporeal

devices

that

are

generally

comprised

of

a

bioreactor

in

which

living

hepatocytes

are

seeded

In

a

clinical

setting

toxic

plasma

of

ALF

patients

is

perfused

through

a

BAL

system

and

detoxified

by

viable

hepatocytes

A

major

advantage

of

BAL

systems

as

compared

to

other

non-biological

liver

support

systems

is

the

capacity

to

provide

a

full

range

of

metabolic

functions

to

compensate

for

the

complex

metabolic

disorders

seen

in

ALF

Although

many

BAL

systems

have

demonstrated

their

detoxifying

capacity

or

liver-specific

functions

in

in

vitro

ex

vivo

and

in

phase

I

clinical

studies

no

BAL

system

has

shown

to

significantly

improve

survival

in

ALF

patients

bridged

to

transplantation

in

a

controlled

trial

-LRB-

for

review

-RRB-

Important

issues

for

the

development

of

an

effective

BAL

system

are

local

plasma

flow

and

oxygen

transport

Optimal

cell

function

i.e.

detoxifying

capacity

is

only

obtained

when

a

BAL

system

is

adequately

perfused

with

plasma

to

enable

efficient

mass

transfer

In

this

situation

sufficient

nutrients

-LRB-

e.g.

glucose

fatty

acids

-RRB-

and

oxygen

are

supplied

whereas

unwanted

metabolites

-LRB-

e.g.

ammonia

-RRB-

are

efficiently

detoxified

and

metabolic

end

products

-LRB-

e.g.

urea

-RRB-

subsequently

removed

In

principle

oxygen

-LRB-

-RRB-

transfer

is

the

main

limitation

in

the

efficiency

of

a

BAL

because

of

the

low

solubility

of

oxygen

in

plasma

and

high

demand

for

oxygen

of

functionally

active

hepatocytes

The

AMC-Bioartificial

Liver

-LRB-

AMC-BAL

Academic

Medical

Center

Amsterdam

The

Netherlands

patent

No

WO

-RRB-

was

developed

with

a

special

design

for

on-site

oxygenation

of

hepatocytes

and

direct

contact

of

plasma

to

the

cells

to

enhance

bidirectional

solute

exchange

The

AMC-BAL

has

shown

promising

results

in

in

vitro

set-ups

small

and

large

animal

ALF

models

and

finally

in

a

phase

I

clinical

study

with

ALF

patients

But

to

increase

the

efficiency

of

the

AMC-BAL

further

optimization

of

plasma

perfusion

and

oxygenation

of

hepatocytes

may

be

useful

Numerical

techniques

and

Computational

Fluid

Dynamics

-LRB-

CFD

-RRB-

simulations

are

useful

tools

to

gain

insight

in

local

flow

field

and

oxygen

transport

in

hollow

fiber

as

well

as

in

other

types

of

hepatocyte

systems

These

numerical

techniques

can

also

be

used

to

determine

the

optimal

working

parameters

and

to

further

optimize

the

design

of

a

BAL

system

In

this

respect

we

used

CFD

simulations

as

a

methodological

approach

to

analyze

the

configuration

of

the

AMC-BAL

We

constructed

three-dimensional

computer

models

of

two

representative

unit

volumes

micro

models

of

the

laboratory-scale

AMC-BAL

Fluid

flow

and

oxygen

transport

and

consumption

were

simulated

in

these

micro

models

to

gain

insight

in

the

flow

field

and

local

cellular

oxygen

availability

Numerical

parameter

studies

were

performed

to

assess

possible

improvements

in

local

oxygen

availability

of

hepatocytes

Several

parameters

were

tested

-LRB-

-RRB-

effect

of

the

internal

oxygenator

system

-LRB-

-RRB-

of

the

oxygenation

gas

-LRB-

-RRB-

culture

medium

flow

rate

-LRB-

-RRB-

incorporation

of

an

external

oxygenator

in

the

extracorporeal

circuit

-LRB-

-RRB-

the

number

of

oxygen

capillaries

-LRB-

-RRB-

the

effect

of

plasma

perfusion

versus

normal

culture

medium

and

-LRB-

-RRB-

the

effect

of

changes

of

hepatocyte

oxygen

consumption

characteristics

in

time

Finally

we

discuss

the

implication

of

this

information

for

the

optimization

of

the

AMC-BAL

into

a

more

efficient

bioartificial

liver

Materials

and

methods

The

internal

geometry

of

the

laboratory-scale

AMC-BAL

is

schematically

drawn

in

Fig.

in

a

longitudinal

and

transverse

cross-section

The

bioreactor

is

built

from

a

cylindrical

polycarbonate

housing

-LRB-

Fig.

-RRB-

in

which

two

pieces

of

three-dimensional

-LRB-

-RRB-

non-woven

polyester

matrix

mat

-LRB-

Fig.

g

-RRB-

are

spirally

wound

around

a

massive

inner

core

-LRB-

Fig.

-RRB-

A

space

between

the

two

mat

segments

-LRB-

Fig.

-RRB-

is

left

open

for

an

additional

hepatocyte

seeding

port

-LRB-

not

shown

-RRB-

In

the

hydrophilic

matrix

high-density

hepatocyte

culture

is

possible

Between

the

matrix

windings

hydrophobic

gas

capillaries

-LRB-

Fig.

-RRB-

are

positioned

in

parallel

along

the

entire

bioreactor

as

an

internal

oxygenator

system

to

supply

additional

oxygen

to

the

hepatocytes

Culture

gas

-LRB-

air

-RRB-

is

perfused

through

these

capillaries

Plasma

enters

the

bioreactor

through

an

inlet

port

-LRB-

Fig.

-RRB-

and

flows

through

the

inflow

zone

-LRB-

Fig.

-RRB-

further

passes

the

hydrophilic

matrix

mat

and

through

the

void

inter-capillary

space

-LRB-

Fig.

-RRB-

Plasma

exits

the

bioreactor

via

the

outflow

zone

-LRB-

Fig.

-RRB-

through

the

outlet

port

-LRB-

Fig.

-RRB-

Plasma

and

culture

gas

are

counter-current

flows

Figure

Longitudinal

-LRB-

left

-RRB-

and

transverse

-LRB-

right

-RRB-

view

of

the

internal

geometry

of

the

AMC-BAL

with

a

gas

outlet

b

gas

inlet

c

plasma

inlet

port

d

plasma

outlet

port

e

first

mat

segment

f

interspace

g

second

mat

segment

h

polyurethane

potting

to

separate

gas

and

fluid

compartment

i

inner

core

j

inflow

zone

k

outflow

zone

l

polycarbonate

housing

m

gas

capillaries

n

inter-capillary

space

through

which

plasma

flows

The

inline

and

triangular

micro

models

are

designated

Computer

Model

Since

the

entire

BAL

geometry

is

too

large

and

complex

to

model

three-dimensional

unit

volumes

micro

models

were

isolated

from

the

geometry

-LRB-

Fig.

-RRB-

Each

three-dimensional

micro

model

-LRB-

Fig.

-RRB-

consists

of

pieces

of

mat

-LRB-

thickness

μm

height

μm

length

mm

Fig.

g

-RRB-

separated

by

a

void

interspace

section

-LRB-

length

mm

Fig.

-RRB-

At

both

sides

of

the

mat

gas

capillaries

-LRB-

outer

diameter

μm

-RRB-

and

an

inter-capillary

space

are

present

The

two

micro

models

differ

only

in

their

gas

capillaries

position

Either

the

capillaries

are

in

a

rectangular

-LRB-

inline

micro

model

Fig.

-RRB-

or

in

a

triangular

-LRB-

triangular

micro

model

Fig.

-RRB-

pattern

These

two

configurations

are

the

most

distinct

that

could

be

isolated

as

the

position

of

the

capillaries

relative

to

each

other

changes

continuously

along

the

course

of

the

spiral

mat

-LRB-

Fig.

-RRB-

These

two

micro

models

were

therefore

considered

to

be

representative

for

the

entire

AMC-BAL

Simulations

on

both

models

will

allow

us

to

assess

the

influence

of

the

capillary

arrangement

Figure

micro

models

Upper

left

inline

micro

model

upper

right

triangular

micro

model

-LRB-

c

capillary

wall

M

non-woven

matrix

mat

f

inter-capillary

space

-RRB-

lower

left

inline

micro

model

with

double

number

of

capillaries

lower

right

triangular

micro

model

with

double

number

of

capillaries

Both

models

were

created

in

the

modeling

software

Gambit

-LRB-

Fluent

Inc.

