Automatic

Regulation

of

Hemodynamic

Variables

in

Acute

Heart

Failure

by

a

Multiple

Adaptive

Predictive

Controller

Based

on

Neural

Networks

Automated

drug-delivery

systems

that

can

tolerate

various

responses

to

therapeutic

agents

have

been

required

to

control

hemodynamic

variables

with

heart

failure

This

study

is

intended

to

evaluate

the

control

performance

of

a

multiple

adaptive

predictive

control

based

on

neural

networks

-LRB-

MAPCNN

-RRB-

to

regulate

the

unexpected

responses

to

therapeutic

agents

of

cardiac

output

-LRB-

CO

-RRB-

and

mean

arterial

pressure

-LRB-

MAP

-RRB-

in

cases

of

heart

failure

The

NN

components

in

the

MAPCNN

learned

nonlinear

responses

of

CO

and

MAP

determined

by

hemodynamics

of

dogs

with

heart

failure

The

MAPCNN

performed

ideal

control

against

unexpected

-LRB-

-RRB-

drug

interactions

-LRB-

-RRB-

acute

disturbances

and

-LRB-

-RRB-

time-variant

responses

of

hemodynamics

-LSB-

average

errors

between

setpoints

-LRB-

ml

kg

min

in

CO

and

mmHg

in

MAP

-RRB-

and

observed

responses

and

ml

kg

min

in

CO

and

and

mmHg

-LRB-

and

mmHg

without

a

vasodilator

-RRB-

in

MAP

-RSB-

during

closed-loop

control

The

MAPCNN

could

also

regulate

the

hemodynamics

in

actual

heart

failure

of

a

dog

Robust

regulation

of

hemodynamics

by

the

MAPCNN

was

attributable

to

the

ability

of

on-line

adaptation

to

adopt

various

responses

and

predictive

control

using

the

NN

Results

demonstrate

the

feasibility

of

applying

the

MAPCNN

using

a

simple

NN

to

clinical

situations

INTRODUCTION

Hemodynamic

variables

in

a

critical

care

patient

with

heart

failure

must

be

monitored

during

and

after

cardiac

surgery

The

hemodynamic

conditions

must

then

be

regulated

using

infusion

of

several

drugs

In

particular

cardiac

output

-LRB-

CO

-RRB-

and

mean

arterial

pressure

-LRB-

MAP

-RRB-

are

primary

target

variables

because

increased

CO

is

required

with

suppressing

myocardial

oxygen

consumption

and

MAP

must

be

kept

at

the

lowest

level

that

can

adequately

maintain

coronary

circulation

with

decreasing

systemic

vascular

resistance

-LRB-

SVR

-RRB-

Combined

infusion

of

an

inotropic

agent

such

as

dobutamine

-LRB-

DBT

-RRB-

or

dopamine

and

a

vasodilator

such

as

sodium

nitroprusside

-LRB-

SNP

-RRB-

or

nitroglycerin

has

proven

effective

for

patients

with

heart

failure

to

regulate

hemodynamics

Inotropic

agents

increase

the

force

and

velocity

of

cardiac

muscle

contraction

and

result

in

enhancing

CO.

Vasodilators

reduce

SVR

and

result

in

the

decrease

of

the

afterload

of

the

heart

which

thereby

decreases

MAP

and

increases

stroke

volume

secondarily

Multivariable

automated

drug-delivery

systems

have

been

developed

to

help

busy

physicians

or

anesthesiologists

use

several

drugs

in

many

critical

tasks

to

regulate

the

various

hemodynamics

that

occur

during

heart

failure

In

simulation

and

animal

studies

undertaken

during

early

system

development

adaptive

controllers

demonstrated

the

feasibility

of

application

of

a

multivariable

drug-delivery

system

to

simultaneously

control

CO

and

MAP

using

a

combination

of

an

inotropic

agent

and

a

vasodilator

In

subsequent

stages

multiple

models

and

adaptive

predictive

controllers

have

been

developed

to

adequately

adjust

the

hemodynamic

parameters

in

the

presence

of

nonlinear

physiological

and

drug

interactions

Fuzzy

controls

have

also

shown

optimal

performance

in

regulation

of

multivariable

hemodynamics

with

heart

failure

However

patients

with

heart

failure

may

have

nonlinear

and

time-variant

responses

under

unexpected

variability

to

drugs

and

drug

interactions

with

disturbances

Under

such

unknown

conditions

the

model-based

controllers

might

require

the

preparation

of

numerous

linear

models

to

describe

the

various

heart-failure

patient

responses

to

drugs

and

the

fuzzy

controllers

might

require

many

rules

based

on

the

expert

knowledge

and

heuristics

of

physicians

or

anesthesiologists

for

drug

therapy

of

heart

failure

The

controllers

that

can

adjust

adaptively

to

unexpected

responses

with

heart

failure

are

required

in

actual

clinical

situations

Because

neural

networks

-LRB-

NN

-RRB-

might

be

one

of

the

simple

tools

used

for

nonlinear

and

time-variant

system

responses

in

the

presence

of

the

unknown

response

variability

and

interactions

with

exogenous

perturbation

the

application

of

the

NN

to

drug-delivery

systems

has

been

desired

To

our

knowledge

the

multivariable

controller

using

the

NN

for

hemodynamic

variables

with

heart

failure

has

not

been

tested

whereas

the

NN

controllers

have

engendered

the

MAP

controls

such

as

post-operative

and

during

acute

Therefore

this

study

is

intended

to

develop

a

multiple

adaptive

predictive

control

based

on

NN

-LRB-

MAPCNN

-RRB-

for

hemodynamic

variables

and

to

evaluate

its

control

performance

under

unexpected

responses

to

drugs

during

CO

and

MAP

regulation

using

SNP

and

DBT

in

heart

failure

To

be

assured

of

a

control

algorithm

before

animal

experiments

the

MAPCNN

was

tested

under

largely

unexpected

-LRB-

-RRB-

drug

interactions

-LRB-

-RRB-

acute

disturbances

and

-LRB-

-RRB-

time-variant

hemodynamic

responses

which

can

be

freely

operated

Finally

the

performance

of

the

MAPCNN

was

tested

by

actual

hemodynamics

of

a

canine

left

heart

failure

MATERIALS

AND

METHODS

This

section

fundamentally

includes

three

parts

-LRB-

i

-RRB-

Modeling

of

Pharmacological

Response

which

explains

the

method

for

the

development

of

a

computer

response

model

that

allows

testing

of

the

MAPCNN

-LRB-

ii

-RRB-

Development

of

Controller

and

-LRB-

iii

-RRB-

Evaluation

of

Controller

which

is

the

actual

test

of

the

MAPCNN

In

addition

the

animal

study

was

divided

into

two

parts

First

to

model

the

pharmacological

response

in

-LRB-

i

-RRB-

animal

experiments

were

performed

using

dogs

with

heart

failure

Five

of

eleven

dogs

were

used

for

every

drug

infusion

Then

for

additional

validation

of

the

developed

controller

after

computer

simulations

an

animal

experiment

was

performed

using

one

dog

with

heart

failure

Modeling

of

Pharmacological

Response

To

produce

the

response

models

to

therapeutic

agents

in

acute

heart

failure

the

following

animal

study

which

conformed

to

the

Guide

for

the

Care

and

Use

of

Laboratory

Animals

published

by

the

US

National

Institutes

of

Health

was

performed

Microsphere

embolization

of

the

left

main

coronary

artery

induced

acute

ischemic

heart

failure

in

dogs

-LRB-

n

kg

-RRB-

that

were

anesthetized

with

pentobarbital

sodium

and

ventilated

artificially

A

double-lumen

catheter

was

introduced

into

the

right

femoral

vein

for

administration

of

pharmaceutical

agents

using

a

computer-controllable

infusion

pump

-LRB-

Nihon

Kohden

Tokyo

Japan

-RRB-

An

in-line

electromagnetic

flow

probe

-LRB-

Nihon

Kohden

-RRB-

was

used

to

measure

CO

MAP

was

measured

through

a

fluid-filled

catheter

and

a

pressure

transducer

-LRB-

Nihon

Kohden

-RRB-

The

CO

and

MAP

were

digitized

at

a

sampling

rate

through

a

digital-to-analog

converter

connected

to

a

laboratory

computer

The

total

number

of

all

animals

used

for

modeling

was

The

orders

of

drug

infusions

were

the

following

four

-LRB-

i

-RRB-

and

μg

kg

min

in

DBT

and

and

μg

kg

min

in

SNP

-LRB-

n

of

animals

-RRB-

-LRB-

ii

-RRB-

and

μg

kg

min

in

DBT

-LRB-

n

-RRB-

-LRB-

iii

-RRB-

μg

kg

min

in

DBT

-LRB-

n

-RRB-

and

-LRB-

iv

-RRB-

and

μg

kg

min

in

SNP

-LRB-

n

-RRB-

Specifically

five

of

all

animals

were

used

for

each

drug

infusion

rate

The

hemodynamic

variables

-LSB-

n

except

for

the

two

animals

in

the

above

case

-LRB-

iii

-RRB-

the

μg

kg

min

in

DBT

-LRB-

n

-RRB-

because

of

no

measurements

-RSB-

were

changed

to

ml

kg

min

in

CO

-LRB-

p

paired

t-test

-RRB-

and

mmHg

in

MAP

-LRB-

not

significant

-RRB-

before

-LRB-

CO

mean

S.E.M

ml

kg

min

and

MAP

mmHg

-RRB-

and

immediately

after

-LRB-

CO

mean

S.E.M

ml

kg

min

and

MAP

mmHg

-RRB-

the

heart

failure

for

hemodynamics

immediately

before

each

drug

infusion

see

Fig.

