Evaluation

of

Important

Treatment

Parameters

in

Supraphysiological

Thermal

Therapy

of

Human

Liver

Cancer

Cells

This

study

was

aimed

at

simulating

the

effect

of

various

treatment

parameters

like

heating

rate

-LRB-

HR

-RRB-

peak

temperature

-LRB-

PT

-RRB-

and

hold/total

treatment

time

on

the

viability

of

human

liver

cancer

cells

subjected

to

different

thermal

therapy

conditions

The

problem

was

approached

by

investigating

the

injury

kinetics

obtained

using

experimentally

measured

viability

of

the

cells

heated

to

temperatures

of

°C

for

min

at

HRs

of

and

°C

min

An

empirical

expression

obtained

between

the

activation

energy

-LRB-

E

-RRB-

and

HR

was

extended

to

obtain

the

E

values

over

a

broad

range

of

HRs

from

to

°C

min

that

mimic

the

actual

conditions

encountered

in

a

typical

thermal

therapy

protocol

Further

the

effect

of

the

HR

-LRB-

°C

min

-RRB-

and

PT

-LRB-

°C

-RRB-

on

the

cell

survival

was

studied

over

a

range

of

hold

times

A

significant

drop

in

survival

from

to

with

the

simultaneous

increase

in

HR

and

PT

was

observed

as

the

hold

time

increased

from

to

min

For

complete

cell

death

the

hold

time

increased

with

the

increase

in

the

HR

for

a

given

PT

while

the

total

time

showed

presence

of

minima

for

and

°C

at

HRs

of

and

°C

min

respectively

Introduction

Primary

liver

cancer

is

the

fifth

most

common

malignancy

in

the

world

with

a

global

annual

incidence

of

about

one

million

new

patients

In

the

American

Cancer

Society

estimated

new

cases

of

Hepatocellular

Carcinoma

-LRB-

HCC

-RRB-

and

the

estimated

deaths

were

Surgical

resection

the

gold

standard

for

the

treatment

of

primary

liver

cancer

shows

low

success

rate

-LRB-

-RRB-

and

a

high

recurrence

-LRB-

-RRB-

rate

due

to

many

surgical

complications

Liver

transplantation

is

limited

because

of

fewer

donors

Combination

treatment

methods

using

chemotherapy

embolization

and

chemoembolization

have

a

limited

effect

even

with

the

newer

drugs

available

and

their

beneficial

effects

on

the

patient

survival

remain

controversial

in

randomized

studies

Use

of

radiation

therapy

is

limited

to

alleviating

the

symptoms

such

as

pain

or

just

to

shrink

the

tissue

rather

than

destroying

it

Ablation

therapies

that

use

heat

to

destroy

the

tumor

are

gaining

increasing

attention

as

an

alternative

because

the

treatment

procedure

is

faster

simpler

less

painful

and

cheaper

There

are

two

known

approaches

for

the

application

of

these

ablative

procedures

hyperthermia

where

the

treatment

modalities

use

temperatures

ranging

from

to

°C

for

periods

of

min

to

few

hours

Another

approach

is

thermal

therapy

where

the

destruction

of

the

tumor

takes

place

by

the

application

of

heat

at

temperatures

higher

than

°C

within

very

short

time

periods

of

few

minutes

to

seconds

The

tumor

is

heated

using

any

one

of

radiofrequency

microwave

laser

or

high

intensity

focused

ultrasound

energy

sources

Several

clinical

trials

have

been

performed

to

test

the

efficacy

of

these

thermal

ablative

therapies

in

treatment

of

liver

cancer

using

the

above-mentioned

energy

sources

The

results

have

shown

survivals

of

after

year

after

years

after

years

and

after

years

for

hyperthermic

radiofrequency

ablation

in

studies

conducted

on

patients

Survival

of

after

year

in

patients

has

been

reported

for

hyperthermic

interstitial

laser

therapy

survivals

of

after

years

after

years

and

after

have

been

reported

for

microwave

coagulation

therapy

In

spite

of

all

the

above-mentioned

clinical

trials

no

data

exists

showing

the

effect

of

thermal

therapy

on

the

survival

of

liver

cancer

cells

Effect

of

hyperthermic

temperatures

on

human

liver

cancer

cell

lines

has

also

been

investigated

in

few

in

vitro

studies

Callari

et

al.

used

HTC

hepatoma

cells

to

study

the

action

of

retinol

on

viable

cell

recovery

after

in

vitro

hyperthermia

at

temperatures

between

°C

and

°C

for

h.

Hasumura

et

al.

studied

the

effect

of

TNF

along

with

hyperthermia

on

and

human

hepatoma

cells

between

temperatures

of

°C

and

°C

However

of

the

studies

demonstrated

the

effect

of

temperatures

above

°C

any

liver

cancer

cell

lines

Since

in

thermal

therapy

the

injury

accumulates

at

very

high

temperatures

within

a

short

period

of

time

knowledge

of

the

injury

kinetics

is

very

useful

for

predicting

the

cell/tumor

for

these

thermal

histories

Several

thermal

therapy

studies

have

been

performed

to

obtain

the

injury

kinetics

in

different

cell

lines

Landry

et

al.

heated

HeLa

cells

up

to

°C

using

water

bath

with

thermal

equilibrium

time

of

min

for

°C

To

reduce

this

equilibrium

time

Borrelli

et

al.