Sheffield

UK

-RRB-

All

dimensions

were

derived

from

a

laboratory-scale

AMC-BAL

or

were

supplied

by

the

manufacturer

The

curvature

of

the

mat

was

neglected

and

the

inflow

and

outflow

zones

before

and

after

the

mat

segments

in

the

AMC-BAL

were

not

included

in

the

micro

models

Each

standard

micro

model

contains

the

equivalent

capillary

wall

surface

of

whole

capillary

Since

the

entire

laboratory-scale

AMC-BAL

contains

capillaries

each

micro

model

can

thus

be

considered

as

part

of

AMC-BAL

Consequently

one

AMC-BAL

can

be

regarded

as

a

combination

of

separate

micro

models

in

parallel

Modeling

Fluid

Flow

Theoretical

Model

To

simulate

fluid

flow

the

commercial

CFD

package

Fluent

-LRB-

Fluent

Inc.

Sheffield

UK

-RRB-

was

used

to

numerically

solve

the

steady-state

Navier

Stokes

equations

Standard

pressure

discretization

scheme

and

second

order

upwind

momentum

discretization

scheme

were

used

Pressure

velocity

coupling

scheme

was

SIMPLE

Fluid

properties

were

set

to

those

of

culture

medium

to

allow

future

validation

with

in

vitro

experiments

Culture

medium

was

modeled

as

an

incompressible

isothermal

Newtonian

fluid

composed

of

water

-LRB-

ρ

-RRB-

and

serum

-LRB-

ρ

-RRB-

with

a

resulting

density

of

Dynamic

viscosity

μ

of

culture

medium

with

g/l

bovine

serum

albumin

-LRB-

BSA

-RRB-

at

°C

was

set

to

mPa

s.

Plasma

viscosity

at

°C

was

set

to

mPa

s.

Resistance

to

Flow

of

the

Non-woven

Polyester

Mat

The

non-woven

polyester

matrix

was

modeled

as

an

isotropic

homogeneous

porous

zone

A

measure

for

the

viscous

resistance

of

the

non-woven

polyester

matrix

used

in

Fluent

was

determined

in

an

experimental

set-up

by

establishing

the

pressure

drop

flow

rate

relationship

A

sample

of

this

matrix

fabric

sheet

was

clamped

between

two

connecting

tubes

These

tubes

were

placed

in

a

closed

circuit

with

an

overflow

reservoir

which

provided

a

constant

static

pressure

load

over

the

matrix

sample

Pressure

difference

over

the

matrix

sheet

was

measured

using

a

calibrated

differential

pressure

transducer

-LRB-

Fuji

Electrics

FCX

Japan

-RRB-

Flow

rate

was

measured

gravimetrically

De-ionized

water

was

used

Static

pressure

load

was

set

so

average

velocities

in

the

experiment

were

in

the

same

order

of

magnitude

as

could

be

expected

in

the

AMC-BAL

-LRB-

mm/s

-RRB-

A

viscous

resistance

factor

of

m

was

calculated

as

an

average

of

measurements

Resistance

to

flow

of

hepatocyte

cell

layers

-LRB-

section

Modeling

oxygen

transport

and

consumption

-RRB-

was

modeled

using

the

same

viscous

resistance

factor

Boundary

Conditions

We

assumed

that

total

flow

rate

-LRB-

ml/min

-RRB-

inside

the

research

scale

AMC-BAL

is

homogenously

distributed

In

this

way

each

micro

model

has

the

same

flow

rate

of

ml/min

i.e.

of

the

total

flow

rate

Pressure

inlet

boundary

conditions

were

used

outlet

boundary

condition

was

a

zero

pressure

outflow

the

capillary

walls

were

no-slip

walls

and

symmetry

boundary

conditions

were

used

at

the

side

walls

of

the

model

Modeling

Oxygen

Transport

and

Consumption

Theoretical

Model

To

simulate

oxygen

transport

and

consumption

Fluent

solves

the

steady-state

convection

diffusion-reaction

equation

-LRB-

Eq

-RRB-

Discretization

scheme

was

set

to

QUICK

The

transported

scalar

φ

is

the

local

oxygen

concentration

-LRB-

vol

-RRB-

which

is

also

the

product

of

the

oxygen

solubility

α

and

the

local

oxygen

partial

pressure

-LRB-

-RRB-

according

to

Henry

's

Law

-LRB-

φ

α

-RRB-

Oxygen

solubility

α

is

ml

ml

fluid

in

culture

medium

and

ml

ml

fluid

in

plasma

D

is

the

oxygen

diffusion

coefficient

which

is

in

culture

medium

and

in

plasma

Oxygen

consumption

by

the

primary

porcine

hepatocytes

in

the

AMC-BAL

was

modeled

by

an

additional

source

term

Sφ

which

was

only

implemented

in

regions

that

were

designated

to

contain

hepatocytes

This

source

term

-LRB-

Eq

-RRB-

was

based

on

the

Michaelis

Menten

kinetics

of

consumption

by

hepatocytes

As

such

uptake

is

dependent

on

the

local

hepatocyte

density

ρcell

and

in

a

non-linear

way

dependent

on

the

local

availability

Michaelis

Menten

parameters

of

primary

porcine

hepatocytes

were

obtained

from

Balis

et

al.

Values

of

culture

day

were

taken

as

they

are

characterized

by

a

highly

demanding

uptake

-LRB-

VM

nmol/s

cells

KM

mmHg

-RRB-

These

values

were

measured

in

culture

whereas

hepatocyte

culture

in

the

AMC-BAL

is

three-dimensional

and

at

high

density

For

this

reason

a

lower

consumption

may

be

expected

as

the

specific

uptake

rate

per

cell

is

reported

to

decrease

at

increasing

cell

densities

On

the

other

hand

consumption

may

rise

significantly

when

a

metabolic

load

is

applied

to

the

cells

As

such

the

proposed

consumption

characteristics

are

justified

by

assuming

these

values

to

represent

the

most

limiting

case

for

oxygen

availability

Consequently

attention

must

be

paid

when

comparing

simulation

results

to

other

numerical

studies

Hepatocyte

Distribution

in

the

Micro

Models

In

an

in

vitro

setting

the

laboratory

scale

AMC-BAL

is

seeded

with

billion

porcine

hepatocytes

via

three

different

loading

ports

while

gently

rotating

the

bioreactor

to

assure

a

homogeneous

cell

distribution

As

we

assumed

that

one

micro

model

is

one

part

of

an

entire

laboratory

scale

AMC-BAL

one

micro

model

contained

million

cells

Since

no

detailed

information

on

the

internal

hepatocyte

distribution

in

the

AMC-BAL

is

available

two

cell

distributions

are

hypothesized

In

cell

distribution

all

hepatocytes

are

homogeneously

distributed

in

the

non-woven

matrix

-LRB-

resulting

hepatocyte

density

ρcell

of

cells/ml

-RRB-

In

previous

macroscopic

and

microscopic

studies

of

an

early

prototype

AMC-BAL

the

majority

of

the

hepatocytes

were

immobilized

within

the

three-dimensional

matrix

However

given

the

undifferentiated

method

of

hepatocyte

seeding

it

is

possible

that

hepatocytes

also

adhere

to

the

surface

of

gas

capillaries

Therefore

in

cell

distribution

of

the

hepatocytes

are

located

in

the

matrix

-LRB-

ρcell

cells/ml

-RRB-

and

in

a

hepatocyte

layer

around

the

capillaries

The

hepatocyte

layer

was

set

to

be

μm

with

a

ρcell

of

cells/ml

This

cell

layer

thickness

is

in

the

range

of

what

is

used

in

other

numerical

and

is

consistent

with

the

size

of

primary

porcine

hepatocyte

cell

clusters

found

in

vitro

All

proposed

cell

densities

were

also

considered

to

be

realistic

The

complete

AMC-BAL

can

not

be

modeled

by

using

only

one

cell

distribution

or

only

one

micro

model

Therefore

each

cell

distribution

was

applied

to

both

micro

models

leading

to

four

basic

configurations

in

total

All

four

micro

model

configurations

were

assessed

independently

With

a

combination

of

these

micro

models

the

entire

AMC-BAL

can

be

modeled

in

future

studies

Diffusion

Constant

Through

Non-woven

Matrix

Free

diffusion

through

the

mat

zone

is

hindered

by

the

non-woven

arrangement

of

hydrophilic

polyester

fibers

which

are

considered

to

be

impermeable

to

To

compensate

for

this

hindered

diffusion

a

correction

factor

for

the

diffusion

coefficient

in

the

mat

volume

was

determined

On

a

microscopic

view

of

the

non-woven

matrix

the

mat

porosity

was

determined

to

be

A

modified

two-dimensional

inline

micro

model

was

constructed

with

polyester

fiber

circles

randomly

located

within

the

boundaries

of

the

mat

volume

On

this

modified

inline

micro

model

the

distribution

was

simulated

using

hepatocyte

distribution

-LRB-

Fig.