-RRB-

The

period

between

two

trials

of

drug

infusions

was

min

in

each

animal

To

prevent

the

washout

process

of

a

catheter

in

the

above

case

-LRB-

i

-RRB-

both

the

drug

infusions

of

DBT

and

SNP

-LRB-

n

-RRB-

a

double-lumen

catheter

was

used

FIGURE

dose

responses

in

canine

left

heart

failure

-LRB-

n

-RRB-

A.

Step

responses

of

the

change

of

cardiac

output

-LRB-

ΔCO

left

-RRB-

and

mean

arterial

blood

pressure

-LRB-

ΔMAP

right

-RRB-

from

the

baseline

after

induced

acute

heart

failure

during

infusion

of

-LRB-

a

-RRB-

dobutamine

-LRB-

DBT

-RRB-

at

and

μg

kg

min

and

-LRB-

b

-RRB-

sodium

nitroprusside

-LRB-

SNP

-RRB-

at

and

μg

kg

min

Data

digitized

at

Hz

were

averaged

every

s.

Data

are

mean

S.E.M.

B.

Unit

impulse

responses

of

ΔCO

-LRB-

left

-RRB-

and

ΔMAP

-LRB-

right

-RRB-

calculated

from

data

of

-LRB-

a

-RRB-

DBT

infusion

at

and

μg

kg

min

and

-LRB-

b

-RRB-

SNP

infusion

at

and

μg

kg

min

in

dogs

CO

response

of

SNP

at

μg

kg

min

was

eliminated

because

of

impossible

fit

to

step

response

In

this

study

component

models

comprising

a

first

order

dynamic

system

cascaded

with

a

nonlinear

sigmoidal

function

were

used

to

model

the

responses

of

CO

and

MAP

with

heart

failure

After

pharmacodynamics

for

the

evaluation

of

controllers

was

represented

by

a

linear

first-order

transfer

function

a

sigmoidal

function

was

applied

to

the

linear

model

to

express

the

nonlinear

characteristic

with

a

component

model

approximating

the

positive

step

response

The

procedure

to

produce

the

model

responses

can

be

described

as

follows

First

simple

models

for

responses

to

therapeutic

agents

were

produced

from

experimental

data

in

canine

left-heart

failure

Figure

shows

the

step

responses

of

CO

and

MAP

changed

-LRB-

ΔCO

and

ΔMAP

-RRB-

from

baseline

values

immediately

before

each

drug

infusion

after

inducing

the

acute

heart

failure

during

-LRB-

a

-RRB-

DBT

and

-LRB-

b

-RRB-

SNP

infusions

The

step

responses

of

ΔCO

and

ΔMAP

during

infusion

of

DBT

at

and

μg

kg

min

or

SNP

at

and

μg

kg

min

were

averaged

every

s.

Then

each

single-input

single-output

response

-LSB-

Δŷ

-LRB-

t

-RRB-

-RSB-

of

the

four

step

responses

-LRB-

DBT-CO

DBT-MAP

SNP-CO

and

SNP-MAP

loops

as

input

output

relationships

-RRB-

was

approximated

to

the

linear

first-order

delay

system

with

a

pure

time

delay

in

the

continuous-time

domain

as

where

K

is

a

proportional

gain

L

is

a

pure

time

delay

and

Tc

is

a

time

constant

If

t

L

then

Δŷ

-LRB-

t

-RRB-

The

fitted

parameters

to

the

averaged

step

responses

-LRB-

n

-RRB-

in

the

single

infusion

of

DBT

or

SNP

were

acquired

by

least

squares

method

and

used

for

calculation

of

the

following

unit

impulse

response

-LRB-

i.e.

the

response

to

the

infusion

of

μg

kg

min

of

a

given

drug

-RRB-

Second

the

linear-model

response

-LSB-

Δy

-LRB-

t

-RRB-

-RSB-

was

calculated

by

the

convolution

integral

in

the

discrete-time

domain

where

In

those

equations

u

-LRB-

t

-RRB-

is

the

drug

infusion

rate

ΔT

is

the

sampling

interval

and

Nm

is

the

finite

number

of

terms

in

the

model

for

the

unit

impulse

response

The

unit

impulse

response

is

g

-LRB-

t

-RRB-

as

calculated

from

the

derived

values

of

the

step

response

of

Eq

-LRB-

-RRB-

The

proportional

gain

of

a

unit

impulse

response

is

Ku

Tc

and

L

are

the

same

values

as

Eq

-LRB-

-RRB-

For

the

simulation

study

ΔT

and

Nm

were

set

respectively

to

s

and

According

to

this

method

the

unit

impulse

responses

of

ΔCO

and

ΔMAP

during

infusions

of

DBT

at

and

μg

kg

min

and

SNP

at

and

μg

kg

min

were

calculated

from

the

fitting

parameters

to

the

average

step

responses

-LRB-

Fig.

the

CO

response

to

SNP

at

μg

kg

min

was

excepted

because

of

the

impossible

fit

to

the

step

response

-RRB-

Although

some

differences

existed

among

unit

impulse

responses

at

those

infusion

rates

as

shown

in

Fig.

in

the

present

study

median

values

-LRB-

i.e.

μg

kg

min

in

DBT

and

μg

kg

min

in

SNP

-RRB-

were

used

for

the

following

simulations

because

they

characterized

the

effects

of

drugs

on

hemodynamics

well

Numerical

data

in

Ku

Tc

L

and

g

-LRB-

t

-RRB-

used

for

the

simulation

study

are

shown

in

Table

-LRB-

left

-RRB-

TABLE

Model

parameters

in

linear-fitting

and

nonlinear-fitting

functions.Drug-responseLinearNonlinefsarProportional

gain

-LRB-

Ku

-RRB-

Time

constant

-LRB-

Tc

-RRB-

Pure

time

delay

-LRB-

L

-RRB-

range

-LRB-

-RRB-

Coefficient

of

gain

-LRB-

-RRB-

SNP-MAP

Fitting

parameters

-LRB-

Ku

Tc

L

and

-RRB-

in

a

single-input

single-output

relationship

The

Ku

-LSB-

ml

μg

in

DBT-CO

and

SNP-CO

loops

or

mmHg

-LRB-

μg

kg

min

-RRB-

in

DBT-MAP

and

SNP-MAP

loops

-RSB-

Tc

-LRB-

s

-RRB-

and

L

-LRB-

s

-RRB-

are

the

parameters

of

Eq

-LRB-

-RRB-

The

and

are

the

parameters

of

Eq

-LRB-

-RRB-

shows

a

multiple

coefficient

of

determination

Third

to

express

the

nonlinear

response

to

a

single

drug

infusion

the

Δy

-LRB-

t

-RRB-

in

Eq

-LRB-

-RRB-

as

the

linear

model

response

was

modified

through

a

sigmoidal

function

in

which

is

the

parameter

of

the

response

range

which

shows

the

difference

between

the

maximum

and

minimum

values

of

Δy

-LRB-

t

-RRB-

as

the

nonlinear

model

response

and

is

the

parameter

of

the

coefficient

of

gain

Parameters

and

were

determined

by

nonlinear

least-squares

method

for

the

simulation

study

-LSB-

Table

-LRB-

right

-RRB-

and

Fig.

-RSB-

Figure

contains

the

average

values

in

ΔCO

and

ΔMAP

responses

of

the

final

s

during

infusions

of

DBT

at

and

μg

kg

min

and

SNP

at

and

μg

kg

min

-LRB-

Fig.

-RRB-

The

ΔCO

and

ΔMAP

responses

tested

in

simulations

were

over

the

ranges

of

the

averaged

responses

in

actual

hemodynamics

of

dogs

with

heart

failure

FIGURE

A.

Nonlinear

responses

of

ΔCO

and

ΔMAP

in

infusion

of

DBT

or

SNP

Circles

-LRB-

-RRB-

show

experimental

data

for

dogs

with

heart

failure

solid

lines

are

curves

fitted

to

the

averaged

data

Dashed

lines

show

the

limits

of

the

tested

range

-LSB-

one-third

-LRB-

-RRB-

to

three-times

-LRB-

-RRB-

responses

compared

with

the

averaged

data

-LRB-

-RRB-

in

Eq

-LRB-

-RRB-

-RSB-

in

simulations

B.

Multi-input

multi-output

model

responses

for

ΔCO

and

ΔMAP

System

inputs

are

the

infusion

rates

of

DBT

and

SNP

outputs

are

the

ΔCO

and

ΔMAP

The

outputs

were

determined

by

the

first-order

dynamic

systems

cascaded

with

nonlinear

sigmoidal

functions

The

proportional

gains

of

patient

sensitivities

to

drugs

and

drug

interactions

are

shown

as

and

Finally

the

model

responses

containing

patient

sensitivities

to

therapeutic

agents

and

drug

interactions

are

expressed

as

where

ΔCOmod

-LRB-

t

-RRB-

is

the

model

response

containing

sensitivities

to

drugs

and

drug

interactions

of

DBT

and

SNP

-LRB-

t

-RRB-

and

-LRB-

t

-RRB-

respectively

indicate

the

nonlinear

responses

to

single

infusions

of

DBT

and

SNP

and

and

respectively

represent

the

proportional

gain

of

patient

sensitivity

to

DBT

and

SNP

The

model

response

containing

sensitivities

to

drugs

and

drug

interactions

of

SNP

and

DBT

is

ΔMAPmod

-LRB-

t

-RRB-

The

respective

nonlinear

responses

to

single

infusions

of

SNP

and

DBT

are

-LRB-

t

-RRB-

and

-LRB-

t

-RRB-

The

respective

proportional

gains

of

patient

sensitivity

to

SNP

and

DBT

are

denoted

as

and

-LRB-

see

Fig.