heated

cells

to

°C

on

thick

mylar

pieces

Cell

injury

kinetics

was

obtained

by

measuring

the

cell

survival

using

clonogenic

assay

in

both

the

studies

In

addition

studies

on

human

bladder

carcinoma

skeletal

muscle

renal

cell

and

Dunning

prostate

cancer

in

the

temperature

range

of

°C

obtained

cell

injury

kinetics

using

dye

uptake

assays

and

thus

showed

that

dye

uptake

assay

is

a

reasonable

conservative

estimate

of

the

cell

survival

Also

two

recent

in

vitro

studies

in

human

benign

prostatic

hyperplasia

tissue

and

rodent

prostate

cancer

tissue

showed

that

the

cell

injury

kinetics

measured

by

membrane

integrity

vital

dye

assay

and

histology

assays

are

very

similar

Therefore

a

key

observation

from

the

above

studies

is

that

vital

dye

uptake

assay

can

be

used

as

an

alternate

and

reliable

conservative

maker

as

it

provides

rapidity

automation

and

better

control

A

key

difference

of

high

temperature

short

time

thermal

therapy

protocols

from

the

traditional

hyperthermia

protocols

is

the

significant

injury

accumulation

during

the

non-isothermal

portion

of

the

thermal

history

-LRB-

heating

up/cooling

down

period

-RRB-

Therefore

injury

accumulation

tends

to

be

a

complex

function

of

hold

time

as

well

ramp

up

and

cooling

time

Hence

accurate

prediction

of

the

cell

injury

kinetics

requires

the

knowledge

of

heating/cooling

rates

in

addition

to

peak

temperatures

-LRB-

PTs

-RRB-

and

hold/total

time

This

model

also

better

represents

the

thermo-clinical

applications

because

the

rate

at

which

the

PTs

are

achieved

at

different

locations

inside

the

tumor

vary

with

the

applicator

location

and

plays

a

paramount

role

in

determining

the

amount

of

injury

accumulated

The

knowledge

of

the

injury

accumulated

in

reaching

a

PT

or

the

PT

required

to

obtain

a

desired

injury

under

different

heating

rates

-LRB-

HRs

-RRB-

are

some

of

the

very

important

parameters

in

designing

better

and

optimal

clinical

protocols

This

study

was

used

to

investigate

experimentally

and

through

simulations

the

parameters

affecting

thermal

therapy

of

primary

human

liver

cancer

cells

between

°C

and

°C

using

uptake

cell

membrane

integrity

assay

The

cells

were

thermally

challenged

on

a

programmable

heating

stage

which

can

control

and

record

the

entire

thermal

history

profile

allowing

us

to

recreate

typical

thermal

therapy

protocols

Cell

membrane

integrity

dye

uptake

-LRB-

-RRB-

was

used

as

an

irreversible

injury

marker

The

first-order

Arrhenius

rate

model

was

used

to

extract

the

kinetic

parameters

activation

energy

E

-LRB-

kJ

mol

-RRB-

and

frequency

factor

A

-LRB-

s

-RRB-

The

survival

data

was

fitted

into

the

Arrhenius

model

for

various

HRs

and

the

E

and

A

values

were

predicted

by

minimizing

the

least

square

between

the

model

predictions

and

the

experimental

data

for

suspended

and

attached

cells

Based

on

the

predicted

E

values

a

relationship

between

the

E

and

HR

was

obtained

experimentally

and

was

further

used

to

simulate

the

survival

map

for

different

hold

periods

by

varying

the

target

PT

and

the

HR

Finally

the

hold

time

and

the

total

injury

time

necessary

for

complete

cell

death

-LRB-

Survival

-RRB-

was

predicted

for

target

PTs

of

°C

and

HRs

of

°C

min

representing

the

typical

transient

thermo-clinical

protocol

Materials

and

methods

Cell

Culture

and

Sample

Preparation

Human

liver

cancer

cells

-LRB-

ATCC

VA

-RRB-

were

propagated

in

MEM

cell

culture

media

with

Fetal

Bovine

Serum

-LRB-

Hyclone

UT

-RRB-

and

penicillin/streptomycin

-LRB-

Invitrogen

CA

-RRB-

They

were

then

incubated

in

and

humidified

air

at

°C

in

T

flasks

The

cells

were

trypsinized

with

Trypsin-EDTA

-LRB-

ATCC

VA

-RRB-

for

min

centrifuged

at

rpm

for

min

and

re-suspended

in

the

media

to

an

appropriate

concentration

Suspended

cell

samples

were

prepared

by

placing

μl

of

cell

suspension

onto

the

center

of

the

diameter

coverglass

covering

it

with

another

coverglass

to

prevent

evaporation

during

heating

For

attached

cell

studies

cell

suspension

was

scattered

over

about

cover

glasses

lying

in

a

diameter

Petri

dish

Overnight

attachment

of

the

cells

on

top

of

the

coverglass

was

allowed

in

the

incubator

and

then

the

cell

sample

was

prepared

in

the

same

way

as

the

suspended

sample

Heating

Stage

Attached

and

suspended

cell

samples

were

heated

on

a

programmable

heating

stage

at

different

HRs

Figure

shows

the

setup

diagram

of

the

heating

stage

and

the

feedback

control

used

Cement

T-type

thermocouple

-LRB-

Omega

Engg

Inc.

CT

-RRB-

was

used

for

temperature

detection

which

is

interfaced

with

a

data

acquisition

board

-LRB-

DAB

-RRB-

-LRB-

Keithly

Inc.

Cleveland

OH

-RRB-

connected

to

the

computer

port

The

interface

between

the

user

and

the

DAB

is

through

a

Visual

Basic

code

that

calculates

the

output

voltage

based

on

the

set

point

and

instantaneous

temperature

and

controls

it

based

on

proportional

and

derivative

constants

used

in

the

feedback

loop

Table

shows

the

combinations

of

proportionality

-LRB-

kp

-RRB-

and

derivative

-LRB-

kd

-RRB-

constants

used

in

the

feedback

loop

to

achieve

different

HRs

-LRB-

and

°C

min

-RRB-

An

OPAMP

-LRB-

Analog

Devices

Inc

MA

-RRB-

circuit

is

used

to

amplify

the

feedback

voltage

signal

from

the

DAB

and

heat

the

stage

The

stage

was

calibrated

using

fixed

temperature

tempi

labels

and

sticks

-LRB-

MSC

Industrial

Supply

Co.

NY

-RRB-

to

an

accuracy

of

°C

for

all

PTs

at

each

HR

used

in

the

study

Figure

Block

diagram

of

the

amplifying

OPAMP

circuit

and

feedback

control

of

the

heating

stage

The

OPAMP

circuit

amplifies

the

voltage

signal

from

the

data

acquisition

board

to

heat

the

stage

while

the

feedback

control

system

through

the

VB

code

controls

the

amount

of

voltage

based

on

the

instantaneous

temperature

of

the

stage.Table

Values

of

proportionality

-LRB-

kp

-RRB-

and

derivative

-LRB-

kd

-RRB-

constants

for

different

HRs

to

obtain

desired

PTs.HR

-LRB-

°C

-RRB-

PT

-LRB-

°C

-RRB-

.01550.0925650.01550.0925700.01550.0925200600.0350.108650.0350.108700.0350.121300600.0850.255650.0850.255700.09030.275