-RRB-

Standard

boundary

conditions

were

used

and

culture

flow

rate

was

zero

diffusion

coefficient

in

the

mat

zone

of

the

modified

micro

model

was

the

same

as

for

free

culture

medium

since

culture

medium

occupies

the

void

spaces

between

the

polyester

fibers

Subsequently

an

analogous

simulation

was

performed

on

a

regular

inline

micro

model

i.e.

with

the

mat

modeled

as

homogeneous

medium

with

an

adjusted

diffusion

coefficient

in

the

mat

zone

to

match

the

results

of

the

modified

model

-LRB-

Fig.

-RRB-

A

correction

factor

of

-LRB-

Dmat

-RRB-

for

diffusion

was

necessary

to

take

into

account

the

presence

of

the

non-woven

polyester

matrix

mat

This

correction

factor

is

in

accordance

with

the

equation

of

Rayleigh

-LRB-

correction

factor

-RRB-

which

has

been

experimentally

verified

for

various

sheets

of

porous

media

Figure

Determination

of

the

correction

factor

for

diffusion

through

the

non-woven

polyester

mat

-LRB-

A

-RRB-

distribution

-LSB-

mmHg

-RSB-

on

modified

inline

micro

model

-LRB-

polyester

fibers

drawn

-RRB-

under

standard

boundary

conditions

no

medium

flow

-LRB-

B

-RRB-

identical

distribution

-LSB-

mmHg

-RSB-

obtained

with

identical

simulation

settings

but

with

mat

as

homogeneous

medium

with

an

adjusted

diffusion

constant

-LRB-

with

a

factor

of

-RRB-

to

account

for

hindered

diffusion

Diffusion

Constant

Through

Zones

Containing

Hepatocytes

Oxygen

can

diffuse

through

both

continuous

fluid

spaces

as

well

as

through

hepatocytes

In

regions

seeded

with

hepatocytes

the

resulting

effective

diffusion

coefficient

Deff

will

be

lower

than

in

free

medium

since

diffuses

more

slowly

through

hepatocytes

The

extent

to

which

the

diffusivity

is

reduced

will

logically

depend

on

the

local

hepatocyte

density

Since

experimental

data

on

diffusion

constants

through

hepatocyte

cell

layers

with

different

cell

densities

is

not

readily

available

a

theoretical

approach

was

chosen

Riley

et

al.

developed

an

empirical

relation

-LRB-

Eq

-RRB-

that

relates

the

effective

diffusion

coefficient

Deff

to

the

local

free

diffusion

coefficient

the

intracellular

diffusion

coefficient

Dcell

and

the

cell

volume

fraction

φ

This

equation

based

on

Monte

Carlo

simulations

shows

a

good

agreement

with

available

data

throughout

a

wide

range

of

cell

volume

fractions

-LRB-

φ

-RRB-

Dcell

was

set

to

which

is

an

average

of

intracellular

diffusion

constants

in

hepatocytes

reported

by

Jones

Cell

volume

fraction

φ

is

the

local

volume

percentage

of

space

that

is

occupied

by

hepatocytes

and

was

calculated

as

the

product

of

the

local

hepatocyte

cell

density

and

the

average

hepatocytes

cell

volume

Local

free

diffusion

coefficient

is

dependent

on

the

perfusion

fluid

e.g.

culture

medium

or

plasma

and

on

the

location

of

hepatocytes

in

the

model

either

in

the

inter-capillary

space

or

in

the

mat

zone

diffusivities

in

different

regions

of

both

micro

models

are

presented

in

Table

TABLE

diffusion

constants

in

different

zones

of

the

micro

models.Region

in

the

micro

-LSB-

-RSB-

ρcell

-LSB-

cells/ml

-RSB-

φDeff

-LSB-

-RSB-

Cult

med

PlasmaCult

med.PlasmaNo

hepatocytes

Inter-capillary

In

Cell

distribution

In

Cell

distribution

In

In

hepatocyte

cell

layer

around

capillaries

part

in

mat

In

hepatocyte

cell

layer

around

capillaries

part

in

inter-capillary

The

ratio

of

the

effective

diffusion

constant

to

the

free

diffusion

constant

is

calculated

from

the

local

free

oxygen

diffusion

constant

and

the

local

cell

volume

fraction

φ

using

Eq

The

local

effective

diffusion

coefficients

Deff

in

culture

medium

and

plasma

per

region

are

presented

in

the

last

column

The

obtained

local

diffusion

coefficients

are

in

the

range

of

reported

values

for

hepatocytes

and

other

cell

types

Boundary

Conditions

Oxygen

partial

pressure

-LRB-

-RRB-

of

incoming

culture

medium

was

set

to

mmHg

which

was

an

average

of

three

culture

medium

measurements

using

an

blood-gas

analyzer

-LRB-

Radiometer

Copenhagen

-RRB-

Axial

and

radial

transport

resistances

in

gas

capillaries

were

neglected

since

the

culture

gas

flow

rate

through

the

gas

capillaries

and

their

permeability

are

high

As

such

supply

through

gas

capillaries

was

modeled

by

imposing

a

constant

mmHg

on

the

capillaries

outer

walls

which

corresponded

to

the

of

culture

gas

used

in

vitro

-LRB-

air

-RRB-

All

other

boundary

faces

have

no-flux

boundary

conditions

Grid

Dependency

One

micro

model

mesh

contained

approximately

million

finite

volume

mesh

elements

Further

increase

in

the

number

of

cells

rendered

identical

simulation

results

Simulations

Overview

and

Assessment

As

previously

stated

four

micro

model

configurations

were

used

-LRB-

a

-RRB-

the

inline

micro

model

with

cell

distribution

-LRB-

b

-RRB-

the

inline

micro

model

with

cell

distribution

-LRB-

c

-RRB-

the

triangular

micro

model

with

cell

distribution

and

finally

-LRB-

d

-RRB-

the

triangular

micro

model

with

cell

distribution

Fifteen

case

studies

-LRB-

Table

-RRB-

were

performed

on

each

configuration

TABLE

Overview

of

gas

-LRB-

mmHg

-RRB-

medium

-LRB-

mmHg

-RRB-

Qmedium

-LRB-

ml/min

-RRB-

capillariesKM

-LRB-

mmHg

-RRB-

Reference

case

-LRB-

-RRB-

Standard

boundary

conditionsCulture

Effect

of

the

internal

oxygenator

-LRB-

-RRB-

gas

-LRB-

-RRB-

gas

medium

Increasing

oxygen

availability

-LRB-

-RRB-

gas

-LRB-

-RRB-

gas

carbogenCulture

-LRB-

-RRB-

medium

-LRB-

-RRB-

medium

carbogenCulture

-LRB-

-RRB-

Fluid

flow

rate

Qmedium

-LRB-

-RRB-

Fluid

flow

rate

Qmedium

-LRB-

-RRB-

No

capill

-LRB-

-RRB-

No

capill

gas

Clinical

versus

experimental

setting

-LRB-

-RRB-

-LRB-

-RRB-

Plasma

gas

Changes

of

hepatocyte

consumption

in

time

-LRB-

-RRB-

KM

day

-LRB-

-RRB-

KM

day

Each

case

is

applied

to

the

four

basic

micro

model

configurations

-LRB-

inline

and

triangular

micro

model

each

with

cell

distribution

or

-RRB-

The

first

case

study

was

simulated

using

standard

boundary

conditions

as

described

in

previous

paragraphs

This

reference

case

study

-LRB-

-RRB-

is

the

internal

control

for

all

other

case

studies

with

the

same

micro

model

configuration

The

effect

of

the

internal

oxygenation

system

was

assessed

by

disabling

culture

gas

flow

-LRB-

-RRB-

and

by

assessing

the

effect

of

an

external

oxygenator

that

oxygenates

incoming

medium

to

a

doubled

as

an

alternative

for

internal

oxygenation

-LRB-

-RRB-

To

increase

oxygen

availability

to

the

hepatocytes

different

strategies

were

assessed

First

by

using

a

more

oxygen

rich

culture

gas

i.e.

a

doubled

gas

-LRB-

-RRB-

or

carbogen

gas

-LRB-

-RRB-

-LRB-

-RRB-

Second

by

incorporating

an

external

oxygenator

to

increase

incoming

medium

to

a

doubled

-LRB-

-RRB-

or

carbogen

-LRB-

-RRB-

level

Third

by

changing

culture

medium

flow

rate

to

a

doubled

-LRB-

-RRB-

or

-LRB-

-RRB-

flow

rate

Finally

by

doubling

the

number

of

capillaries

-LRB-

-RRB-

or

by

combining

the

double

number

of

capillaries

with

a

doubled

culture

gas

-LRB-

-RRB-

In

cases

with

a

doubled

number

of

capillaries

cell

density

in

the

hepatocyte

layer

around

the

capillaries

was

kept

constant

This

lead

to

a

cell

layer

thickness

of

μm

keeping

the

number

of

hepatocytes

around

all

capillaries

equal

to

of

total

as

was

initially

proposed

In

micro

models

with

double

number

of

capillaries

the

distance

between

the

capillaries

is

halved

-LRB-

see

Fig.