-RRB-

In

particular

and

can

be

defined

as

the

strength

of

the

drug

interaction

when

the

two

treatments

for

DBT-CO

and

SNP-MAP

loops

are

performed

Development

of

Controller

Control

Design

Figure

portrays

a

block

diagram

of

a

MAPCNN

system

for

adaptation

to

various

patient

responses

with

heart

failure

Treating

the

multiple

loops

in

the

therapy

for

heart

failure

separately

allows

setting

of

a

clear

goal

of

NN

learning

for

the

various

patient

responses

during

closed-loop

control

On

the

other

hand

in

the

completely

separated

controllers

the

total

control

performance

will

be

late

because

one

controller

performs

the

drug

therapy

after

detection

of

the

drug

interaction

disturbance

induced

by

performing

an

action

taken

by

the

other

controller

Therefore

the

MAPCNN

in

this

study

includes

two

module

controllers

for

the

DBT-CO

loop

considering

the

effects

of

SNP

on

CO

and

the

SNP-MAP

loop

considering

the

effects

of

DBT

on

MAP

FIGURE

A

block

diagram

showing

multiple

adaptive

predictive

control

using

neural

networks

-LRB-

MAPCNN

-RRB-

to

regulate

CO

and

MAP

The

r

is

a

target

value

and

e

-LRB-

t

-RRB-

is

the

error

between

the

target

value

and

observed

value

The

value

e

-LRB-

t

i

-RRB-

represents

the

error

between

the

target

value

and

output

predicted

by

the

NN

Thick

lines

show

the

learning

loop

in

the

NN

dotted

lines

show

the

prediction

loop

using

the

NN

Figure

depicts

one

of

the

two

NN

structures

in

MAPCNN

tested

for

the

simulation

study

The

MAPCNN

is

a

control

system

in

which

the

NN

recursively

learns

patient

characteristics

using

their

observed

responses

to

drug

infusions

only

once

every

s

during

closed-loop

control

-LRB-

Learning

Loop

-RRB-

It

subsequently

determines

the

future

outputs

using

the

learned

NN

-LRB-

Prediction

Loop

-RRB-

A

multilayer

feed-forward

NN

with

two

hidden

layers

-LRB-

ΔyNN

-RRB-

emulated

the

nonlinear

responses

in

ΔCOmod

and

ΔMAPmod

The

ΔyNN

is

predicted

through

NN

as

where

Δymod

-LRB-

t

-RRB-

and

Δymod

-LRB-

t

-RRB-

are

model

responses

of

past

ΔCO

or

ΔMAP

-LRB-

t

-RRB-

and

-LRB-

t

-RRB-

or

-LRB-

t

-RRB-

and

-LRB-

t

-RRB-

represent

the

past

infusion

rates

of

DBT

or

SNP

Here

to

determine

the

length

of

the

history

of

model

response

and

infusion

rates

as

inputs

to

the

NN

the

accuracy

of

NN

learning

was

tested

under

various

lengths

of

components

-LRB-

for

a

detailed

protocol

refer

to

the

following

paragraph

Learning

of

Initial

Weights

in

NN

-RRB-

Figure

shows

the

average

values

-LRB-

final

points

-RRB-

in

the

absolute

error

between

the

ΔCOmod

and

ΔCONN

responses

-LRB-

left

-RRB-

or

ΔMAPmod

and

ΔMAPNN

responses

-LRB-

right

-RRB-

from

the

trained

NN

-LSB-

times

in

Eq

-LRB-

-RRB-

-RSB-

under

various

input

output

components

to

the

NN

input

The

numbers

of

the

input

units

-LRB-

m

-RRB-

to

a

single

NN

component

and

of

the

units

in

the

first

-LRB-

-RRB-

and

second

-LRB-

-RRB-

hidden

layers

of

the

NN

were

set

to

the

same

as

that

of

components

to

the

NN

input

For

example

if

the

inputs

to

the

NN

were

-LRB-

the

past

min

in

both

the

two

drug

inputs

and

the

past

min

in

the

model

response

-RRB-

then

m

Learning

rates

of

the

two

NN

in

both

the

CO

and

MAP

controls

were

set

to

The

starting

weights

of

NN

were

given

at

random

every

trial

In

the

past

history

of

infusion

rates

the

error

between

the

NN

and

model

responses

in

the

past

infusion

rates

-LRB-

eight

components

in

Fig.

four

in

DBT

and

four

in

SNP

-RRB-

showed

adequate

accuracy

although

that

in

the

past

infusion

rates

-LRB-

four

components

-RRB-

was

not

demonstrably

accurate

in

both

the

CO

and

MAP

responses

Here

it

was

predicted

that

the

pure

time

delays

to

drug

inputs

were

different

among

patients

and

that

the

NN

was

required

to

express

the

characteristics

of

the

transient

response

to

a

drug

input

adequately

considering

the

effect

of

the

other

drug

input

Therefore

to

adjust

the

NN

response

to

the

changes

of

hemodynamics

with

noise

and

disturbances

during

the

real-time

control

the

infusion

rates

of

the

past

min

in

both

drugs

-LRB-

total

components

components

in

each

drug

-RRB-

were

on

the

safe

side

selected

for

both

the

CO

and

MAP

controls

in

the

present

study

In

the

past

history

of

model

response

the

accuracy

of

NN

learning

was

the

almost

equal

among

the

cases

of

the

past

and

min

-LRB-

and

components

in

Fig.

-RRB-

in

both

the

CO

and

MAP

responses

whereas

that

in

the

past

s

-LRB-

component

-RRB-

showed

inadequate

accuracy

Accordingly

the

length

of

the

past

history

of

model

response

was

determined

as

min

-LRB-

components

-RRB-

in

both

the

CO

and

MAP

controls

FIGURE

A

A

single

component

of

a

four-layer

feed-forward

NN

with

two

hidden

layers

in

MAPCNN

to

emulate

the

characteristics

of

a

patient

The

number

of

units

in

each

hidden

layer

of

the

NN

was

set

to

-LRB-

numerically

equal

to

the

input

units

-RRB-

A

hyperbolic

tangent

function

was

used

as

the

output

of

each

unit

B.

Average

values

-LRB-

final

points

-RRB-

in

the

absolute

error

between

the

ΔCOmod

and

ΔCONN

responses

-LRB-

left

-RRB-

or

ΔMAPmod

and

ΔMAPNN

responses

-LRB-

right

-RRB-

from

the

trained

NN

-LSB-

times

in

Eq

-LRB-

-RRB-

-RSB-

under

various

lengths

of

input

output

components

to

NN

input

C

The

absolute

error

between

the

model

response

and

the

predicted

response

by

NN

in

-LRB-

a

-RRB-

ΔCO

-LRB-

left

-RRB-

or

-LRB-

b

-RRB-

ΔMAP

-LRB-

right

-RRB-

In

the

simulation

study

the

number

of

input

units

to

a

single

NN

component

was

m

the

numbers

of

units

in

the

first

and

second

hidden

layers

of

the

NN

were

being

equal

to

the

input

units

The

weights

in

the

single

NN

were

in

the

input

to

first

hidden

layer

in

the

first

to

second

hidden

layer

in

the

second

hidden

layer

to

output

layer

and

for

biases

-LRB-

Fig.

-RRB-

The

two

NN

for

the

controls

of

DBT-CO

and

SNP-MAP

loops

had

identical

structures

In

the

learning

loop

a

single

NN

was

trained

by

the

output

of

ΔCOmod

or

ΔMAPmod

to

the

random

inputs

of

DBT

and

SNP

using

the

backpropagation

algorithm

in

an

on-line

mode

showing

that

the

error

function

is

calculated

after

presentation

of

an

input

The

prediction

loop

in

the

MAPCNN

determines

the

optimal

DBT

or

SNP

infusion

rate

that

minimizes

the

cost

function

using

the

updated

NN

through

the

learning

loop

every

s.