Heating

Studies

and

Dye

Uptake

Assay

Suspended

and

attached

cell

samples

were

heated

to

different

time

temperature

histories

Isothermal

heating

was

carried

out

for

suspended

and

attached

cells

at

temperatures

between

°C

and

°C

for

min

The

cell

sample

was

placed

on

the

center

of

the

heating

stage

after

the

PT

was

reached

The

time

for

each

cell

sample

to

equilibrate

to

any

given

PT

was

experimentally

calculated

to

be

s

and

was

added

to

the

hold

time

during

heating

HRs

of

and

°C

min

were

employed

for

heating

attached

cells

non-isothermally

between

temperatures

of

°C

and

°C

for

a

hold

time

of

min

using

the

entire

temperature

time

history

which

includes

the

rise

hold

and

the

cooling

period

The

HRs

were

assumed

to

be

constant

for

the

entire

thermal

history

and

were

obtained

by

taking

a

tangent

to

the

exponential

curve

of

the

temperature

rise

Therefore

the

cell

sample

was

placed

on

the

center

of

the

heating

stage

before

starting

the

heating

cycle

The

cooling

time

for

each

sample

from

a

given

PT

was

calculated

based

on

the

experimentally

measured

cooling

rate

of

°C

min

Cellular

injury

post

heating

for

isothermal

and

non-isothermal

studies

was

quantified

using

-LRB-

Sigma-Aldrich

MO

-RRB-

vital

dye

assay

by

counting

the

number

of

cells

stained

with

dye

-LRB-

dead

only

-RRB-

and

the

total

number

of

the

cells

stained

with

Hoechst

-LRB-

Sigma-Aldrich

-RRB-

Thermally

treated

cell

samples

were

placed

in

a

μl

drop

of

μM

and

μM

Hoechst

dye

solution

in

a

Petri

dish

and

incubated

for

h

The

incubation

time

of

h

was

based

on

the

experiments

conducted

after

and

h

of

incubation

-LRB-

data

not

included

-RRB-

which

confirmed

that

membrane

damage

equilibrates

within

this

period

and

a

significant

amount

of

media

is

pulled

between

the

cover

glasses

to

stain

the

cells

Control

samples

underwent

the

same

procedure

without

heating

After

h

the

dead

and

the

total

number

of

cells

were

counted

with

a

fluorescent

microscope

-LRB-

Nikon

Eclipse

TS

Tokyo

-RRB-

using

a

objective

Multiple

fields

with

at

least

cells

were

counted

for

each

run

Normalized

Cell

Survival

For

all

the

cell

samples

the

normalized

cell

survival

-LRB-

Se

-RRB-

was

calculated

as

follows

NH

and

NE

are

the

number

of

total

and

dead

cells

stained

with

Hoechst

and

respectively

subscripts

t

and

c

represent

thermally

treated

and

control

cells

respectively

The

calculated

cell

survival

was

based

on

three

separate

experiments

with

two

runs

for

every

data

point

in

each

experiment

The

Cell

Injury

Model

Thermally

induced

cellular

injury

was

considered

as

a

first-order

irreversible

process

as

shown

below

and

as

used

in

many

previous

heating

studies

where

V

represents

the

viable

state

of

a

cell

I

represents

the

injured

state

of

a

cell

and

k

is

the

cell

injury

rate

The

predicted

cell

viability

-LRB-

Sc

-RRB-

was

calculated

using

the

following

equation

δ

is

the

total

treatment

time

-LRB-

s

-RRB-

The

Arrhenius

was

adopted

in

this

study

as

it

has

been

extensively

used

in

previous

studies

to

obtain

the

cell

injury

as

shown

below

A

is

frequency

factor

-LRB-

s

-RRB-

E

is

activation

energy

-LRB-

J

mol

-RRB-

and

R

is

the

universal

gas

constant

-LRB-

J

mol

K

-RRB-

A

and

E

are

related

by

an

empirical

formula

obtained

by

compiling

the

injury

kinetics

of

various

proteins

cells

and

tissues

Determination

of

Arrhenius

Model

Parameters

The

kinetic

parameters

E

and

A

were

determined

by

fitting

Eqs

-LRB-

-RRB-

and

-LRB-

-RRB-

in

Eq

-LRB-

-RRB-

as

obtained

by

He

and

They

were

further

refined

using

a

simple

optimization

subroutine

to

minimize

the

root

mean

square

error

between

the

experimental

data

and

model

prediction

N

is

the

total

number

of

data

points

vector

X

contains

variables

E

and

A.

Se

i

and

Sc

i

represent

the

ith

measured

data

point

and

model

fit

respectively

The

goodness

of

the

fit

-LRB-

-RRB-

is

calculated

as

follows

Sav

is

the

measured

average

survival

from

the

studies

Results

The

results

were

generated

by

counting

the

number

of

total

and

dead

cells

from

the

micrographs

of

the

cell

samples

as

shown

in

Fig.

and

using

Eq

-LRB-

-RRB-

to

calculate

the

normalized

cell

survival

for

each

sample

Figure

b

represent

the

control

sample

where

the

number

of

dead

cells

stained

with

-LRB-

red

-RRB-

dye

is

very

less

compared

to

the

total

number

of

cells

stained

with

Hoechst

-LRB-

blue

-RRB-

dye

and

the

cell

survival

is

higher

than

The

cell

survival

decreases

slightly

as

the

number

of

dead

cells

compared

to

the

total

number

of

cells

increases

for

the

cell

sample

heated

at

°C

for

min

as

shown

in

Fig.

d

The

survival

drops

dramatically

with

a

sharp

increase

in

the

number

of

dead

cells

compared

to

total

cells

at

°C

as

seen

in

Fig.

f.

Figure

Micrographs

showing

cell

samples

stained

with

Hoechst

-LRB-

Blue-all

cells

-RRB-

and

-LRB-

Red-dead

cells

only

-RRB-

-LRB-

a

and

b

-RRB-

control

samples

without

heating

-LRB-

c

and

d

-RRB-

samples

heated

at

°C

for

min

-LRB-

e

and

f

-RRB-

samples

heated

at

°C

for

min

Isothermal

Heating

Studies

The

isothermal

heating

studies

were

used

to

understand

the

effect

of

different

temperature

time

histories

on

the

viability

of

attached

and

suspended

cells

and

to

quantify

the

cellular

injury

associated

with

these

histories

All

the

cell

samples

reached

the

PTs

in

s

at

an

approximate

HR

of

°C

min

resulting

in

a

negligible

difference

between

the

hold

time

and

the

total

time

of

the

treatment

Thus

heating

at

the

rate

of

°C

min

was

referred

as

isothermal

heating

The

data

in

Fig.