-RRB-

In

the

next

case

studies

we

studied

the

effect

of

plasma

versus

culture

medium

since

this

is

the

main

difference

in

perfusion

in

a

clinical

setting

as

compared

to

an

experimental

setting

Standard

boundary

conditions

-LRB-

-RRB-

and

a

doubled

gas

-LRB-

-RRB-

were

used

and

compared

with

cases

-LRB-

-RRB-

and

-LRB-

-RRB-

Finally

time-related

changes

in

oxygen

consumption

characteristics

of

hepatocytes

were

investigated

by

varying

KM

values

KM

values

of

culture

day

-LRB-

-RRB-

and

-LRB-

-RRB-

were

compared

to

the

reference

case

-LRB-

-RRB-

According

to

Balis

et

al.

KM

values

change

remarkably

throughout

the

first

days

whereas

VM

values

remain

constant

We

therefore

kept

VM

constant

in

these

simulations

The

proposed

simulation

cases

on

the

four

different

micro

model

configurations

were

assessed

by

examining

distributions

However

not

every

simulated

profile

can

be

shown

due

to

brevity

reasons

To

evaluate

the

effect

of

the

parameters

discussed

in

the

parameter

study

the

local

effective

hepatocyte

utilization

ratioVratio

-LRB-

Eq

-RRB-

was

studied

Vratio

is

the

ratio

of

the

observed

oxygen

consumption

rate

to

the

maximal

hepatocyte

oxygen

consumption

rate

i.e.

VM

and

ranges

between

and

-LRB-

asymptotically

-RRB-

A

threshold

for

Vratio

of

was

chosen

as

introduced

by

and

corresponds

with

a

minimal

level

of

mmHg

when

KM

mmHg

Consequently

oxygen

availability

in

the

AMC-BAL

was

quantified

by

determining

the

percentage

of

hepatocytes

with

Vratio

Results

Fluid

Flow

and

Shear

Stress

Distribution

Figure

represents

an

example

of

colorimetric

contour

plots

of

fluid

flow

and

shear

stress

distributions

in

two

different

micro

models

with

different

hepatocyte

distributions

In

the

upper

part

velocity

magnitudes

-LRB-

m/s

left

legend

-RRB-

in

a

transverse

plane

midway

through

the

first

mat

segment

are

shown

for

the

reference

case

-LRB-

case

-RRB-

of

an

inline

micro

model

with

hepatocyte

distribution

-LRB-

Fig.

-RRB-

and

for

a

triangular

micro

model

with

hepatocyte

distribution

and

with

a

double

number

of

capillaries

-LRB-

case

-RRB-

-LRB-

Fig.

-RRB-

The

contour

plots

can

be

mirrored

with

respect

to

the

horizontal

axis

as

micro

models

are

symmetrical

Figure

Colorimetric

contour

plot

of

velocity

magnitudes

-LRB-

m/s

left

legend

upper

part

-RRB-

and

shear

stress

levels

-LRB-

Pa

right

legend

lower

part

-RRB-

in

a

transverse

plane

midway

through

the

first

mat

segment

in

the

reference

case

-LRB-

case

-RRB-

of

an

inline

micro

model

with

hepatocyte

distribution

-LRB-

and

resp

-RRB-

and

in

a

triangular

micro

model

with

hepatocyte

distribution

and

with

double

number

of

capillaries

-LRB-

case

-RRB-

-LRB-

and

resp

-RRB-

Figure

Colorimetric

contour

plot

of

-LRB-

mmHg

left

legend

upper

part

-RRB-

and

effective

hepatocyte

utilization

ratio

Vratio

-LRB-

dimensionless

right

legend

lower

part

-RRB-

in

a

transverse

plane

midway

through

the

first

mat

segment

in

the

reference

case

-LRB-

case

-RRB-

of

an

inline

micro

model

with

hepatocyte

distribution

-LRB-

and

resp

-RRB-

and

in

a

triangular

micro

model

with

hepatocyte

distribution

and

with

double

number

of

capillaries

and

doubled

culture

gas

-LRB-

case

-RRB-

-LRB-

and

resp

-RRB-

-LRB-

Note

different

scale

compared

to

-RRB-

Fluid

flows

in

the

non-woven

matrix

mat

zone

and

in

the

hepatocyte

cell

layers

were

orientated

axially

and

are

uniform

in

size

-LRB-

approx.

μm/s

in

Fig.

and

μm/s

in

Fig.

-RRB-

In

the

inter-capillary

space

flow

velocities

have

a

poiseuille-like

-LRB-

parabolic

-RRB-

profile

with

maximal

velocities

of

approx.

mm/s

in

Fig.

and

mm/s

in

Fig.

In

the

interspace

between

two

mat

segments

flow

lines

expand

radially

due

to

the

sudden

increase

in

local

cross-sectional

area

However

these

flow

lines

reconverge

when

entering

the

second

mat

segment

where

the

velocity

profile

was

identical

compared

to

the

first

mat

segment

-LRB-

not

shown

-RRB-

Static

pressure

drop

over

the

entire

micro

model

was

Pa

in

the

reference

case

of

the

inline

micro

model

with

hepatocyte

distribution

-LRB-

Fig.

-RRB-

and

Pa

for

the

triangular

micro

model

with

hepatocyte

distribution

and

double

number

of

capillaries

-LRB-

Fig.

-RRB-

The

lower

parts

of

Fig.

-LRB-

and

-RRB-

show

corresponding

shear

stress

distributions

-LRB-

Pa

right

legend

-RRB-

Maximal

shear

stresses

were

generally

located

near

the

mat

side

surfaces

and

also

in

case

of

cell

distribution

at

the

boundary

between

the

hepatocyte

cell

layer

and

inter-capillary

space

In

Table

an

overview

is

given

of

maximum

velocity

magnitudes

in

the

inter-capillary

space

uniform

velocity

magnitudes

in

the

mat/hepatocyte

layer

zone

as

well

as

static

pressure

losses

over

the

entire

micro

model

and

maximal

local

shear

stresses

for

all

simulation

cases

Maximum

velocities

in

the

inter-capillary

space

ranged

between

and

mm/s

whereas

uniform

velocities

in

the

mat/hepatocyte

layer

ranged

between

and

μm/s

Simulation

results

showed

that

velocities

in

the

mat

zone

and

in

hepatocyte

layers

were

consistently

two

orders

of

magnitude

smaller

than

in

the

inter-capillary

space

Velocity

profiles

and

shear

stress

profiles

were

similar

for

the

different

simulation

cases

but

differed

in

magnitude

between

cases

when

flow

rate

was

altered

or

when

the

internal

geometry

had

been

changed

e.g.

due

to

additional

gas

capillaries

and/or

hepatocyte

layers

around

the

capillaries

Static

pressure

loss

over

the

entire

micro

model

and

local

shear

stress

levels

were

additionally

influenced

by

the

type

of

fluid

e.g.

plasma

or

culture

medium

Static

pressure

loss

over

the

entire

micro

model

ranged

from

approx.

to

Pa.

Maximum

shear

stress

ranged

between

approx.

and

Pa.

Largest

maximum

values

were

reached

in

hepatocyte

distribution

with

a

flow

rate

TABLE

Overview

of

the

maximum

velocity

in

the

inter-capillary

space

the

uniform

velocity

in

the

mat/hepatocyte

layer

zone

the

static

pressure

loss

over

the

entire

model

and

the

maximal

shear

stress

for

all

simulation

cases

and

for

different

hepatocyte

distributions.CasesHepatocyte

distr

distr

in

mat/hepatocyte

cell

layer

-LRB-

mm/s

-RRB-

Maximum

velocity

in

inter-capillary

space

-LRB-

mm/s

-RRB-

-LRB-

-RRB-

Standard

flow

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

No

capillaries

-LRB-

-RRB-

Static

pressure

loss

over

micro

model

-LRB-

Pa

-RRB-

-LRB-

-RRB-

Standard

flow

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

No

capillaries

-LRB-

-RRB-

Maximum

shear

stress

-LRB-

Pa

-RRB-

-LRB-

-RRB-

Standard

flow

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

No

capillaries

-LRB-

-RRB-

Values

for

the

inline

and

triangular

micro

model

are

identical

Importantly

both

the

inline

and

triangular

micro

model

had

the

same

flow

field

static

pressure

loss

and

shear

stress

distributions

within

a

simulation

case

with

certain

boundary

conditions

and

hepatocyte

distribution

-LRB-

comparison

not

shown

-RRB-

Oxygen

Transport

and

Consumption

Results

of

oxygen

transport

and

consumption

simulations

are

presented

by

means

of

two

contour

plots

of

and

Vratio

distributions

-LRB-

Fig.