Therein

the

cost

function

-LSB-

-LRB-

t

-RRB-

-LRB-

t

-RRB-

-RSB-

comprises

the

weight

of

input

change

-LRB-

-RRB-

the

prediction

range

-LRB-

-RRB-

and

the

setpoint

-LRB-

-RRB-

in

the

controllers

for

the

DBT-CO

loop

or

the

SNP-MAP

loop

The

physiological

responses

predicted

by

the

NN

are

indicated

as

ΔCONN

and

ΔMAPNN

The

controller

based

on

the

NN

for

each

loop

predicts

future

outputs

using

past

inputs

of

infusion

rates

of

DBT

and

SNP

The

optimization

of

the

infusion

rates

-LSB-

-LRB-

t

-RRB-

-LRB-

t

-RRB-

-RSB-

was

performed

using

a

Nelder

Mead

Simplex

algorithm

Determination

of

Control

Parameters

Learning

of

Initial

Weights

in

NN

The

two

NN

respectively

learned

ΔCOmod

response

in

the

DBT-CO

loop

and

ΔMAPmod

response

in

the

SNP-MAP

loop

to

determine

the

initial

weights

in

the

NN

for

the

MAPCNN

The

starting

weights

in

the

NN

before

learning

the

model

response

were

given

at

random

between

and

Subsequently

the

infusion

rates

of

DBT

and

SNP

were

given

at

random

between

and

μg

kg

min

Here

both

the

plus

and

minus

signs

as

drug

inputs

-LRB-

artificial

infusions

-RRB-

to

the

NN

were

used

because

the

learning

of

NN

was

inferred

to

be

more

effective

than

that

under

a

plus

sign

alone

as

the

drug

input

to

the

NN

in

the

trial

and

error

and

previous

studies

Learning

of

the

NN

for

ΔCOmod

or

ΔMAPmod

responses

was

repeated

times

The

ΔCOmod

was

divided

by

and

ΔMAPmod

was

divided

by

for

normalization

during

NN

learning

Figure

shows

the

absolute

error

between

the

ΔCOmod

and

ΔCONN

responses

-LRB-

left

-RRB-

or

ΔMAPmod

and

ΔMAPNN

responses

-LRB-

right

-RRB-

from

the

trained

NN

in

the

average

patient

sensitivity

-LSB-

in

Eq

-LRB-

-RRB-

-RSB-

Learning

rates

of

the

two

NN

for

the

following

simulation

study

were

set

to

showing

a

suitable

number

by

trial

and

error

in

both

the

ΔCOmod

and

ΔMAPmod

Learning

results

of

the

NN

respectively

showed

errors

of

ml

kg

min

in

the

DBT-CO

loop

and

mmHg

in

the

SNP-MAP

loop

Controller

Tuning

Optimal

values

of

the

range

of

prediction

-LRB-

-RRB-

and

the

weight

of

input

-LRB-

-RRB-

in

the

cost

function

-LRB-

-RRB-

of

the

controller

were

explored

using

the

model

patient

responses

ΔCOmod

and

ΔMAPmod

to

determine

the

initial

controller

parameters

The

prediction

range

was

set

to

or

and

the

weight

of

input

was

set

to

or

The

learning

rates

of

ΔCOmod

and

ΔMAPmod

were

fixed

at

To

regulate

the

control

speed

and

stability

simultaneously

the

setpoint

of

ΔCO

was

guided

by

the

linear

function

ml

kg

min

during

the

min

following

the

start

of

the

closed-loop

control

Thereafter

it

was

maintained

at

ml

kg

min

The

setpoint

of

ΔMAP

was

set

to

mmHg

The

duration

of

the

closed-loop

control

was

set

to

min

Figure

shows

simulation

results

of

the

MAPCNN

using

average

responses

of

ΔCOmod

and

ΔMAPmod

-LSB-

and

in

Eq

-LRB-

-RRB-

were

set

to

unity

-RSB-

The

controller

suppressed

a

control

speed

instead

of

facilitating

stable

control

with

the

increase

of

the

weight

of

input

-LRB-

-RRB-

at

each

range

of

prediction

-LRB-

or

-RRB-

On

the

other

hand

when

the

weight

of

the

input

is

small

-LRB-

-RRB-

the

controller

performed

a

slightly

aggressive

control

with

the

decreased

range

of

prediction

-LRB-

-RRB-

The

relationship

at

the

large

weight

of

input

-LRB-

-RRB-

was

opposite

because

of

the

strong

effects

of

the

input

weight

at

the

small

range

of

prediction

-LRB-

-RRB-

For

subsequent

simulations

the

parameters

-LRB-

-RRB-

in

the

MAPCNN

were

set

to

and

considering

the

settling

time

which

reflects

control

speed

and

stability

In

this

case

the

settling

time

within

ml

kg

min

in

ΔCOmod

was

s

its

time

within

mmHg

in

ΔMAPmod

was

s

The

average

absolute

value

of

error

between

a

setpoint

and

model

response

in

ΔCOmod

or

ΔMAPmod

over

the

entire

control

period

-LRB-

average

error

-RRB-

for

min

was

ml

kg

min

in

ΔCO

or

mmHg

in

ΔMAP

FIGURE

Simulation

results

of

the

MAPCNN

under

average

responses

of

ΔCOmod

and

ΔMAPmod

-LSB-

-RSB-

The

input

weight

was

changed

to

or

fixing

the

range

of

prediction

at

-LRB-

A

-RRB-

-LRB-

B

-RRB-

or

-LRB-

C

-RRB-

The

NN

learning

rate

was

set

to

under

all

conditions

Evaluation

of

Controller

Simulations

To

evaluate

the

control

performance

a

simulation

study

in

MAPCNN

which

expressed

the

repeatability

and

freely

operated

physiological

parameters

such

as

nonlinearity

and

interaction

was

performed

under

unexpected

changes

of

patient

responses

to

therapeutic

agents

with

acute

disturbances

using

the

model

response

based

on

experimental

data

of

canine

heart

failure

Increased

CO

to

more

than

ml

kg

min

while

keeping

MAP

within

the

normal

range

-LRB-

mmHg

-RRB-

is

desirable

to

treat

acute

heart

failure

Therefore

the

control

objectives

in

this

study

were

to

increase

the

low

CO

-LRB-

mean

S.E.M.

ml

kg

min

Fig.

-RRB-

at

the

setpoint

of

ml

kg

min

-LRB-

ΔCO

within

min

after

the

start

of

closed-loop

control

-RRB-

using

DBT

infusion

and

to

simultaneously

maintain

the

normal

MAP

-LRB-

mean

S.E.M.

mmHg

Fig.

-RRB-

at

the

setpoint

-LRB-

ΔMAP

mmHg

-RRB-

using

SNP

infusion

when

hypertension

is

induced

by

treatment

for

DBT-CO

loop

in

acute

heart

failure

The

infusion

rates

were

basically

bounded

as

-LRB-

t

-RRB-

in

DBT

and

-LRB-

t

-RRB-

in

SNP

to

avoid

an

overdose

or

drug

toxicity

Hemodynamic

control

was

simulated

under

the

following

cases

drug

interactions

between

DBT

and

SNP

acute

disturbances

and

time-variant

changes

of

physiological

parameters

Drug

Interactions

Grasping

and

estimating

the

acts

of

drug

interactions

are

difficult

for

hemodynamic

control

using

multiple

drugs

To

examine

the

controller

's

robustness

for

wide

ranges

of

patients

sensitivity

to

drugs

and

drug

interactions

parameters

-LRB-

-RRB-

in

Eq

-LRB-

-RRB-

were

changed

to

or

every

min

for

control

-LRB-

Fig.

-RRB-

Hemodynamic

responses

were

unknown

to

the

NN

because

the

NN

learned

only

the

average

model

responses

-LRB-

-RRB-

The

controller

was

also

tested

under

various

combinations

for

sensitivities

to

drugs

and

drug

interactions

The

model

parameters

and

in

Eq

-LRB-

-RRB-

were

set

to

one

of

-LRB-

Low

-RRB-

-LRB-

Mid

-RRB-

and

-LRB-

High

-RRB-

and

all

combinations

were

tested

with

or

without

the

limitations

of

drug

infusion

rates

The

control

duration

was

min

FIGURE

Simulation

results

of

MAPCNN

with

unexpected

patient

sensitivities

and

drug

interactions

A

in

the

top

graph

displays

changes

of

parameters

-LRB-

-RRB-

in

Eq

-LRB-

-RRB-

B

-LRB-

a

-RRB-

and

C

-LRB-

a

-RRB-

in

the

graph

display

setpoints

ΔCOmod

and

ΔMAPmod

-LRB-

solid

lines

-RRB-

and

predicted

outputs

by

NN

-LRB-

dashed

lines

-RRB-

B

-LRB-

b

-RRB-

and

C

-LRB-

b

-RRB-

are

the

time

courses

of

weights

changed

from

the

baseline

at

the

starting

time

in

the

NN

for

controllers

in

the

DBT-CO

and

SNP-MAP

loops

weights

between

input

and

first

hidden

layers

-LRB-

top

-RRB-

first

and

second

hidden

layers

-LRB-

middle

-RRB-

and

second

hidden

and

output

layers

-LRB-

bottom

-RRB-

D.

Infusion

rates

of

DBT

-LRB-

solid

line

-RRB-

and

SNP

-LRB-

dashed

line

-RRB-

To

know

the

limitation

of

the

control

performance

the

MAPCNN

was

tested

under

very

low

-LRB-

or

-RRB-

and

high

-LRB-

or

-RRB-

sensitivities

to

drugs

and

drug

interactions

The

limitations

of

infusion

rates

of

drugs

were

eliminated

to

emphasize

the

control

performance

The

control

duration

was

min

Acute

Disturbances

Bolus

infusion

of

drugs

during

and

after

cardiac

surgery

often

introduces

severe

disturbances

to

a

controller

Hemorrhage

patient-position

changes

and

changes

in

anesthesia

levels

will

modulate

patient

response

characteristics

To

examine

the

controller

's

performance

during

acute

disturbances

the

MAPCNN

against

acute

hypertension

was

simulated

using

the

ΔCOmod

and

ΔMAPmod

responses

for

min

Exogenous

perturbations

were

added

to

the

patient

responses

ranging

within

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

To

mimic

physiological

variation

random

noises

within

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

were

also

added

-LSB-

Fig.

-LRB-

a

-RRB-

and

B

-LRB-

a

-RRB-

-RSB-

To

implicate

the

limitation

of

the

control

performance

the

MAPCNN

was

tested

under

very

severe

situations

with

random

noise

and

exogenous

perturbations

over

physiological

responses

-LRB-

i

-RRB-

very

huge

amplitudes

of

random

noise

-LRB-

ii

-RRB-

very

large

and

-LRB-

iii

-RRB-

acute

disturbances

First

-LRB-

i

-RRB-

three

levels

of

huge

amplitudes

of

random

noise

-LRB-

level

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

level

ml

kg

min

and

mmHg

and

level

ml

kg

min

and

mmHg

-RRB-

were

added

to

model

responses

-LRB-

-RRB-

during

drug

treatment

for

min

-LSB-

Figs.