b

represents

the

mean

and

the

standard

error

for

measured

cell

viability

of

attached

and

suspended

cells

respectively

using

dye

uptake

assay

Both

the

figures

show

that

for

a

given

PT

the

survival

drops

with

the

increase

in

the

hold

time

At

°C

the

survival

drops

from

to

for

suspended

cells

and

from

to

for

attached

cells

as

the

hold

time

increases

from

to

min

Similar

trend

was

observed

for

heating

at

all

the

PTs

The

figures

also

show

that

for

a

given

hold

time

the

cell

survival

drops

with

the

increase

in

the

PT

for

suspended

cells

For

a

hold

time

of

min

the

cell

survival

drops

from

to

and

from

to

as

the

PT

increases

from

°C

to

°C

and

from

°C

to

°C

respectively

For

a

hold

time

of

min

the

cell

survival

drops

from

to

and

from

to

as

the

PT

increases

for

°C

to

°C

and

from

°C

to

°C

respectively

The

same

trend

is

also

seen

for

the

attached

cells

but

with

slightly

higher

survival

Figure

-LRB-

a

-RRB-

Plot

of

experimentally

measured

and

predicted

survival

of

attached

cells

heated

isothermally

versus

hold

time

in

minutes

for

single

cell

heating

at

PTs

of

and

°C

Cross

-LRB-

-RRB-

filled

circles

-LRB-

-RRB-

filled

diamonds

-LRB-

-RRB-

filled

squares

-LRB-

-RRB-

and

filled

triangles

-LRB-

-RRB-

represents

heating

of

samples

at

and

°C

respectively

The

lines

represent

the

exponential

fit

through

all

the

data

points

based

on

the

predicted

E

and

A

values

-LRB-

b

-RRB-

Plot

of

experimentally

measured

and

predicted

survival

of

suspended

cells

heated

isothermally

versus

hold

time

in

minutes

for

single

cell

heating

at

PTs

of

and

°C

Cross

-LRB-

-RRB-

filled

circles

-LRB-

-RRB-

filled

diamonds

-LRB-

-RRB-

filled

squares

-LRB-

-RRB-

and

filled

triangles

-LRB-

-RRB-

represents

heating

of

samples

at

and

°C

respectively

The

lines

represent

the

exponential

fit

through

all

the

data

points

based

on

the

predicted

E

and

A

values

-LRB-

c

-RRB-

Direct

comparison

between

suspended

and

attached

cell

viability

using

student

t-test

assuming

unequal

variance

Each

data

point

is

an

average

of

three

separate

runs

using

two

different

cell

samples

for

each

run

The

error

bar

in

the

figure

represents

the

standard

error

of

the

mean

Data

points

marked

with

asterisks

indicate

the

data

points

where

viability

of

suspended

and

attached

cells

is

significantly

different

The

figures

also

show

the

effect

of

PTs

on

the

slope

of

the

survival

curve

The

drop

in

the

survival

with

the

increase

in

the

hold

time

is

slow

at

low

PTs

The

survival

curve

gets

steeper

as

the

PT

increases

When

heated

at

°C

for

up

to

min

the

cell

survival

is

still

higher

than

for

both

suspended

and

attached

cells

This

trend

changes

for

°C

where

the

cell

survival

drops

to

after

only

min

of

heating

This

trend

magnifies

sharply

as

the

PTs

increases

to

and

°C

For

suspended

cells

the

survival

at

°C

varies

from

to

almost

zero

survival

as

the

hold

time

increases

from

to

min

The

survival

dropped

from

to

for

an

increase

in

the

hold

time

from

s

to

a

min

at

°C

The

attached

cells

also

showed

a

similar

trend

with

slightly

higher

survival

than

the

suspended

cells

for

all

the

data

points

The

student

t-test

assuming

unequal

variance

was

used

to

observe

the

statistical

significance

between

the

experimentally

measured

cell

viability

of

suspended

and

attached

cells

as

shown

in

Fig.

With

p

as

the

criterion

no

significant

difference

in

the

cell

viability

was

observed

for

most

of

the

data

points

The

data

points

that

were

significantly

different

-LRB-

p

-RRB-

are

°C

min

°C

min

°C

min

and

°C

min

This

difference

for

data

points

of

°C

min

and

°C

min

can

be

neglected

as

the

experimentally

calculated

cell

viability

in

suspended

and

attached

for

both

these

thermal

insults

is

of

the

order

The

p-value

of

for

°C

min

data

point

suggests

the

difference

in

the

cell

viability

is

not

significant

but

is

still

different

As

no

significant

difference

between

the

survival

of

suspended

and

attached

cells

was

observed

for

most

of

the

time

temperature

histories

and

since

attached

cells

better

describe

the

arrangement

of

the

cells

in

a

tissue

only

attached

cells

were

used

for

further

non-isothermal

studies

The

parameters

of

cell

injury

E

and

A

were

obtained

by

fitting

the

Arrhenius

rate

model

into

the

survival

data

This

was

done

by

minimizing

the

function

in

Eq

-LRB-

-RRB-

using

Eqs

-LRB-

-RRB-

and

-LRB-

-RRB-

The

predicted

E

and

A

values

for

suspended

and

attached

cells

for

isothermal

heating

are

shown

in

Table

The

E

and

A

values

obtained

for

suspended

cells

are

-LRB-

kJ

mol

-RRB-

and

-LRB-

s

-RRB-

and

those

for

attached

cells

are

-LRB-

kJ

mol

-RRB-

and

-LRB-

s

-RRB-

respectively

The

predicted

survival

based

on

the

predicted

E

and

A

values

for

attached

and

suspended

cells

is

shown

by

the

solid

lines

in

Fig.

b

respectively

The

goodness

of

the

fit

between

the

predicted

and

experimentally

measured

values

obtained

using

Eq

-LRB-

-RRB-

for

suspended

and

attached

cells

is

and

respectively

Table

Activation

energy

E

-LRB-

kJ

mol

-RRB-

and

frequency

factor

A

-LRB-

s

-RRB-

using

all

the

data

point

for

different

HRs.HR

-LRB-

°C

min

-RRB-

Activation

energy

E

-LRB-

kJ

mol

-RRB-

Frequency

factor

A

-LRB-

-RRB-

-LRB-

Isothermal

Attached

-RRB-

-LRB-

Isothermal

Suspended

-RRB-

Non-Isothermal

Heating

Studies

The

study

focused

next

on

the

investigation

of

the

effect

of

different

HRs

on

the

cell

viability

of

attached

cells

and

extraction

of

kinetic

parameters

of

the

cellular

injury

associated

with

each

HR

The

HRs

of

and

°C

min

were

employed

in

this

study

as

they

all

showed

a

considerable

difference

in

the

rise-time

at

all

the

PTs

The

total

injury

time

-LRB-

rise

hold

and

cooling

time

-RRB-

was

taken

into

account

to

quantify

the

thermal

injury

for

all

the

HRs

The

data

in

Fig.