-RRB-

Also

Table

presents

detailed

information

for

each

simulated

case

and

micro

model

configuration

on

the

percentage

of

hepatocytes

that

consume

oxygen

at

a

minimal

Vratio

level

of

TABLE

Percentages

of

total

hepatocyte

cell

amount

that

attain

a

Vratio

Hepatocytes

with

Vratio

CaseHepatocyte

distribution

distribution

-LRB-

-RRB-

Triangular

-LRB-

-RRB-

Inline

-LRB-

-RRB-

Triangular

-LRB-

-RRB-

Mat

-LRB-

-RRB-

Capill

-LRB-

-RRB-

Mat

-LRB-

-RRB-

Capill

-LRB-

-RRB-

Reference

case

-LRB-

-RRB-

Standard

boundary

The

effect

of

the

internal

oxygenator

-LRB-

-RRB-

gas

-LRB-

-RRB-

gas

medium

Increasing

oxygen

availability

-LRB-

-RRB-

gas

-LRB-

-RRB-

gas

-LRB-

-RRB-

medium

-LRB-

-RRB-

medium

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

Qmedium

-LRB-

-RRB-

No

capillaries

-LRB-

-RRB-

No

capillaries

gas

Clinical

versus

experimental

setting

-LRB-

-RRB-

-LRB-

-RRB-

Plasma

gas

Changes

in

hepatocyte

consumption

in

time

-LRB-

-RRB-

KM

day

-LRB-

-RRB-

KM

day

In

the

case

of

hepatocyte

distribution

distinction

is

made

between

the

percentage

of

the

total

number

of

hepatocytes

in

the

mat

and

the

percentage

of

total

number

of

hepatocytes

in

the

cell

layers

around

the

capillaries

Reference

Case

Simulations

-LRB-

Case

-RRB-

Figure

illustrates

the

distribution

in

a

transverse

plane

midway

through

the

first

mat

segment

in

the

reference

case

-LRB-

case

-RRB-

for

the

inline

micro

model

with

hepatocyte

distribution

Highest

-LRB-

mmHg

-RRB-

was

found

close

to

the

capillary

wall

A

large

gradient

extended

radially

from

the

capillary

and

was

steeper

at

the

side

of

the

capillary

in

the

mat

zone

At

a

radial

distance

of

μm

from

the

capillary

in

the

mat

zone

dropped

already

below

mmHg

A

region

where

oxygen

was

depleted

-LRB-

mmHg

-RRB-

is

present

in

the

center

of

the

hepatocyte-seeded

mat

throughout

both

mat

zones

Analogous

distributions

were

found

in

cross-sections

of

the

micro

model

further

downstream

to

the

plane

of

Fig.

but

with

overall

decreasing

average

oxygen

level

Oxygen

content

of

the

perfused

culture

medium

in

the

inter-capillary

space

dropped

from

its

initial

value

of

mmHg

to

approx.

mmHg

midway

the

first

mat

segment

and

further

decreased

downstream

to

mmHg

at

the

end

of

the

first

mat

segment

At

the

start

of

the

second

mat

segment

culture

medium

in

the

inter-capillary

space

was

increased

to

mmHg

and

again

decreased

to

mmHg

at

the

end

of

the

mat

segment

As

a

standard

for

cellular

oxygen

availability

the

effective

hepatocyte

utilization

ratio

Vratio

was

calculated

-LRB-

Fig.

-RRB-

Complying

with

distribution

hepatocytes

in

the

center

of

the

mat

zone

can

not

consume

oxygen

at

all

-LRB-

Vratio

-RRB-

whereas

hepatocytes

closest

to

the

capillaries

have

enough

oxygen

available

to

consume

oxygen

at

near

maximum

capacity

-LRB-

Vratio

-RRB-

Approximately

of

all

hepatocytes

in

the

model

consumed

oxygen

with

Vratio

-LRB-

Table

-RRB-

A

change

to

hepatocyte

distribution

was

characterized

by

a

larger

radial

gradient

around

the

capillaries

and

a

more

extended

zone

of

zero

oxygen

content

in

the

mat

segments

Due

to

the

additional

presence

of

a

dense

hepatocyte

layer

around

the

capillary

dropped

below

mmHg

from

a

radial

distance

of

μm

from

a

capillary

-LRB-

compare

to

μm

in

hepatocyte

distribution

-RRB-

Nevertheless

of

all

hepatocytes

attained

a

Vratio

of

more

than

Fifty

four

percent

of

the

hepatocytes

in

cell

layers

around

the

capillaries

reached

the

threshold

of

Vratio

whereas

of

the

hepatocytes

in

the

mat

zone

and

Vratio

distributions

for

the

reference

case

of

the

other

three

micro

model

configurations

are

not

shown

for

brevity

reasons

Simulation

results

also

showed

that

inline

and

triangular

micro

models

using

the

same

hepatocyte

distribution

showed

qualitative

and

quantitative

identical

distributions

The

Effect

of

the

Internal

Oxygenator

-LRB-

Case

-RRB-

Disabling

culture

gas

flow

-LRB-

gas

case

-RRB-

led

to

a

reduction

of

cells

with

Vratio

to

approximately

for

all

micro

model

configurations

Replacing

the

internal

oxygenator

by

an

external

oxygenator

which

doubles

culture

medium

-LRB-

case

-RRB-

led

to

a

Vratio

fraction

of

approx.

for

all

micro

model

configurations

More

specifically

in

cell

distribution

this

was

true

for

only

and

of

the

hepatocytes

around

the

capillaries

and

for

of

the

hepatocytes

in

the

mat

zone

for

case

and

respectively

Increasing

Oxygen

Availability

-LRB-

Case

-RRB-

Doubling

culture

gas

-LRB-

case

-RRB-

almost

doubled

Vratio

percentages

-LRB-

Table

-RRB-

from

approximately

to

in

micro

models

with

hepatocyte

distribution

an

increase

of

A

increase

-LRB-

-RRB-

was

obtained

in

micro

models

with

cell

distribution

This

increase

mainly

occurred

in

the

hepatocyte

layer

around

capillaries

i.e.

in

case

to

in

case

A

further

gas

increase

to

carbogen

level

-LRB-

case

-RRB-

led

to

an

approximate

quadruple

and

triple

Vratio

fraction

compared

to

the

reference

case

for

distribution

and

respectively

In

the

latter

hepatocytes

in

both

the

mat

zone

as

well

as

in

the

cell

layers

have

increased

threshold

percentages

Furthermore

about

more

hepatocytes

attained

the

threshold

in

the

triangular

capillary

arrangement

compared

to

inline

when

using

hepatocyte

distribution

In

distribution

inline

and

triangular

configurations

rendered

quasi-identical

results

Doubling

culture

medium

-LRB-

case

-RRB-

led

to

a

and

increase

in

Vratio

percentages

for

cell

distribution

and

respectively

In

the

latter

the

relative

increase

was

higher

in

the

mat

zone

as

compared

to

the

hepatocyte

layers

Further

increase

of

medium

to

carbogen

level

-LRB-

case

-RRB-

led

to

a

and

increase

in

Vratio

percentages

compared

to

the

reference

case

for

distribution

and

respectively

Inline

and

triangular

models

rendered

identical

results

under

the

same

hepatocyte

distribution

Doubling

culture

medium

flow

rate

-LRB-

case

-RRB-

resulted

in

a

and

increase

in

Vratio

fraction

for

distribution

and

respectively

Further

increase

of

culture

medium

flow

rate

up

to

a

-LRB-

case

-RRB-

resulted

in

an

and

increase

for

distribution

and

respectively

Typically

in

cases

with

increased

flow

rate

in

cell

distribution

Vratio

percentages

in

the

mat

zone

changed

remarkably

whereas

in

the

hepatocyte

layers

there

was

only

a

minor

increase

Again

inline

and

triangular

models

rendered

identical

results

under

the

same

hepatocyte

distribution

A

increase

in

the

number

of

capillaries

-LRB-

case

-RRB-

resulted

in

a

doubled

percentage

of

cells

that

attain

the

Vratio

threshold

in

cell

distribution

-LRB-

-RRB-

and

-LRB-

-RRB-

In

the

latter

this

increase

occurred

in

the

mat

zone

as

well

as

in

the

cell

layer

around

the

capillaries

The

combination

of

a

double

number

of

gas

capillaries

and

a

doubled

gas

-LRB-

case

-RRB-

increased

the

threshold

percentages

to

almost

quadruple

-LRB-

-RRB-

for

cell

distribution

and

triple

-LRB-

-RRB-

for

cell

distribution

Again

only

minor

differences

existed

between

inline

and

triangular

micro

models

Figure

shows

the

distribution

in

a

transverse

plane

midway

through

the

first

mat

segment

in

the

triangular

micro

model

with

cell

distribution

-LRB-

case

-RRB-

In

this

case

highest

levels

-LRB-

mmHg

-RRB-

were

only

found

close

to

the

capillary

walls

A

very

steep

radial

gradient

was

noted

in

the

hepatocyte

cell

layer

around

the

capillaries

in

the

center

of

the

mat

zone

was

mmHg

As

in

the

reference

case

distributions

of

cross-sections

further

downstream

showed

analogous

results

as

compared

to

Fig.

but

with

overall

decreasing

average

oxygen

level

The

distribution

of

Vratio

corresponding

to

the

distribution

of

case

is

depicted

in

Fig.