-LRB-

a

-RRB-

and

B

-LRB-

a

-RRB-

-RSB-

The

random

noises

among

the

three

levels

had

the

same

pattern

except

for

the

amplitude

Next

-LRB-

ii

-RRB-

the

MAPCNN

was

evaluated

under

very

huge

disturbances

-LRB-

level

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

level

ml

kg

min

and

mmHg

and

level

ml

kg

min

and

mmHg

Fig.

-RRB-

Finally

-LRB-

iii

-RRB-

the

MAPCNN

was

tested

under

very

acute

disturbances

with

model

responses

in

high

sensitivities

to

drugs

and

drug

interactions

-LRB-

-RRB-

At

min

after

the

start

of

control

for

min

the

acute

disturbances

of

three

levels

-LSB-

-LRB-

level

-RRB-

-LRB-

level

-RRB-

and

-LRB-

level

-RRB-

min

to

reaching

the

offset

values

of

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

after

the

start

of

the

disturbances

-RSB-

were

added

-LRB-

Fig.

-RRB-

In

those

simulations

the

limitations

of

infusion

rates

of

drugs

were

eliminated

to

elucidate

the

limitations

of

the

control

performance

Time-variant

Changes

Patient

responses

to

therapeutic

agents

have

a

nonlinear

and

time-variant

nature

If

the

delay

of

a

plant

which

reflects

the

infusion

rate

of

drugs

through

the

catheter

internal

patient

circulation

and

perfusion

delay

and

the

drug-recirculation

characteristics

of

a

patient

is

not

known

accurately

or

changes

during

drug

infusions

infusion

delays

will

engender

an

unstable

condition

Therefore

the

controller

robustness

was

tested

under

the

change

of

the

infusion

delay

in

this

study

The

pure

time

delays

-LSB-

L

in

the

unit

impulse

response

of

Eq

-LRB-

-RRB-

-RSB-

of

patient

responses

to

therapeutic

agents

were

varied

from

to

s

in

CO

responses

and

to

s

in

MAP

responses

to

DBT

and

SNP

infusions

during

the

closed

loop

control

-LSB-

Fig.

-LRB-

a

-RRB-

-RSB-

The

parameters

-LRB-

-RRB-

in

Eq

-LRB-

-RRB-

were

varied

from

to

to

examine

the

controller

performance

under

time-variant

and

wide

ranges

of

patient

sensitivities

to

drugs

and

drug

interactions

-LSB-

Fig.

-LRB-

b

-RRB-

-RSB-

The

exogenous

perturbations

were

added

to

the

time-variant

patient

responses

ranging

within

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

Random

noises

within

ml

kg

min

and

mmHg

were

added

to

ΔCOmod

and

ΔMAPmod

responses

-LSB-

Fig.

-LRB-

a

-RRB-

and

C

-LRB-

a

-RRB-

-RSB-

The

control

duration

was

min

Animal

Study

To

evaluate

the

control

performance

in

MAPCNN

under

the

unknown

physiological

responses

such

as

nonlinearity

and

drug

interaction

the

simultaneous

control

of

CO

and

MAP

was

performed

using

a

dog

with

acute

heart

failure

Acute

ischemic

heart

failure

in

an

anesthetized

and

ventilated

dog

-LRB-

kg

-RRB-

was

induced

by

microsphere

embolization

of

the

left

main

coronary

artery

A

double-lumen

catheter

was

introduced

into

the

right

femoral

vein

for

administration

of

drugs

using

an

infusion

pump

-LRB-

Nihon

Kohden

Tokyo

Japan

-RRB-

CO

was

measured

by

an

electromagnetic

flow

probe

-LRB-

Nihon

Kohden

-RRB-

and

MAP

was

measured

through

a

pressure

transducer

-LRB-

Nihon

Kohden

-RRB-

at

a

sampling

rate

through

a

digital-to-analog

converter

The

control

objective

was

to

increase

the

low

CO

-LRB-

ml

kg

min

-RRB-

at

the

setpoint

-LRB-

-RRB-

using

DBT

infusion

and

to

maintain

the

MAP

-LRB-

mmHg

-RRB-

at

the

setpoint

-LRB-

ΔMAP

mmHg

-RRB-

using

SNP

infusion

in

acute

heart

failure

The

closed-loop

control

duration

was

min

The

infusion

rates

were

bounded

as

-LRB-

t

-RRB-

in

DBT

and

-LRB-

t

-RRB-

in

SNP

RESULTS

Simulations

Drug

Interactions

Figure

shows

simulation

results

of

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

unknown

patient

sensitivities

to

drugs

and

drug

interactions

The

ΔCO

in

the

DBT-CO

loop

converged

on

the

setpoint

-LRB-

ml

kg

min

-RRB-

within

approximately

min

according

to

the

guided

setpoint

during

the

first

control

period

regardless

of

unanticipated

patient

sensitivities

and

drug

interactions

-LRB-

-RRB-

The

control

for

the

ΔMAP

in

the

SNP-MAP

loop

minimally

suppressed

the

hypertension

-LRB-

vs.

mmHg

with

or

without

SNP

infusion

-RRB-

induced

by

the

DBT

infusion

At

and

min

of

the

closed-loop

control

patient

sensitivities

and

drug

interactions

were

widely

changed

-LRB-

to

and

to

-RRB-

The

ΔCO

converged

on

the

setpoint

robustly

whereas

the

ΔCO

showed

transient

and

large

changes

-LRB-

showing

the

setpoint

to

and

to

ml

kg

min

at

approximately

and

min

-RRB-

Although

ΔMAP

was

decreased

acutely

by

the

change

of

patient

sensitivity

and

drug

interaction

-LRB-

to

mmHg

at

approximately

min

-RRB-

it

returned

robustly

to

a

normal

level

The

average

errors

between

setpoints

and

observed

responses

were

ml

kg

min

in

CO

and

mmHg

-LRB-

mmHg

without

SNP

infusion

-RRB-

in

MAP

during

closed-loop

control

Weights

and

biases

of

two

NN

were

adjusted

to

optimal

values

-LSB-

Fig.

-LRB-

b

-RRB-

and

C

-LRB-

b

-RRB-

-RSB-

when

the

unexpected

changes

occurred

The

infusion

rates

of

DBT

and

SNP

were

adjusted

smoothly

to

optimal

levels

corresponding

to

the

unknown

patient

responses

to

drugs

Table

shows

average

errors

between

setpoints

and

model

responses

in

ΔCO

and

ΔMAP

during

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

the

various

sensitivities

to

drugs

and

drug

interactions

The

control

performance

was

overall

accurate

and

a

tendency

excited

for

dependence

on

the

sensitivity

of

CO

to

DBT

-LRB-

i.e.

parameter

-RRB-

the

control

performance

was

increased

as

the

sensitivity

of

CO

to

DBT

increased

-LRB-

-RRB-

However

in

some

cases

great

hypertension

was

observed

during

control

as

displayed

in

Fig.

although

the

CO

control

was

smoothly

completed

under

such

cases

the

great

hypertension

was

induced

because

of

the

high

interaction

of

DBT

infusion

used

for

CO

treatment

-LRB-

i.e.

-RRB-

The

maximum

values

of

the

hypertension

in

cases

-LRB-

Low

Low

Low

and

High

-RRB-

-LRB-

Low

Low

Mid

and

High

-RRB-

and

-LRB-

Low

Mid

Low

and

High

-RRB-

were

and

mmHg

respectively

Here

Low

Mid

and

High

In

case

the

infusion

rates

of

DBT

were

slightly

disturbed

and

the

estimation

error

between

the

NN

and

ΔCO

responses

oscillated

However

the

ΔCO

in

case

was

unaffected

by

the

oscillation

of

DBT

infusion

because

of

the

low

sensitivity

of

CO

to

DBT

-LRB-

Low

-RRB-

Infusion

rates

of

SNP

in

all

cases

were

saturated

at

around

min

because

of

the

limitation

of

drug

infusion

After

the

saturation

the

infusion

rate

of

SNP

in

case

was

decreased

at

around

min

TABLE

Average

errors

between

setpoints

and

model

responses

in

CO

and

MAP

under

various

sensitvities

to

drugs

and

drug

interactions.CO

-LRB-

-RRB-

LowMid.HighCO

-LRB-

-RRB-

MAP

-LRB-

-RRB-

MAP

-LRB-

-RRB-

LowMid.HighLowMid.HighLowMid.HighLowLow5

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Mid

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Mid

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Mid

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

The

numbers

show

the

average

errors

in

CO

-LRB-

left

-RRB-

and

MAP

-LRB-

right

-RRB-

Low

Mid

and

High

in

the

parameters

in

Eq

-LRB-

-RRB-

The

sign

of

shows

the

cases

of

large

hypertension

-LRB-

for

detailed

results

see

Fig.