c

represents

the

mean

and

the

standard

error

of

the

measured

cell

viability

using

dye

uptake

assay

for

attached

cells

at

HRs

of

and

°C

min

respectively

All

the

figures

show

that

for

a

given

HR

the

cell

survival

drops

with

the

increase

in

the

hold

time

and

the

PT

similar

to

that

observed

in

isothermal

heating

At

the

HR

of

C

min

the

survival

drops

from

for

no

hold

time

to

for

a

hold

time

of

min

for

a

PT

of

°C

This

trend

remains

the

same

for

the

PTs

of

°C

and

°C

and

for

all

the

HRs

The

survival

drops

from

at

°C

to

at

°C

and

further

to

at

°C

for

no

hold

time

at

HR

of

°C

min

This

trend

continues

for

all

the

HRs

and

at

all

the

hold

times

The

figures

also

illustrates

that

for

any

given

PT

and

for

a

given

hold

time

the

cell

survival

increases

with

the

increase

in

the

HR

At

°C

for

no

hold

time

the

survival

increases

from

at

°C

min

to

at

°C

min

and

further

to

at

°C

min

At

°C

for

a

hold

time

of

min

the

survival

increases

from

at

°C

min

to

at

°C

min

and

then

to

at

°C

min

This

trend

also

continues

for

°C

for

any

given

hold

time

Figure

Plot

of

experimentally

measured

and

predicted

survival

of

attached

cells

heated

at

various

heating

rates

versus

time

in

minutes

for

single

cell

heating

at

temperature

°C

-LRB-

a

-RRB-

°C

min

-LRB-

b

-RRB-

°C

min

-LRB-

c

-RRB-

°C

min

Filled

diamonds

-LRB-

-RRB-

filled

squares

-LRB-

-RRB-

and

filled

triangles

-LRB-

-RRB-

represents

heating

of

samples

at

and

°C

respectively

The

lines

represent

the

exponential

fit

through

all

the

data

points

based

on

the

predicted

E

and

A

values

A

trend

was

observed

in

the

Arrhenius

parameters

obtained

from

the

non-isothermal

heating

studies

as

the

E

and

the

corresponding

A

value

decreased

with

the

increase

in

the

HR

Table

shows

the

predicted

E

and

A

values

for

HRs

of

and

°C

min

The

activation

energy

decreases

from

kJ

mol

at

°C

min

to

kJ

mol

at

°C

min

and

then

to

kJ

mol

at

°C

min

The

solid

lines

in

the

Fig.

c

represent

the

predicted

cell

survival

based

on

above

values

respectively

The

goodness

of

fit

between

the

predicted

and

measured

cell

survival

for

all

data

points

obtained

using

Eq

-LRB-

-RRB-

is

for

all

the

HRs

used

in

this

study

Figure

Plot

of

the

normalized

survival

of

attached

cells

for

various

hold

times

at

different

peak

temperatures

and

heating

rates

based

on

the

predicted

E

and

A

values

-LRB-

a

-RRB-

min

-LRB-

b

-RRB-

min

-LRB-

c

-RRB-

min

-LRB-

d

-RRB-

min

Relation

Between

Activation

Energy

and

HRs

The

following

relation

was

obtained

by

fitting

a

polynomial

trend

line

through

the

data

in

Table

that

includes

the

isothermal

heating

at

°C

min

E

represents

the

activation

energy

and

HR

represents

the

HR

The

above

equation

was

then

used

to

obtain

the

values

of

activation

energy

over

a

range

of

HRs

from

to

°C

min

in

order

to

simulate

the

effects

of

various

parameters

on

the

cell

survival

The

values

of

the

activation

energy

shows

a

small

decrease

from

to

kJ

mol

over

a

large

increase

in

the

HR

increased

from

to

°C

min

Effects

of

PTs

HRs

and

Hold

Time

on

the

Cell

Survival

Based

on

the

E

and

A

values

obtained

at

HRs

of

°C

min

using

the

E

HR

relation

the

cell

survival

was

predicted

at

different

hold

times

for

PTs

between

°C

and

°C

The

combined

effect

of

the

increase

in

the

hold

time

and

PT

on

the

cell

survival

is

shown

in

the

Fig.

d

for

all

the

HRs

mentioned

above

For

a

given

hold

time

and

HR

the

cell

survival

drops

consistently

with

the

increase

in

the

PT

For

a

HR

of

°C

min

the

cell

survival

drops

from

at

°C

to

at

°C

and

then

to

no

cell

survival

at

temperature

above

°C

when

the

hold

time

is

min

The

trend

remains

the

same

for

any

HR

and

hold

time

combination

The

drop

in

the

cell

survival

for

any

hold

time

is

lower

when

the

PTs

are

°C

and

less

The

survival

drops

slightly

from

at

°C

to

at

°C

for

heating

at

°C

min

for

a

hold

time

of

min

This

drop

is

higher

from

to

when

the

temperature

increases

to

°C

This

trend

is

magnified

with

the

increase

in

the

PT

to

°C

where

the

survival

drops

to

and

to

almost

complete

cell

destruction

for

a

further

°C

rise

in

the

PT

At

any

given

hold

time

and

PT

the

cell

survival

increases

with

the

increase

in

the

HR

The

survival

increased

from

to

at

°C

for

a

hold

time

of

min

and

from

to

for

a

hold

time

of

min

at

°C

as

the

HR

increased

from

to

°C

min

For

a

given

PT

and

a

HR

the

cell

survival

drops

with

the

increase

in

the

hold

time

At

°C

and

°C

min

the

cell

survival

drops

from

to

when

the

hold

time

increases

from

to

min

For

the

same

increase

in

the

hold

time

the

survival

drops

from

to

zero

at

°C

and

°C

min

For

any

hold

time

almost

complete

cell

destruction

takes

place

at

all

the

HRs

when

the

PTs

are

°C

and

above

For

HRs

of

°C

min

and

lower

the

PT

to

acquire

almost

complete

cell

death

decreases

with

the

increase

in

hold

time

For

zero

hold

time

°C

shows

a

survival

of

and

less

for

HRs

of

°C

min

and

less

When

the

hold

time

is

min

complete

cell

death

is

observed

at

°C

for

all

the

HRs

below

°C

min

and

at

°C

for

HR

of

°C

min

The

survival

at

°C

decreases

considerably

with

hold

time

at

these

low

HRs

but

is

still

significantly

high

-LRB-

-RRB-

while

the

survival

at

°C

shows

a

very

less

drop

For

a

HR

of

°C

min

the

survival

at

°C

drops

from

to

with

the

increase

in

the

hold

time

from

to

min

At

°C

this

drop

is

from

to

This

trend

is

depicted

in

Fig.