The

entire

hepatocyte

layer

-LRB-

-RRB-

around

the

capillaries

and

large

parts

of

the

mat

zone

-LRB-

-RRB-

had

a

Vratio

of

at

least

Consequently

in

case

of

all

hepatocytes

had

a

Vratio

higher

than

-LRB-

Table

-RRB-

Clinical

Versus

Experimental

Setting

-LRB-

Case

-RRB-

Changing

fluid

properties

from

culture

medium

to

plasma

resulted

in

a

decrease

in

Vratio

percentages

in

micro

models

with

cell

distribution

and

a

decrease

in

cell

distribution

-LRB-

case

-RRB-

Doubling

gas

in

the

clinical

setting

-LRB-

case

-RRB-

showed

a

relative

rise

of

and

compared

to

the

clinical

reference

case

-LRB-

case

-RRB-

in

cell

distribution

and

respectively

Compared

to

the

analog

case

in

in

vitro

settings

-LRB-

case

-RRB-

the

change

of

fluid

properties

also

corresponds

with

a

respective

and

decrease

of

the

Vratio

fraction

Changes

in

Hepatocyte

Consumption

in

Time

-LRB-

case

-RRB-

Changing

KM

values

to

the

situation

on

day

-LRB-

case

-RRB-

or

-LRB-

case

-RRB-

causes

slight

increases

in

absolute

level

Also

gradients

are

less

steep

and

the

oxygen

depleted

zone

in

the

center

of

the

matrix

is

slightly

smaller

-LRB-

not

shown

-RRB-

However

Vratio

fractions

decreased

and

for

cell

distribution

and

and

for

distribution

compared

to

day

-LRB-

case

-RRB-

for

day

and

respectively

Discussion

Fluid

Flow

and

Shear

Stress

Distribution

Perfusion

of

a

micro

model

was

largely

influenced

by

the

presence

of

the

non-woven

mat

Although

the

cross-sectional

area

of

the

inter-capillary

space

and

the

non-woven

mat

are

roughly

the

same

size

fluid

flow

in

the

mat

zone

was

generally

two

orders

of

magnitude

smaller

as

compared

to

the

flow

in

the

inter-capillary

space

This

effect

is

caused

by

the

higher

resistance

to

flow

of

the

non-woven

mat

forcing

the

majority

of

fluid

flow

through

the

inter-capillary

spaces

which

have

a

negligible

flow

resistance

This

also

causes

the

overall

pressure

loss

to

be

minimal

Since

the

same

hydraulic

permeability

is

used

for

the

hepatocyte

layers

fluid

velocities

there

are

also

in

the

range

of

micrometer

per

second

Consequently

apart

from

the

incorporation

of

additional

gas

capillaries

-LRB-

case

-RRB-

also

the

presence

of

hepatocyte

layers

around

the

capillaries

-LRB-

cell

distribution

-RRB-

increased

flow

velocities

and

pressure

loss

in

the

model

as

the

free

cross-sectional

area

of

the

inter-capillary

space

is

reduced

Fluid

flow

simulations

for

the

inline

and

triangular

variant

of

the

different

case

studies

render

identical

results

for

velocity

profiles

pressure

loss

and

shear

stress

distributions

This

was

expected

as

the

micro

models

consist

of

the

identical

geometrical

entities

which

are

only

changed

in

location

relative

to

each

other

From

a

fluid

dynamical

point

of

view

we

conclude

that

the

change

in

capillary

arrangement

along

the

course

of

the

spiral

mat

in

the

AMC-BAL

does

not

influence

fluid

flow

pressure

drop

or

shear

stress

distribution

The

static

pressure

loss

over

one

micro

model

can

be

regarded

as

the

total

pressure

drop

over

the

entire

AMC-BAL

without

the

inflow

and

outflow

zone

-LRB-

Fig.

g

-RRB-

since

the

AMC-BAL

can

be

represented

by

micro

models

in

parallel

This

pressure

drop

i.e.

max

Pa

mmHg

is

negligible

when

compared

to

the

pressure

losses

in

the

extracorporeal

circuit

These

low

pressure

gradients

are

in

accordance

with

the

in

vivo

situation

in

the

liver

lobule

in

which

pressure

drops

of

approximately

mmHg

over

the

sinusoids

are

normal

This

is

considered

advantageous

for

cell

culture

inside

the

AMC-BAL

Shear

stress

was

also

assessed

as

it

is

a

possible

determinant

of

cellular

damage

and

reduced

metabolic

function

Shear

stress

is

directly

proportional

to

the

local

velocity

gradient

and

the

fluid

viscosity

Consequently

shear

stresses

are

generally

more

elevated

in

cases

with

higher

velocity

magnitudes

in

the

inter-capillary

space

-LRB-

e.g.

in

case

of

increased

flow

rate

doubled

number

of

capillaries

cell

distribution

-RRB-

and

where

fluid

viscosity

is

increased

-LRB-

e.g.

when

plasma

was

used

instead

of

culture

medium

clinical

setting

case

-RRB-

Results

show

that

only

hepatocytes

located

at

the

side

of

the

mat

and

at

the

border

of

the

hepatocyte

layers

with

the

inter-capillary

space

are

subjected

to

a

certain

level

of

shear

stress

In

vivo

values

of

hepatocyte

wall

shear

stress

are

difficult

to

obtain

and

comparison

is

therefore

difficult

In

human

liver

sinusoid

wall

shear

stress

τ

can

be

calculated

as

-LRB-

with

static

pressure

drop

Δp

mmHg

sinusoid

diameter

D

μm

length

L

mm

and

considering

laminar

flow

and

a

cylindrical

shape

of

the

sinusoid

-RRB-

In

mice

sinusoids

shear

stress

was

calculated

to

be

Pa.

However

in

vivo

hepatocytes

are

not

directly

subjected

to

this

shear

stress

as

they

are

shielded

by

the

sinusoid

endothelial

lining

As

a

result

the

maximal

tolerable

level

of

shear

stress

is

lower

than

Pa.

Tilles

et

al.

showed

in

in

vitro

studies

on

rat

hepatocytes

that

hepatocyte

function

measured

as

albumin

and

urea

synthesis

rates

was

significantly

decreased

-LRB-

resp

and

-RRB-

when

hepatocytes

were

directly

exposed

to

shear

stresses

higher

than

Pa

compared

to

low

shear

stresses

-LRB-

Pa

-RRB-

Under

standard

conditions

maximum

shear

stress

values

in

the

AMC-BAL

do

not

exceed

Pa.

Additionally

the

majority

of

the

hepatocytes

are

not

subjected

to

significant

shear

stresses

Small

zones

with

increased

shear

stress

exist

but

maximal

values

are

considered

to

be

acceptable

and

not

detrimental

for

the

viability

and

function

of

hepatocytes

However

shear

stresses

may

increase

up

to

Pa

when

flow

rate

is

increased

-LRB-

case

-RRB-

Moreover

should

plasma

be

used

in

this

case

instead

of

culture

medium

maximal

shear

stress

values

may

then

reach

up

to

Pa

-LRB-

not

simulated

obtained

by

data

extrapolation

-RRB-

which

is

in

the

critical

range

-LRB-

-RRB-

Additionally

very

high

flow

rates

e.g.