-RRB-

FIGURE

Simulation

results

of

MAPCNN

under

cases

of

great

hypertension

-LRB-

A

-RRB-

with

and

-LRB-

B

-RRB-

without

the

limitation

of

drug

infusion

rates

Parameters

-LRB-

-RRB-

in

Eq

-LRB-

-RRB-

are

Low

Low

Low

and

High

in

case

Low

Low

Mid

and

High

in

case

and

Low

Mid

Low

and

High

in

case

Low

Mid

and

High

are

and

respectively

The

hemodynamic

responses

-LRB-

top

-RRB-

the

error

between

the

model

response

and

the

predicted

response

by

NN

during

control

-LRB-

middle

-RRB-

and

infusion

rates

of

DBT

and

SNP

-LRB-

bottom

-RRB-

in

ΔCO

-LRB-

left

-RRB-

or

ΔMAP

-LRB-

right

-RRB-

To

elucidate

the

control

performance

without

the

limitation

of

infusion

rates

of

drug

inputs

the

MAPCNN

was

also

tested

under

the

same

cases

and

-LRB-

Fig.

-RRB-

However

great

hypertension

was

not

improved

by

SNP

infusion

without

the

drug

input

limitation

-LRB-

and

mmHg

in

cases

and

-RRB-

compared

with

those

with

the

limitation

of

the

drug

input

In

cases

and

the

drug

infusion

rates

in

DBT

were

disturbed

and

the

estimation

errors

between

the

NN

and

ΔCO

responses

had

some

oscillations

In

addition

in

all

cases

the

infusion

rates

of

SNP

were

decreased

after

increasing

to

around

μg

kg

min

irrespective

of

the

remaining

the

hypertension

Figure

shows

the

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

-LRB-

A

-RRB-

very

low

-LRB-

or

-RRB-

and

-LRB-

B

-RRB-

high

-LRB-

or

-RRB-

sensitivities

to

drugs

and

drug

interactions

Under

very

low

sensitivities

to

drugs

and

drug

interactions

the

ΔCO

response

was

not

able

to

reach

the

setpoint

-LRB-

ml

kg

min

-RRB-

because

of

the

slight

sensitivity

of

CO

to

DBT

-LRB-

or

-RRB-

but

it

finally

converged

on

a

stable

value

-LRB-

Fig.

left

-RRB-

Estimation

errors

between

the

NN

and

model

responses

in

ΔCO

had

oscillations

under

such

conditions

On

the

other

hand

under

very

high

sensitivities

to

drugs

and

drug

interactions

both

the

ΔCO

and

ΔMAP

responses

oscillated

depending

on

the

degree

of

sensitivities

to

drugs

-LSB-

maximum

amplitudes

between

observed

values

and

setpoints

-LRB-

-RRB-

ml

kg

min

and

-LRB-

-RRB-

mmHg

in

or

-LRB-

-RRB-

ml

kg

min

and

-LRB-

-RRB-

mmHg

in

Fig.

-RSB-

However

the

MAPCNN

had

a

tendency

to

suppress

oscillations

in

the

ΔCO

and

ΔMAP

responses

gradually

The

estimation

error

between

the

NN

and

model

responses

and

the

infusion

rates

of

drugs

were

also

disturbed

FIGURE

Simulation

results

of

MAPCNN

with

-LRB-

A

-RRB-

very

low

-LRB-

or

-RRB-

or

-LRB-

B

-RRB-

very

high

-LRB-

or

-RRB-

patients

sensitivities

to

drugs

and

drug

interactions

The

hemodynamic

responses

-LRB-

top

-RRB-

the

error

between

the

model

response

and

the

predicted

response

by

NN

during

control

-LRB-

middle

-RRB-

and

infusion

rates

of

DBT

and

SNP

-LRB-

bottom

-RRB-

in

ΔCO

-LRB-

left

-RRB-

or

ΔMAP

-LRB-

right

-RRB-

The

limitations

of

drug

infusion

rates

were

eliminated

Acute

Disturbances

Figure

shows

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

unexpected

acute

disturbances

with

background

noise

The

ΔCO

converged

on

the

setpoint

-LRB-

ml

kg

min

-RRB-

within

approximately

min

according

to

the

guided

setpoint

during

the

first

control

period

regardless

of

the

added

random

noise

-LRB-

ml

kg

min

-RRB-

with

expected

patient

responses

-LRB-

-RRB-

The

appropriate

infusion

of

SNP

for

control

of

ΔMAPmod

with

random

noise

-LRB-

mmHg

-RRB-

suppressed

hypertension

-LRB-

vs.

mmHg

with

or

without

SNP

treatment

-RRB-

induced

by

DBT

infusion

At

and

min

of

the

closed-loop

control

acute

disturbances

were

added

to

the

ΔCOmod

-LRB-

and

ml

kg

min

-RRB-

and

ΔMAPmod

-LRB-

and

mmHg

-RRB-

responses

The

MAPCNN

suppressed

the

transient

change

of

CO

minimally

and

the

CO

converged

on

the

setpoint

as

quickly

as

possible

The

induced

transient

hypertension

was

suppressed

robustly

by

optimal

infusion

of

SNP

-LRB-

vs.

mmHg

with

or

without

SNP

treatment

in

the

added

disturbance

at

min

-RRB-

Average

errors

between

setpoints

and

observed

responses

were

ml

kg

min

in

CO

and

mmHg

-LRB-

mmHg

without

SNP

-RRB-

in

MAP

during

closed-loop

control

Weights

and

biases

of

two

NN

were

adjusted

to

the

optimal

values

when

the

unexpected

changes

occurred

-LSB-

Fig.

-LRB-

c

-RRB-

and

B

-LRB-

c

-RRB-

-RSB-

Changes

of

biases

were

linked

to

those

of

the

acute

disturbances

and

physiological

variation

The

infusion

rates

of

DBT

and

SNP

were

adjusted

smoothly

to

optimal

levels

corresponding

to

the

unknown

disturbances

FIGURE

Simulation

results

of

MAPCNN

with

unknown

disturbances

In

the

graph

A

-LRB-

a

-RRB-

and

B

-LRB-

a

-RRB-

show

changes

of

acute

disturbances

and

random

noise

added

to

ΔCOmod

and

ΔMAPmod

responses

A

-LRB-

b

-RRB-

and

B

-LRB-

b

-RRB-

represent

setpoints

ΔCOmod

and

ΔMAPmod

-LRB-

solid

lines

-RRB-

and

predicted

outputs

by

NNs

-LRB-

dashed

lines

-RRB-

A

-LRB-

c

-RRB-

and

B

-LRB-

c

-RRB-

indicate

weight

changes

in

NN

for

the

controllers

in

DBT-CO

and

SNP-MAP

loops

weights

between

the

input

and

first

hidden

layers

-LRB-

top

-RRB-

first

and

second

hidden

layers

-LRB-

middle

-RRB-

and

second

hidden

and

output

layers

-LRB-

bottom

-RRB-

C.

Infusion

rates

of

DBT

-LRB-

solid

line

-RRB-

and

SNP

-LRB-

dashed

line

-RRB-

Figure

shows

the

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

very

large

amplitudes

of

random

noise

-LSB-

levels

-LRB-

in

both

ΔCOmod

and

ΔMAPmod

-RRB-

-LRB-

-RRB-

and

-LRB-

-RRB-

Fig.

-LRB-

a

-RRB-

and

B

-LRB-

a

-RRB-

-RSB-

Although

the

ΔCO

and

ΔMAP

responses

-LSB-

Figs.