d

as

the

drop

in

the

slope

of

the

vertical

portion

with

the

increase

in

the

hold

time

Hold

and

Total

Injury

Time

for

Complete

Cell

Destruction

The

relationship

between

activation

energies

and

HRs

was

further

used

to

predict

the

hold

time

and

total

injury

time

required

to

attain

complete

cell

destruction

at

different

target

PTs

and

HRs

that

represents

different

scenarios

of

a

clinical

thermal

therapy

protocol

Figure

b

shows

the

calculated

hold

time

and

total

time

in

minutes

resulting

in

complete

cell

death

at

target

PTs

between

°C

and

°C

and

HRs

between

and

°C

min

which

represents

the

transient

clinical

problem

strictly

under

thermal

therapy

conditions

Figure

-LRB-

a

-RRB-

Plot

of

hold

time

in

minutes

to

attain

complete

destruction

of

attached

cells

at

various

PTs

between

°C

and

°C

and

at

HRs

from

to

°C

min

-LRB-

b

-RRB-

Plot

of

total

time

-LRB-

min

-RRB-

to

attain

complete

destruction

of

attached

cells

at

various

PTs

between

°C

and

°C

and

at

HRs

from

to

°C

min

Figure

shows

that

for

a

given

target

PT

the

hold

time

increases

with

the

increase

in

the

HRs

It

increases

from

to

min

from

to

min

from

to

min

from

to

min

and

from

to

min

at

a

target

PT

of

and

°C

respectively

The

increase

in

the

hold

is

negligible

at

°C

Further

the

hold

time

decreases

with

the

increase

in

target

PT

for

any

given

HR

At

°C

min

the

hold

time

for

complete

cell

destruction

decreases

from

min

at

°C

to

min

at

°C

For

very

low

HRs

of

and

°C

min

complete

cell

destruction

is

achieved

for

target

PTs

of

°C

and

above

without

any

hold

time

Similarly

no

hold

time

is

required

when

the

target

PTs

are

°C

and

above

at

°C

min

and

°C

and

above

at

°C

min

Heating

targeted

at

PTs

of

°C

and

°C

kills

all

the

cells

without

any

hold

period

for

any

of

the

above

used

HR

These

results

demonstrate

that

significant

cell

death

takes

place

during

the

ramp

up

and

ramp

down

period

Figure

shows

the

variation

in

the

total

injury

time

-LRB-

rise

hold

and

cooling

time

-RRB-

to

achieve

complete

cell

destruction

with

the

change

in

the

target

PTs

and

HRs

For

and

°C

the

total

injury

time

showed

a

minima

with

the

decrease

in

the

HR

For

example

the

total

time

at

the

target

PT

of

°C

decreases

from

for

°C

min

to

for

°C

min

and

then

again

increases

to

min

for

°C

min

At

°C

the

total

time

decreases

from

min

to

min

and

then

increases

to

min

for

a

decrease

of

HR

from

to

°C

min

and

again

to

°C

min

respectively

The

trend

remains

the

same

at

°C

the

transition

of

hold

time

being

at

a

higher

rate

of

°C

min

For

target

PTs

of

and

°C

this

trend

reverses

as

the

total

injury

time

consistently

increases

with

the

decrease

in

the

HR

unlike

for

all

other

target

PTs

The

total

time

increased

almost

twice

from

and

at

and

°C

respectively

as

the

HR

dropped

from

to

°C

min

For

the

target

PTs

-LRB-

°C

to

°C

-RRB-

where

no

hold

time

is

required

to

attain

complete

cell

death

total

injury

time

was

obtained

as

and

min

at

HRs

of

and

°C

min

respectively

The

trend

in

the

change

of

the

total

injury

time

with

change

in

target

PT

for

any

given

HR

remains

the

same

as

that

for

the

hold

time

Discussion

Injury

Kinetics

of

Attached

and

Suspended

Cells

The

comparison

of

the

survival

data

for

the

suspended

and

the

attached

cells

-LRB-

Fig.

b

-RRB-

indicate

that

the

suspended

cells

are

a

slightly

more

susceptible

to

heat

than

the

attached

ones

He

and

also

obtained

similar

results

for

human

renal

cell

carcinoma

within

the

same

temperature

range

where

the

reason

for

this

difference

between

suspended

and

attached

cells

was

assumed

to

be

the

difference

in

their

protein

synthesis

and

gene

expression

It

may

be

assumed

that

some

of

the

above

differences

also

exist

between

attached

and

suspended

cells

used

in

this

study

The

results

shows

a

clear

difference

between

the

frequency

factors

for

both

the

cell

types

but

the

activation

energies

does

not

show

much

variation

But

since

the

difference

in

the

survival

of

suspended

and

attached

cells

is

small

either

of

the

cell

type

can

be

used

in

studying

the

cell

injury

kinetics

in

cells

Comparison

with

Previous

Hyperthermic

Studies

Hyperthermic

studies

are

mainly

characterized

by

the

presence

of

a

shoulder

region

followed

a

slope

in

the

survival

curve

In

these

studies

the

shoulder

region

is

typically

associated

with

considerably

higher

-LRB-

-RRB-

cell

survival

within

a

long

heating

period

of

few

hours

and

has

been

observed

in

the

temperature

range

of

°C

in

many

studies

Chinese

hamster

ovary

-LRB-

CHO

-RRB-

cells

showed

a

small

-LRB-

-RRB-

drop

in

the

survival

followed

by

reduction

in

the

slope

of

the

survival

curve

when

heated

at

°C

for

h.