the

normal

culture

flow

rates

may

cause

detachment

of

hepatocytes

and

therefore

should

not

be

used

in

spite

of

any

possible

increase

in

local

availability

Subsequently

case

-LRB-

culture

medium

flow

rate

-RRB-

can

already

be

discarded

in

the

search

for

optimal

availability

based

on

fluid

dynamical

grounds

Oxygen

Transport

and

Consumption

We

assessed

the

oxygen

availability

in

different

case

studies

and

in

different

micro

model

configurations

In

this

paragraph

the

results

are

discussed

per

case

Reference

Case

Simulations

-LRB-

Case

-RRB-

Highest

oxygen

concentrations

in

the

mat

zone

are

located

near

the

gas

capillaries

and

near

the

border

of

the

mat

and

the

inter-capillary

space

In

zones

with

limited

flow

velocities

cellular

oxygen

supply

is

clearly

dependent

on

diffusion

which

causes

large

radial

gradients

On

the

other

hand

diffusive

transport

from

the

culture

medium

towards

the

hepatocytes

also

causes

an

axial

gradient

in

culture

medium

oxygen

content

As

a

consequence

culture

medium

only

oxygenates

the

mat

near

the

very

start

of

the

first

mat

segment

and

near

the

side

of

the

mat

The

depth

of

penetration

into

the

mat

decreases

rapidly

further

downstream

since

as

the

majority

of

oxygen

content

in

the

convective

flow

is

already

consumed

in

the

first

part

of

the

micro

model

Nevertheless

oxygen

level

in

the

culture

medium

is

not

totally

depleted

at

the

end

of

the

micro

model

as

the

fluid

transit

time

is

not

sufficiently

long

for

all

oxygen

to

diffuse

to

the

hepatocytes

In

contrast

the

concentration

in

the

gas

capillaries

remains

constant

along

the

micro

model

axis

so

the

zone

around

the

capillaries

which

is

oxygenated

has

a

constant

radius

throughout

the

entire

micro

model

This

pattern

of

oxygenation

leads

to

about

higher

Vratio

percentages

in

hepatocyte

distribution

as

compared

to

since

more

hepatocytes

are

close

to

the

gas

capillaries

in

cell

distribution

So

despite

steeper

gradients

near

the

gas

capillaries

and

consequently

a

larger

zone

of

depleted

oxygen

in

the

mat

zone

in

case

of

hepatocyte

distribution

this

cell

distribution

leads

to

significantly

higher

Vratio

percentages

However

this

effect

is

related

to

the

maximal

oxygen

diffusion

distance

which

is

limited

by

the

Michaelis

Menten

oxygen

consumption

parameters

local

hepatocyte

density

and

local

diffusion

coefficient

in

general

and

by

the

specific

local

gas

capillary

and

culture

medium

in

this

reference

case

Since

regions

which

are

oxygenated

by

one

gas

capillary

in

particular

do

not

overlap

or

influence

each

other

in

the

reference

case

simulations

diffusive

oxygen

supply

by

the

capillaries

is

independent

of

relative

capillary

location

Convective

oxygen

transport

is

also

identical

as

flow

distribution

is

irrespective

of

capillary

placement

-LRB-

section

Fluid

flow

and

shear

stress

distribution

-RRB-

Consequently

inline

and

triangular

capillary

pattern

give

identical

results

concerning

oxygen

transport

and

consumption

in

these

reference

cases

when

the

same

hepatocyte

distribution

is

used

as

is

confirmed

by

simulation

results

Concerning

oxygen

transport

we

can

conclude

that

the

oxygen

supply

in

the

AMC-BAL

is

not

fully

adequate

to

provide

all

hepatocytes

with

sufficient

oxygen

to

maintain

consumption

at

minimally

of

the

maximal

uptake

rate

-LRB-

Vratio

-RRB-

Given

that

the

AMC-BAL

can

be

modeled

as

a

combination

of

micro

model

configurations

of

the

hepatocytes

in

the

AMC-BAL

are

adequately

oxygenated

In

other

words

between

and

of

the

hepatocytes

are

subjected

to

a

of

less

than

mmHg

under

the

current

conditions

Normal

physiological

values

in

the

liver

sinusoids

are

between

mmHg

in

the

periportal

area

and

mmHg

in

the

pericentral

area

But

it

is

difficult

to

determine

the

effect

on

viability

and

function

of

hepatocytes

below

this

threshold

Studies

indicate

that

hepatocyte

respiration

becomes

impaired

below

mmHg

With

respect

to

these

values

further

investigation

of

simulation

results

showed

that

under

current

conditions

and

of

the

hepatocytes

in

cell

distribution

and

have

a

below

mmHg

and

will

suffer

from

hypoxia

The

remaining

of

the

hepatocytes

are

likely

to

be

characterized

by

shifts

to

more

anaerobic

metabolic

processes

However

it

should

be

noted

that

the

low

Vratio

percentages

are

largely

influenced

by

the

very

stringent

hepatocyte

oxygen

consumption

ratios

used

in

this

numerical

model

Also

hepatocytes

which

are

subjected

to

low

oxygen

levels

for

a

prolonged

period

of

time

might

show

changes

in

oxygen

consumption

characteristics

-LRB-

VM

KM

-RRB-

to

compensate

for

the

lack

of

oxygen

This

could

account

for

account

for

higher

oxygen

availability

in

vitro

The

use

of

different

-LRB-

VM

KM

-RRB-

values

throughout

the

model

to

address

this

behavior

can

be

implemented

in

future

work

Nevertheless

further

increase

in

availability

may

prove

useful

to

increase

the

cell

viability

and

subsequently

the

efficiency

of

the

AMC-BAL

The

Effect

of

the

Internal

Oxygenator

-LRB-

Case

-RRB-

Disabling

the

internal

oxygenator

leads

to

detrimental

results

and

reduces

the

percentage

of

adequately

oxygenated

hepatocytes

to

virtually

zero

This

confirms

the

importance

of

the

internal

oxygenator

and

illustrates

the

small

contribution

of

the

incoming

convective

oxygen

flux

by

culture

medium

Incoming

culture

medium

flow

adds

only

nmol

per

second

to

the

micro

model

while

maximal

oxygen

uptake

VM

equals

nmol/s

cells

As

such

theoretically

no

more

than

cells

i.e.