-LRB-

b

-RRB-

and

B

-LRB-

b

-RRB-

-RSB-

approached

the

setpoints

they

depended

directly

on

the

appearance

patterns

and

the

amplitudes

in

large

random

noise

The

infusion

rates

in

DBT

and

SNP

and

the

estimation

errors

between

the

NN

and

model

responses

were

also

reflected

by

changes

of

random

noise.FIGURE

Simulation

results

of

MAPCNN

with

large

random

noise

A

-LRB-

a

-RRB-

and

B

-LRB-

a

-RRB-

show

changes

of

large

random

noise

added

to

ΔCOmod

and

ΔMAPmod

responses

Noise

level

-LRB-

in

ΔCOmod

and

mmHg

in

ΔMAPmod

-RRB-

level

-LRB-

ml

kg

min

and

mmHg

-RRB-

and

level

-LRB-

ml

kg

min

and

mmHg

-RRB-

A

-LRB-

b

-RRB-

and

B

-LRB-

b

-RRB-

represent

setpoints

ΔCOmod

and

ΔMAPmod

responses

-LRB-

-RRB-

A

-LRB-

c

-RRB-

and

B

-LRB-

c

-RRB-

indicate

the

error

between

the

model

response

and

the

predicted

response

by

NN

during

control

A

-LRB-

d

-RRB-

and

B

-LRB-

d

-RRB-

are

Infusion

rates

of

DBT

and

SNP

The

limitations

of

drug

infusion

rates

were

eliminated

Figure

shows

the

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

huge

disturbances

-LSB-

levels

-LRB-

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

-RRB-

-LRB-

ml

kg

min

and

mmHg

-RRB-

and

-LRB-

ml

kg

min

and

mmHg

-RRB-

-RSB-

In

the

disturbance

of

level

the

ΔCO

and

ΔMAP

responses

converged

on

the

setpoints

whereas

the

estimation

error

between

the

NN

and

model

responses

in

ΔCO

exhibited

some

oscillations

around

min

At

level

the

CO

control

was

completed

well

However

the

MAP

did

not

reach

the

setpoint

because

of

the

large

disturbance

and

the

interaction

from

DBT

used

for

the

CO

control

In

addition

the

infusion

rate

of

SNP

was

decreased

at

around

min

irrespective

of

the

hypertension

of

approximately

mmHg

The

MAP

response

did

not

oscillate

and

converged

on

a

steady

state

being

far

from

the

setpoint

At

level

neither

the

ΔCO

nor

ΔMAP

responses

reached

the

setpoints

The

infusion

rate

of

SNP

was

increased

instantaneously

by

receiving

a

great

disturbance

at

min

and

it

was

decreased

at

around

min

regardless

of

remaining

the

large

hypertension

of

approximately

mmHg

The

estimation

error

between

the

NN

and

model

responses

in

ΔCO

showed

oscillation

at

approximately

min.FIGURE

Simulation

results

of

MAPCNN

with

-LRB-

A

-RRB-

very

huge

and

-LRB-

B

-RRB-

acute

disturbances

A

huge

disturbance

level

-LRB-

ml

kg

min

in

ΔCOmod

and

mmHg

in

ΔMAPmod

-RRB-

level

-LRB-

ml

kg

min

and

mmHg

-RRB-

and

level

-LRB-

ml

kg

min

and

mmHg

-RRB-

B

acute

disturbance

level

-LRB-

min

to

the

added

disturbance

of

ml

kg

min

in

ΔCO

and

mmHg

in

ΔMAP

-RRB-

level

-LRB-

min

-RRB-

and

level

-LRB-

min

-RRB-

in

Eq

-LRB-

-RRB-

The

hemodynamic

responses

-LRB-

top

-RRB-

the

error

between

the

model

response

and

the

predicted

response

by

NN

during

control

-LRB-

middle

-RRB-

and

infusion

rates

of

DBT

and

SNP

-LRB-

bottom

-RRB-

in

ΔCO

-LRB-

left

-RRB-

or

ΔMAP

-LRB-

right

-RRB-

The

limitations

of

drug

infusion

rates

were

eliminated

Figure

shows

the

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

very

acute

disturbances

with

high

sensitivities

to

drugs

and

drug

interactions

-LSB-

levels

-LRB-

min

to

the

added

disturbances

of

ml

kg

min

in

ΔCO

and

mmHg

in

ΔMAP

-RRB-

-LRB-

min

-RRB-

and

-LRB-

min

-RRB-

-RSB-

At

levels

and

although

the

ΔCO

and

ΔMAP

responses

showed

small

oscillations

because

of

the

acute

disturbances

they

converged

on

the

setpoints

by

min

In

level

-LRB-

step

input

of

disturbance

-RRB-

the

ΔCO

and

ΔMAP

received

the

effects

of

the

step

input

of

the

very

acute

disturbances

at

min

directly

Although

ΔCO

and

ΔMAP

responses

were

disturbed

until

min

those

values

tended

to

converge

on

the

setpoints

eventually

In

particular

the

infusion

rate

of

SNP

at

level

was

increased

acutely

to

μg

kg

min

against

the

large

hypertension

of

mmHg

induced

by

the

very

acute

disturbance

with

high

amplitude

of

mmHg

at

min

in

turn

the

excessive

hypotension

after

the

acute

hypertension

was

induced

by

the

high

sensitivity

of

MAP

to

the

SNP

used

for

the

MAP

control

-LRB-

-RRB-

However

the

infusion

rate

of

SNP

was

adjusted

to

the

optimal

value

at

approximately

min

Time-variant

Changes

Figure

shows

the

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

the

unknown

time-variant

responses

containing

time

delays

to

therapeutic

agents

with

acute

disturbances

The

ΔCO

converged

on

the

setpoint

-LRB-

ml

kg

min

-RRB-

within

approximately

min

according

to

the

guided

setpoint

during

the

first

control

irrespective

of

time-variant

patient

sensitivities

and

drug

interactions

with

added

noise

it

showed

only

slight

oscillation

-LRB-

ml

kg

min

-RRB-

The

SNP

infusion

for

the

control

of

ΔMAP

suppressed

the

hypertension

-LRB-

and

mmHg

with

and

without

SNP

treatment

-RRB-

induced

by

DBT

infusion

beforehand

At

min

of

the

closed-loop

control

acute

disturbances

-LRB-

ml

kg

min

in

CO

and

mmHg

in

MAP

-RRB-

were

added

to

the

patient

responses

The

ΔCO

and

ΔMAP

quickly

converged

on

the

setpoint

within

approximately

min

whereas

the

transient

hypertension

was

induced

-LRB-

vs.

mmHg

with

or

without

SNP

-RRB-

The

average

errors

between

setpoints

and

observed

responses

were

ml

kg

min

in

CO

and

mmHg

-LRB-

mmHg

without

a

vasodilator

-RRB-

in

MAP

during

closed-loop

control

The

weights

and

biases

of

two

NN

were

adjusted

to

optimal

values

when

the

unexpected

changes

occurred

-LSB-

Fig.

-LRB-

c

-RRB-

and

C

-LRB-

c

-RRB-

-RSB-

Changes

of

biases

were

linked

to

those

of

the

time-variant

responses

and

acute

disturbances

The

infusion

rates

of

DBT

and

SNP

were

adjusted

to

optimal

levels

corresponding

to

the

unknown

time-variant

responses

FIGURE

Simulation

results

of

MAPCNN

under

unknown

time-variant

responses

with

disturbances

A

-LRB-

a

-RRB-

in

the

graph

displays

changes

of

the

parameters

of

the

time

delays

-LRB-

L

-RRB-

in

the

unit

impulse

response

of

Eq

-LRB-

-RRB-

A

-LRB-

b

-RRB-

indicates

changes

of

the

parameters

-LRB-

-RRB-

in

Eq

-LRB-

-RRB-

B

-LRB-

a

-RRB-

and

C

-LRB-

a

-RRB-

show

changes

of

acute

disturbances

and

random

noise

added

to

ΔCOmod

and

ΔMAPmod

responses

B

-LRB-

b

-RRB-

and

C

-LRB-

b

-RRB-

denote

setpoints

ΔCOmod

and

ΔMAPmod

-LRB-

solid

lines

-RRB-

and

predicted

outputs

by

NN

-LRB-

dashed

lines

-RRB-

B

-LRB-

c

-RRB-

and

C

-LRB-

c

-RRB-

are

the

weight

changes

in

NN

for

controllers

in

DBT-CO

and

SNP-MAP

loops

weights

between

input

and

first

hidden

layers

-LRB-

top

-RRB-

first

and

second

hidden

layers

-LRB-

middle

-RRB-

and

second

hidden

and

output

layers

-LRB-

bottom

-RRB-

D.

Infusion

rates

of

DBT

-LRB-

solid

line

-RRB-

and

SNP

-LRB-

dashed

line

-RRB-

Animal

Study

Figure

shows

results

of

closed-loop

control

by

MAPCNN

-LRB-

and

-RRB-

under

the

actual

response

of

canine

left

heart

failure

The

CO

in

the

DBT-CO

loop

converged

on

the

setpoint

within

approximately

min

regardless

of

the

unknown

response

containing

nonlinear

drug

interaction

and

the

effects

of

arterial

baroreflex

with

physiological

variation

in

actual

heart

failure

The

control

for

the

ΔMAP

in

the

SNP-MAP

loop

suppressed

the

acute

hypertension

-LRB-

mmHg

-RRB-

induced

by

the

DBT

infusion

Whereas

the

large

disturbance

like

arrhythmia

was

induced

at

around

min

during

the

control

the

CO

and

MAP

were

appropriately

controlled

by

the

MAPCNN

adjusting

the

infusion

rates

of

DBT

and

SNP

to

the

optimal

levels

The

average

errors

between

setpoints

and

observed

responses

were

ml

kg

min

in

CO

and

mmHg

in

MAP

during

closed-loop

control

FIGURE

Results

of

hemodynamic

regulation

by

means

of

MAPCNN

under

canine

left

heart

failure

Raw

data

of

CO

-LRB-

top

-RRB-

and

MAP

-LRB-

middle

-RRB-

responses

during

DBT

and

SNP

infusions

Bottom

in

the

graph

is

the

Infusion

rates

of

DBT

-LRB-

solid

line

-RRB-

and

SNP

-LRB-

dashed

line

-RRB-

DISCUSSION

The

development

of

automatic

drug-delivery

systems

requires

a

controller

that

can

adapt

to

the

various

patient

responses

in

clinical

situations

The

MAPCNN

was

confirmed

to

be

robust

with

respect

to

uncertainty

in

drug

interactions

acute

disturbances

time-variant

responses

containing

time

delays

to

therapeutic

agents

-LRB-

Figs.

and

-RRB-

and

the

actual

response

of

a

dog

with

heart

failure

-LRB-

Fig.

-RRB-

because

of

its

ability

to

learn

nonlinear

and

time-variant

changes

of

the

system

during

the

on-line

control

The

infusion

of

DBT

increased

MAP

as

well

as

CO

in

acute

left

heart

failure

of

dogs

-LSB-

Fig.

-LRB-

a

-RRB-

-RSB-

The

DBT

infusion

does

not

generally

act

on

the

SVR

whereas

both

the

CO

and

SVR

affect

MAP

Therefore

the

increase

of

MAP

during

DBT

infusion

in

this

study

would

have

resulted

mainly

from

increasing

the

CO

induced

by

the

actions

of

the

beta

receptors

-LRB-

β1

β2

-RRB-

of

cardiac

smooth

rather

than

the

SVR

On

the

other

hand

the

SNP

infusion

resulted

in

the

decrease

of

MAP

and

the

increase

of

CO

between

middle

and

high

doses

-LSB-

Fig.

-LRB-

b

-RRB-

-RSB-

because

of

the

decrease

of

SVR

-LRB-

afterload

of

a

heart

-RRB-

by

SNP

and

secondarily

increased

CO.