Human

melanoma

cells

when

heated

between

°C

and

°C

also

showed

a

considerably

high

survival

-LRB-

-RRB-

followed

by

reduction

in

the

slope

at

°C

even

after

h

of

heating

In

this

study

heating

at

°C

for

min

-LRB-

data

not

included

-RRB-

and

at

°C

for

min

also

shows

a

significantly

higher

-LRB-

-RRB-

survival

for

attached

and

suspended

cells

indicating

the

possibility

of

a

shoulder

region

for

these

short

time

protocols

However

whether

they

biologically

behave

in

a

similar

fashion

to

the

hyperthermic

shoulders

by

demonstrating

thermotolerance

has

not

been

studied

and

further

investigation

is

clearly

warranted

to

verify

these

facts

Another

important

aspect

of

the

single

cell

heating

studies

is

the

presence

of

a

break

point

after

which

the

slope

of

the

Arrhenius

plot

drops

significantly

with

the

increasing

temperature

The

break

point

is

believed

to

be

the

indication

of

an

achieved

thermotolerance

and

change

in

the

mechanism/target

of

the

thermally

induced

cellular

injury

beyond

it

Such

break

points

have

been

observed

at

°C

for

human

cell

lines

and

°C

for

rodent

cell

lines

We

have

observed

no

significant

break

point

for

our

studies

between

temperatures

of

°C

However

one

interesting

observation

in

our

study

was

that

heating

at

°C

for

min

for

attached

and

suspended

cells

shows

a

sudden

change

in

the

slope

of

the

survival

curve

The

survival

drops

from

at

min

to

after

min

of

heating

suggesting

the

possibility

of

a

distinct

change

in

the

response

to

heating

at

°C

for

cells

Comparison

of

Arrhenius

Parameters

This

study

shows

a

linear

relationship

between

activation

energies

and

HRs

for

a

temperature

range

of

°C

The

activation

energies

between

kJ

mol

and

kJ

mol

were

obtained

for

HRs

of

°C

min

which

are

within

the

range

of

the

activation

energies

obtained

in

most

of

the

dye

uptake

assays

Thermal

injury

in

Dunning

attached

prostate

cancer

cells

from

°C

to

°C

gave

activation

energy

of

kJ

mol

Activation

energy

values

obtained

in

renal

cell

carcinoma

studies

are

kJ

mol

and

in

skeletal

muscle

tissue

is

kJ

mol

The

activation

energies

for

clonogenic

assays

for

various

studies

like

prostate

cancer

cells

-LRB-

°C

-RRB-

human

bladder

carcinoma

cells

-LRB-

°C

-RRB-

and

CHO

-LRB-

°C

-RRB-

were

found

to

be

and

kJ

mol

respectively

These

values

are

higher

than

the

ones

obtained

in

this

study

which

is

not

surprising

since

clonogenic

assay

yields

higher

activation

energies

than

dye

uptake

assays

Since

the

activation

energies

obtained

in

this

study

are

in

the

same

range

of

the

values

obtained

for

other

dye

uptake

assays

we

suggest

that

the

mechanism

of

thermal

injury

and

its

measurement

is

consistent

with

other

studies

Clinical

Relevance

Clinical

thermal

therapy

is

a

transient

conduction

problem

as

the

tumor

gets

heated

by

deposition

of

energy

from

the

source

and

by

diffusion

of

the

heat

from

the

applicator

Based

on

the

size

and

heat

absorption

pattern

of

the

tumor

different

radial

locations

are

heated

to

different

PTs

at

different

rates

The

regions

closer

to

the

applicator

gets

heated

to

higher

PTs

at

higher

HRs

than

the

ones

that

are

further

away

resulting

in

different

survival

patterns

at

various

locations

inside

the

tumor

Thus

accurate

prediction

of

the

hold

time

of

the

applicator

inside

the

tumor

is

very

important

to

ensure

desired

cellular

injury

accumulation

at

every

location

As

in

these

high

temperature

short

time

thermal

therapy

protocols

a

considerable

-LRB-

-RRB-

injury

accumulates

within

the

non-isothermal

portion

of

the

thermal

history

the

determination

of

the

total

treatment

time

-LRB-

rise

hold

and

cooling

-RRB-

is

also

necessary

to

obtain

desired

injury

accumulation

Since

the

maximum

size

of

a

liver

tumor

that

can

be

treated

using

various

energy

sources

is

limited

to

cm

diameter

the

HRs

between

°C

min

and

°C

min

are

representative

of

all

the

locations

within

the

tumor

for

any

selected

energy

source

while

the

temperatures

between

°C

and

°C

are

descriptive

of

the

actual

temperature

distribution

inside

the

tumor

during

the

thermal

application

Temperatures

higher

than

°C

might

result

in

carbonization

near

the

applicator

as

well

as

overheating

of

the

healthy

tissue

beyond

the

edge

of

the

tumor

while

temperatures

lower

than

°C

may

result

in

insufficient

injury

accumulation

within

the

short

treatment

time

Therefore

design

of

clinical

thermal

therapy

protocols

requires

knowledge

of

the

survival

patterns

for

different

hold

times

and

precise

prediction

of

hold

and

total

treatment

times

to

obtain

desired

cellular

injury

within

the

above

mentioned

range

of

HRs

and

PTs

Such

an

attempt

has

been

made

in

a

previous

study

carried

out

by

He

and

on

renal

cell

carcinoma

The

cell

injury

kinetics

based

on

the

non-isothermal

heating

at

an

average

rate

of

°C

min

were

used

to

predict

the

PTs

necessary

to

obtain

a

considerable

-LRB-

-RRB-

amount

of

cellular

injury

in

cells

during

the

rise

period

This

prediction

was

extended

to

various

HR

activation

energy

combinations

just

by

selecting

HRs

between

°C

min

and

°C

min

and

activation

energies

up

to

kJ

mol

However

experimental

calculations

to

determine

E

as

a

function

of

HRs

was

not

included

in

above

study

The

unique

feature

of

this

study

is

that

for

all

PTs

prediction

of

survival

and

treatment

time

at

any

given

HR

is

based

on

a

specific

experimentally

calculated

E

A

combination

for

that

HR

which

results

in

a

close

approximation

of

the

actual

cellular

injury

for

these

high

temperatures-short

time

thermal

treatments

An

important

assumption

made

in

this

study

is

that

the

HR

used

to

attain

a

target

PT

remains

constant

The

temperature

rise

on

the

heating

stage

based

on

the

constants

kp

and

kd

in

the

feedback

loop

was

found

to

be

exponential

The

HR

was

approximated

by

taking

a

tangent

to

the

temperature

time

curve

resulting

in

a

constant

value

for

the

entire

temperature

rise

However

inside

a

tumor

the

bioheat

equation

is

required

to

model

the

transient

temperature

rise

which

is

rarely

linear

But

as

an

initial

step

in

understanding

the

effect

of

important

parameters

governing

thermal

therapy

this

assumption

may

be

a

good

approximation

to

predict

desired

cellular

injury

and

Figs.

and

may

provide

important

insights

in

this

direction

The

predicted

survival

at

different

hold

times

in

Fig.

d

shows

that

for

any

HR

the

PT

required

to

attain

a

considerable

amount

of

injury

accumulation

-LRB-

-RRB-

decreases

as

the

hold

time

increases

A

smaller

flat

portion

representing

complete

cell

death

and

the

steeper

vertical

portion

representing

considerable

-LRB-

-RRB-

survival

for

zero

hold

time

in

Fig.

intersects

at

°C

and

complete

cell

death

is

observed

for

HRs

of

°C

min

and

lower

This

suggests

that

for

HRs

of

°C

min

and

lower

typically

at

the

boundary

of

the

tumor

PTs

of

only

°C

and

above

are

capable

of

accumulating

significant

amount

of

injury

This

information

is

helpful

in

developing

treatment

protocols

for

small

sized

tumors

where

the

use

of

high

target

PTs

will

not

significantly

damage

the

healthy

tissue

beyond

the

range

of

the

tumor

even

though

the

temperatures

at

those

locations

are

higher

than

°C

As

the

hold

time

increases

the

intersection

shifts

toward

lower

PTs

increasing

the

flat

portion

of

complete

cell

destruction

The

decrease

in

steepness

of

the

vertical

portion

also

implies

that

sufficient

cell

damage

can

be

obtained

at

tumor

boundaries

at

these

low

temperatures

For

example

when

the

hold

time

is

min

more

than

survival

is

observed

even

at

°C

at

the

boundary

of

the

tumor

where

the

HR

is

as

low

as

°C

min

This

shows

that

thermal

protocols

with

higher

hold

times

are

beneficial

for

cell

injury

in

large

size

tumors

Since

it

is

necessary

that

the

intersection

should

coincide

with

the

tumor

boundary

to

maximize

the

damage

within

the

tumor

as

well

as

minimize

the

damage

of

the

surrounding

healthy

tissue

the

contours

obtained

in

Fig.