of

the

total

amount

of

hepatocytes

per

micro

model

would

be

able

to

consume

at

maximal

uptake

rate

In

reality

only

of

the

hepatocytes

can

consume

at

a

Vratio

due

to

the

presence

of

gradients

Replacing

the

internal

oxygenator

by

an

external

oxygenator

which

doubles

the

flow

and

thus

the

convective

oxygen

flux

will

only

increase

the

Vratio

percentage

to

about

Since

this

is

still

considerably

less

than

in

the

reference

cases

external

oxygenation

even

at

elevated

levels

is

a

not

suitable

replacement

for

the

internal

oxygenation

system

as

the

gas

capillaries

constitute

the

main

oxygen

supply

As

such

the

internal

oxygenator

is

an

essential

part

of

the

AMC-BAL

Increasing

Oxygen

Availability

-LRB-

Case

-RRB-

In

the

reference

case

models

merely

of

the

hepatocytes

are

adequately

supplied

with

oxygen

to

consume

at

a

Vratio

depending

on

hepatocyte

distribution

We

therefore

assessed

several

strategies

to

increase

overall

oxygen

availability

Culture

medium

flow

rate

-LRB-

case

-RRB-

does

not

have

a

considerable

effect

on

cellular

oxygen

availability

A

increase

in

flow

rate

resulted

in

an

increase

in

regions

with

Vratio

of

only

This

was

expected

as

the

convective

oxygen

supply

is

only

a

minor

contributor

to

the

overall

oxygen

supply

Consequently

doubling

the

medium

-LRB-

case

-RRB-

does

not

greatly

increases

the

amount

of

regions

with

sufficient

oxygen

either

As

already

discussed

changes

in

culture

medium

properties

are

reflected

in

a

small

increase

of

regions

with

Vratio

in

the

mat

zone

and

more

specifically

in

the

first

mat

segment

as

oxygen

content

of

the

fluid

is

rapidly

decreased

downstream

It

is

interesting

to

note

that

doubling

the

flow

rate

and

doubling

the

medium

both

supply

exactly

the

same

amount

of

oxygen

to

the

micro

model

in

the

latter

oxygen

is

supplied

at

increased

whereas

in

the

former

oxygen

is

supplied

at

standard

level

but

with

a

higher

flow

rate

Nevertheless

doubling

medium

is

preferred

compared

to

increasing

flow

rate

when

aiming

at

a

better

effective

hepatocyte

utilization

ratio

since

the

doubled

flow

rate

does

not

give

the

oxygen

enough

time

to

diffuse

to

the

hepatocytes

as

the

residence

time

before

oxygen

exits

the

micro

model

is

cut

in

half

However

a

disadvantage

of

increasing

in

the

medium

is

the

requirement

of

an

external

oxygenator

which

makes

the

extracorporeal

circuit

more

complex

and

costly

and

increases

the

extracorporeal

plasma

volume

in

a

clinical

setting

Doubling

the

of

the

oxygenation

gas

-LRB-

case

-RRB-

is

much

easier

to

achieve

in

practice

Importantly

the

Vratio

percentage

increases

significantly

to

almost

a

doubled

level

as

compared

to

the

reference

case

In

comparison

culture

medium

flow

rate

has

to

be

increased

more

than

-LRB-

case

-RRB-

to

achieve

similar

results

as

with

a

increase

in

of

the

oxygenation

gas

This

illustrates

how

oxygen

supply

is

only

minor

dependent

on

fluid

flow

rate

However

saturation

of

Vratio

percentages

with

increased

flow

rate

is

not

yet

achieved

at

flow

rate

Nevertheless

a

flow

rate

is

not

preferred

because

of

possible

detachment

of

the

hepatocytes

and

an

increased

risk

of

possible

shear

stress

damage

to

the

hepatocytes

The

effective

hepatocyte

utilization

ratio

can

even

be

further

improved

Culture

medium

can

be

set

to

carbogen

level

-LRB-

case

-RRB-

or

the

number

of

capillaries

can

be

doubled

-LRB-

case

-RRB-

On

average

and

for

both

hepatocyte

distributions

these

two

methods

lead

to

a

increase

in

the

amount

of

hepatocytes

consuming

oxygen

at

Vratio

as

compared

to

the

reference

case

When

both

approaches

are

compared

for

hepatocyte

distribution

the

results

are

slightly

better

when

using

the

carbogen

medium

But

for

hepatocyte

distribution

the

double

number

of

capillaries

leads

to

better

results

An

increase

in

the

number

of

capillaries

is

preferred

over

carbogen

medium

perfusion

since

carbogen

medium

perfusion

leads

to

extremely

high

and

possible

values

of

almost

mmHg

Carbogen

medium

perfusion

also

requires

an

additional

external

oxygenator

Therefore

increasing

the

number

of

capillaries

by

is

a

more

easy

and

safe

method

to

increase

the

effective

hepatocyte

utilization

ratio

The

results

obtained

with

double

capillary

numbers

are

also

better

when

compared

to

the

doubling

of

the

oxygenation

gas

In

cell

distribution

this

is

mainly

caused

by

the

redistribution

of

the

hepatocytes

located

around

the

capillaries

By

increasing

the

number

of

capillaries

the

hepatocyte

layer

thickness

decreased

-LRB-

section

Modeling

oxygen

transport

and

consumption

-RRB-

As

a

consequence

the

region

that

a

gas

capillary

can

sufficiently

oxygenate

now

spans

the

entire

hepatocyte

layer

so

of

the

cell

layer

-LRB-

Table

-RRB-

is

sufficiently

oxygenated

In

cell

distribution

the

total

region

with

Vratio

has

also

increased

by

two

as

each

additional

capillary

supplies

an

additional

-LRB-

constant

-RRB-

volume

of

hepatocytes

with

Vratio

In

contrast

doubling

the

oxygenation

gas

increases

the

region

surrounding

a

single

capillary

with

Vratio

with

a

factor

of

less

than

two

The

ultimate

results

in

improving

cellular

oxygen

availability

and

effective

hepatocyte

utilization

ratio

are

found

when

oxygenation

gas

is

set

to

carbogen

level

-LRB-

case

-RRB-

or

when

a

double

number

of

capillaries

is

used

in

combination

with

a

doubled

oxygenation

gas

-LRB-

case

-RRB-

Vratio

percentages

have

quadrupled

for

cell

distribution

and

tripled

for

cell

distribution

as

compared

to

the

reference

case

for

both

approaches

Simulation

results

show

that

in

case

the

respective

gains

in

Vratio

regions

are

cumulated

when

the

case

of

a

double

number

of

capillaries

and

a

doubled

gas

are

combined

It

can

also

be

noted

that

there

is

a

small

but

significant

difference

between

the

inline

and

triangular

capillary

pattern

in

case

When

carbogen

oxygenation

gas

is

used

the

region

with

Vratio

surrounding

a

capillary

has

grown

to

such

an

extent

that

it

could

overlap

with

the

region

of

surrounding

capillaries

If

a

capillary

is

present

straight

opposed

to

another

-LRB-

inline

pattern

-RRB-

this

overlap

is

present

Consequently

the

intersection

of

the

two

regions

only

contributes

once

to

the

amount

of

region

with

Vratio

In

contrast

when

capillaries

are

in

a

triangular

pattern

the

region

surrounding

the

capillary

can

extent

to

its

fullest

thus

increasing

the

percentage

Vratio

more

compared

to

the

inline

micro

model

This

effect

is

more

pronounced

in

the

cell

distribution

compared

to

distribution

Given

the

possible

toxicity

of

the

hyperoxic

oxygen

levels

when

carbogen

oxygenation

gas

is

used

-LRB-

case

-RRB-

the

preferred

method

to

optimally

and

maximally

increase

oxygen

availability

in

the

AMC-BAL

is

to

double

the

number

of

gas

capillaries

together

with

a

increase

in

culture

gas

We

note

however

that

the

calculated

improvements

in

availability

and

Vratio

percentages

do

not

necessarily

translate

into

identical

increases

in

cell

viability

or

functional

activity

Nevertheless

similar

trends

between

simulation

results

and

the

in

vitro

situation

are

expected

but

have

to

be

validated

Clinical

Versus

Experimental

Setting

-LRB-

Case

-RRB-

An

important

decrease

in

the

amount

of

hepatocytes

with

Vratio

is

caused

by

the

lower

diffusion

coefficient

-LRB-

-RRB-

and

oxygen

solubility

-LRB-

-RRB-

in

plasma

as

compared

to

culture

medium

As

in

reference

case

results

are

independent

of

capillary

pattern

and

are

higher

in

cell

distribution

as

compared

to

cell

distribution

Doubling

the

oxygenation

gas

in

the

clinical

setting

leads

to

approximately

the

same

relative

increase

in

Vratio

percentages

as

it

does

in

the

experimental

setting

As

such

we

conclude

that

any

relative

increase

in

oxygen

availability

found

in

the

experimental

setting

by

any

possible

strategy

can

also

be

applied

to

the

clinical

setting

taking

into

account

that

the

absolute

Vratio

fractions

are

decreased

with

a

constant

percentage

depending

on

hepatocyte

distribution

Changes

in

Hepatocyte

Consumption

in

Time

-LRB-

Case

-RRB-

Higher

KM

values

of

day

and

cause

the

decrease

in

oxygen

consumption

to

start

at

higher

oxygen

levels

compared

to

lower

KM

values

of

day

Consequently

gradients

are

less

steep

and

oxygen

penetrates

further

into

the

mat

zone

or

into

hepatocyte

layers

because

of

the

reduced

local

uptake

Paradoxically

Vratio

fractions

have

decreased

This

is

understood

when

converting

the

Vratio

threshold

to

the

minimal

cellular

to

which

the

hepatocytes

must

be

subjected

to

using

Eq

Whereas

in

the

reference

case

hepatocytes

are

considered

to

be

sufficiently

oxygenated

when

cellular

reaches

at

least

mmHg

threshold

values

are

now

approximately

and

mmHg

for

day

and

respectively

Since

the

overall

level

in

the

latter

cases

is

not

equally

elevated

Vratio

fractions

are

strongly

reduced

Conversely

when

applying

an

identical

threshold

instead

of

Vratio

hepatocyte

percentages

in

case

and

are

increased

with

and

up

to

compared

to

day

As

such

an

increase

in

KM

causes

average

cellular

to

increase

but

whether

there

is

also

an

increase

in

the

number

of

hepatocytes

that

are

sufficiently

oxygenated

is

difficult

to

determine

based

on

computer

simulations

as

this

depends

on

the

criteria

i.e.

minimal

Vratio

versus

minimal

used

Conclusions

A

numerical

model

to

investigate

fluid

flow

and

oxygen

transport

and

consumption

in

the

AMC-BAL

was

developed

and

applied

to

two

representative

micro

models

of

the

AMC-BAL

Two

different

gas

capillary

patterns

i.e.

inline

and

triangular

were

used

and

combined

with

two

proposed

hepatocyte

distributions

leading

to

four

basic

configurations

in

total

Fifteen

case

studies

were

performed

on

each

of

the

configurations

in

order

to

gain

insight

in

the

fluid

flow

shear

stress

distribution

oxygen

availability

and

effective

hepatocyte

utilization

ratio

Vratio

of

the

AMC-BAL

and

to

assess

possible

strategies

to

further

improve

cellular

oxygen

availability

We

found

that

the

AMC-BAL

does

not

provide

sufficient

oxygen

to

all

hepatocytes

to

allow

them

to

consume

oxygen

at

of

their

maximal

uptake

rate

under

standard

operating

conditions

The

internal

oxygenator

is

an

essential

part

of

the

AMC-BAL

Doubling

the

number

of

gas

capillaries

together

with

a

increase

in

the

oxygenation

gas

was

found

to

be

the

optimal

method

to

maximally

increase

availability

Additionally

pressure

drop

over

the

AMC-BAL

and

cellular

shear

stress

levels

were

found

to

be

low

and

advantageous

to

cell

culture

The

developed

model

also

allowed

us

to

assess

the

effect

of

the

transition

from

the

in

vitro

to

the

clinical

setting

and

the

effect

of

the

change

of

hepatocyte

consumption

characteristics

in

time

Since

large

variations

in

simulation

results

between

hepatocyte

distributions

are

shown

an

assessment

of

the

in

vitro

hepatocyte

distribution

in

the

AMC-BAL

is

useful

Subsequently

an

attempt

to

validate

the

numerical

model

with

in

vitro

experiments

should

be

made

Eventually

adoption

of

this

information

may

lead

to

a

more

efficient

and

productive

AMC-BAL

in

the

near

future

computational fluid dynamics
acute liver failure
shear stress
fluid flow
oxygen partial pressure
effective hepatocyte utilization ratio
internal oxygenation
external oxygenator

hepatocyte bioreactor
michaelis–menten oxygen consumption