d

are

very

important

in

the

selection

of

the

hold

times

based

on

the

size

of

the

tumor

Since

the

goal

of

every

clinical

application

is

complete

tumor

destruction

it

is

very

important

to

know

the

hold

time

required

to

destroy

all

the

tumor

cells

for

different

PT

HR

combinations

-LRB-

that

may

represent

different

regions

within

a

tumor

depending

upon

its

geometry

and

the

energy

source

used

-RRB-

Figure

shows

the

hold

time

necessary

to

acquire

complete

damage

in

attached

cells

at

PTs

between

°C

and

°C

and

HRs

between

°C

min

and

°C

min

and

suggests

that

the

hold

time

increases

with

the

simultaneous

decrease

in

the

PT

and

the

HR

Therefore

as

the

distance

from

the

applicator

increases

decreasing

the

PT

and

the

HR

the

hold

time

for

tumor

destruction

increases

For

example

Fig.

shows

that

the

hold

time

increases

from

almost

zero

at

°C

°C

min

to

min

at

°C

°C

min

Significant

increase

in

the

hold

time

for

PTs

of

°C

and

°C

suggests

that

in

the

regions

away

from

the

applicator

-LRB-

HRs

of

°C

min

and

lower

-RRB-

the

injury

accumulation

strongly

depends

on

the

hold

time

However

the

hold

time

is

very

less

for

PTs

of

°C

and

above

even

at

high

HRs

and

decreases

to

almost

zero

as

the

HR

decreases

suggesting

that

the

majority

of

the

cell

damage

at

these

temperatures

occurs

just

within

the

rise

and

cooling

period

At

°C

and

above

for

HRs

of

°C

min

and

lower

the

hold

time

completely

vanishes

and

the

thermally

induced

cellular

injury

is

just

a

function

of

the

non-isothermal

portion

of

the

thermal

history

Therefore

it

is

necessary

to

investigate

the

variation

in

the

total

treatment

time

-LRB-

rise

hold

and

cooling

-RRB-

to

attain

complete

cellular

destruction

at

various

PT

HR

combinations

Figure

shows

the

variation

in

the

total

treatment

time

based

on

the

temperature

distribution

within

the

tumor

depending

upon

its

geometry

and

the

energy

source

used

For

PTs

of

°C

and

above

unlike

hold

time

the

total

treatment

time

increases

with

the

decrease

in

the

HR

This

is

due

to

the

fact

that

for

HRs

above

°C

min

the

hold

time

is

very

small

and

negligible

compared

to

the

rise

time

to

reach

these

high

PTs

and

the

time

to

cool

down

back

to

the

room

temperature

It

was

also

observed

that

for

a

given

target

PT

-LRB-

°C

-RRB-

HR

-LRB-

°C

min

-RRB-

combination

where

the

hold

time

is

zero

the

total

treatment

time

is

lower

than

the

calculated

time

This

suggests

that

if

damage

within

a

tumor

is

desired

at

very

slower

rate

at

PTs

higher

than

°C

the

tumor

actually

gets

destroyed

before

even

reaching

the

target

PT

at

any

location

But

the

interesting

observation

in

Fig.

is

the

presence

of

a

minimal

total

treatment

time

at

PTs

of

and

°C

for

HRs

of

and

°C

min

respectively

This

implies

that

based

on

the

size

of

the

tumor

and

the

energy

source

selected

if

the

temperature

distribution

within

the

tumor

results

in

any

of

the

above

PT

HR

combinations

at

the

boundary

complete

cell

death

can

be

achieved

in

the

entire

tumor

within

a

minimal

total

treatment

time

For

example

if

the

temperature

distribution

is

such

that

the

boundary

of

the

tumor

reaches

°C

at

°C

min

the

entire

tumor

can

be

destroyed

in

min

Thus

based

on

the

size

of

the

tumor

Fig.

b

may

help

in

selecting

hold

and

total

treatment

time

in

order

to

design

an

optimal

clinical

protocol

Since

this

study

is

based

on

experimental

single

cell

data

to

obtain

the

activation

energies

at

different

HR

it

can

serve

as

an

accurate

model

for

designing

better

thermo-surgical

protocols

using

appropriate

energy

sources

of

heat

delivery

Also

for

a

clinician

practicing

the

technique

it

can

serve

as

a

database

from

where

an

optimal

thermal

therapy

protocol

can

be

selected

for

the

treatment

of

liver

cancer

By

selecting

appropriate

blood

flow

and

tissue

properties

and

by

using

the

bioheat

equation

this

in

vitro

protocol

can

be

extended

to

in

vivo

clinical

protocols

Summary

The

investigation

of

injury

kinetics

in

human

liver

cancer

cells

between

temperatures

of

°C

and

°C

at

HRs

of

and

°C

min

-LRB-

isothermal

-RRB-

was

used

to

extract

Arrhenius

parameters

E

and

A

that

showed

a

minor

decay

with

the

increase

in

the

HR

The

extrapolation

of

the

kinetic

parameters

over

a

range

of

heating

conditions

showed

that

the

E

value

decreased

from

to

kJ

mol

as

the

HR

increases

from

to

°C

min

The

measured

and

the

predicted

survival

at

all

the

HRs

dropped

as

the

PT

and

hold

time

increased

A

sharp

drop

in

the

survival

was

observed

after

min

of

heating

at

°C

for

all

HRs

The

measured

and

predicted

cell

survival

increased

with

the

increase

in

the

HR

at

any

PTs

and

hold

time

This

increase

in

the

survival

reduced

significantly

for

target

PTs

of

°C

and

above

and

for

hold

times

of

a

minute

and

higher

The

hold

time

for

complete

cell

damage

decreases

with

the

increase

in

the

target

PT

and

increases

with

the

increase

in

the

HR

No

hold

time

is

required

for

target

PTs

of

°C

and

above

with

the

decrease

in

the

HR

below

°C

min

The

cellular

damage

is

a

dominant

function

of

hold

time

at

target

PTs

of

°C

and

less

and

for

HRs

of

°C

min

and

higher

Total

time

-LRB-

rise

hold

and

cooling

time

-RRB-

plays

a

major

role

in

accumulating

the

cellular

injury

when

the

temperatures

are

°C

and

above

and

when

the

HRs

are

between

°C

min

and

°C

min

Minimal

total

treatment

time

for

complete

cellular

damage

was

observed

at

target

PTs

of

and

°C

and

HRs

of

and

°C

min

respectively

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O 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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O 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O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

heating rates
peak temperatures
hold time
total treatment time
injury kinetics
arrhenius model
clinical protocols