In

addition

the

SNP

treatment

might

have

suppressed

the

increase

in

preload

through

the

decrease

of

SVR

because

of

increasing

venous

compliance

for

retaining

the

blood

in

the

veins

and

lowering

the

venous

return

to

the

heart

in

case

of

congestive

heart

failure

In

the

simultaneous

regulation

of

CO

and

MAP

the

control

for

CO

induced

hypertension

-LRB-

Figs.

and

-RRB-

because

the

primary

control

target

in

this

study

was

the

increase

of

low

CO

in

acute

heart

failure

The

MAPCNN

was

able

to

suppress

the

hypertension

using

optimal

infusion

of

SNP

as

well

as

increasing

CO

using

DBT

to

an

optimal

target

value

because

the

combined

infusion

of

an

inotropic

agent

and

a

vasodilator

would

have

acted

effectively

Application

of

MAPCNN

to

a

multiple

hemodynamic

control

accomplished

the

regulation

of

CO

and

MAP

under

various

changes

of

the

patient

's

responses

to

drugs

and

disturbances

-LRB-

Figs.

and

-RRB-

In

particular

regardless

of

the

large

change

of

patient

sensitivities

as

shown

in

Fig.

the

MAPCNN

robustly

adjusted

the

acute

and

large

changes

to

generate

a

stable

condition

Similarly

to

the

previous

controllers

the

MAPCNN

suppressed

those

disturbances

performed

stabilized

control

under

unexpected

acute

disturbances

-LRB-

Figs.

and

-RRB-

Under

time-variant

patient

responses

with

pure

time

delays

which

are

a

crucial

obstacle

to

stable

control

the

MAPCNN

provided

sufficient

control

performance

-LRB-

Fig.

-RRB-

Regardless

of

actual

nonlinear

response

drug

interaction

and

partial

disturbances

with

arrhythmia

the

MAPCNN

could

regulate

the

CO

and

MAP

simultaneously

-LRB-

Fig.

-RRB-

The

superior

control

performance

resulted

from

the

function

to

adjust

the

weights

and

biases

of

the

NN

to

optimal

points

during

the

on-line

control

-LRB-

Figs.

and

-RRB-

Only

the

two-NN

models

of

average

responses

with

heart

failure

were

considered

in

the

calculation

of

the

appropriate

multiple

drug

infusion

rates

of

DBT

and

SNP

-LRB-

Fig.

-RRB-

to

mitigate

the

enormous

number

of

trials

associated

with

the

control

design

Model

predictive

controllers

or

fuzzy

controllers

might

require

an

extremely

lengthy

set-up

stage

to

prepare

the

model

banks

as

linear

models

of

patients

responses

to

drugs

or

to

provide

the

experienced

rules

describing

various

cases

in

clinical

settings

whereas

the

controllers

are

an

effective

means

of

adjusting

to

various

patients

sensitivities

to

and

describing

nonlinear

responses

to

A

controller

based

on

NN

solves

those

problems

because

it

decreases

the

number

of

models

required

for

the

control

design

of

the

various

changes

of

hemodynamics

clearly

Irrespective

of

the

wide

range

over

physiological

responses

-LRB-

Fig.

-RRB-

in

simulations

and

actual

response

of

a

dog

with

heart

failure

containing

the

effects

of

baroreflex

and

the

full

renin

angiotensin

system

induced

by

long-term

control

CO

and

MAP

in

the

MAPCNN

promptly

approached

the

setpoints

because

of

the

optimization

of

both

the

stability

and

speed

for

the

MAPCNN

-LRB-

Figs.

and

-RRB-

Therefore

the

designed

MAPCNN

will

be

feasible

for

application

to

automatic

drug

therapy

in

heart

failures

However

when

rapid

treatment

using

drugs

against

more

acute

and

large

disturbances

is

required

during

hemodynamic

controls

another

supplemental

system

might

be

required

Diagnoses

of

characteristics

of

patients

responses

to

drugs

or

tuning

weights

of

NNs

during

closed-loop

may

also

be

effective

for

hemodynamic

controls

to

accelerate

the

NN

learning

speed

In

addition

because

the

fluid

infusion

blood

transfusion

anesthesia

and

muscular

blockade

as

well

as

the

therapeutic

agents

controlled

in

this

study

are

common

in

clinical

practice

the

controllers

that

can

adjust

physiological

responses

to

further

multiple

drugs

will

be

desired

The

MAPCNN

tested

herein

can

be

extended

simply

to

multivariate

control

systems

under

such

clinical

conditions

for

drug

therapy

with

heart

failure

The

MAPCNN

was

tested

under

various

conditions

over

physiological

responses

to

elucidate

the

limitations

of

the

control

performance

-LRB-

Figs.

and

-RRB-

Regardless

of

such

severe

conditions

the

hemodynamics

during

MAPCNN

learning

very

large

changes

of

the

sensitivities

to

drugs

and

drug

interactions

and

the

disturbances

using

NN

tended

to

converge

on

the

setpoints

with

some

oscillations

observed

insofar

as

those

responses

were

within

the

possible

range

of

the

control

using

DBT

and

SNP

-LRB-

e.g.

Figures

and

-RRB-

On

the

other

hand

there

existed

cases

for

which

it

was

obviously

impossible

for

MAPCNN

to

control

the

hemodynamics

-LRB-

Figs.

and

-RRB-

For

example

when

the

interaction

from

DBT

for

the

CO

control

to

MAP

was

very

large

-LRB-

-RRB-

and

the

sensitivity

of

MAP

to

SNP

was

small

-LRB-

or

Fig.

-RRB-

the

MAPCNN

was

actually

incapable

of

attenuating

the

induced

hypertension

Those

cases

resulted

from

nonlinear

model

responses

to

drugs

in

the

present

study

the

hemodynamic

responses

therefore

would

have

saturated

because

of

the

range

of

nonlinear

model

responses

regardless

of

the

increase

of

drug

infusion

rates

The

NN

in

the

MAPCNN

under

the

severe

conditions

seems

to

have

tried

to

learn

and

adapt

to

the

situations

during

real-time

control

In

cases

of

large

error

between

actual

responses

and

predicted

responses

where

the

NN

in

the

MAPCNN

learned

the

average

responses

before

the

control

-LRB-

e.g.

the

CO

responses

of

case

in

Fig.

cases

and

in

Fig.

and

cases

and

in

Fig.

-RRB-

the

hemodynamics

during

the

control

exhibited

oscillation

and

the

NN

in

the

MAPCNN

would

have

tried

to

learn

the

severely

changed

situation

again

In

addition

when

the

hemodynamic

response

showed

incorrect

or

opposite

response

to

the

drug

input

compared

with

the

learned

average

response

by

the

NN

before

the

control

-LSB-

e.g.

cases

of

not

reaching

the

setpoint

and

converging

on

a

stable

state

regardless

of

the

DBT

infusion

for

CO

control

because

of

very

low

sensitivity

to

the

drug

-LRB-

or

Fig.

-RRB-

and

of

the

opposite

effect

of

SNP

on

MAP

speciously

because

of

the

very

large

disturbances

-LRB-

levels

and

in

Fig.

-RRB-

compared

with

the

learning

response

-RSB-

the

drug

infusion

rate

of

the

MAPCNN

was

decreased

despite

the

remainder

of

the

low

CO

or

hypertension

during

the

closed-loop

control

with

real-time

NN

learning

Therefore

these

simulation

results

suggest

the

following

two

points

First

in

those

cases

such

as

the

high

interaction

over

the

drug

effect

on

the

target

physiological

parameter

and

the

incorrect

or

opposite

responses

to

drugs

compared

with

those

of

previously

learned

NN

improvement

of

the

strategy

in

drug

treatment

would

be

required

alternatively

the

MAPCNN

would

fall

into

a

situation

of

control

impossibility

Second

the

physiological

variations

related

with

responses

to

anesthesia

antiarrhythmic

drug

and

muscle

relaxant

the

external

disturbances

and

the

artificial

background

noise

must

be

set

to

the

smallest

possible

values

to

bring

out

the

best

performance

of

the

controller

Several

limitations

are

apparent

in

present

study

First

the

modeling

for

the

CO

and

MAP

responses

to

drugs

might

depend

on

the

protocols

of

animal

experiments

such

as

the

order

and

washout

period

of

drug

infusions

The

protocol

in

the

present

animal

study

was

therefore

described

in

detail

-LRB-

reference

Modeling

of

Pharmacological

Response

in

the

MATERIALS

AND

METHODS

section

-RRB-

Second

one

-LRB-

low

CO

and

normal

MAP

-RRB-

of

the

heart-failure

conditions

was

tested

using

the

present

animal

study

The

kinds

of

heart

failures

are

various

in

actual

patients

Therefore

further

animal

studies

will

be

required

Finally

an

electromagnetic

flow

probe

was

used

for

CO

measurement

in

the

present

study

However

in

an

actual

clinical

setting

the

common

technique

for

CO

measurement

-LRB-

e.g.

the

thermodilution

technique

using

a

pulmonary

artery

-RRB-

has

a

slower

response

than

that

of

an

electromagnetic

probe

The

high

accuracy

of

a

flow

probe

such

as

the

time

resolution

-LRB-

at

least

s

as

used

for

this

experiment

-RRB-

and

the

pure

time

delay

from

an

actual

response

-LRB-

as

few

response

delays

as

possible

-RRB-

would

be

required

to

acquire

the

results

that

were

obtained

in

the

present

study

CONCLUSIONS

The

MAPCNN

was

designed

and

evaluated

in

simulation

and

animal

studies

to

regulate

the

nonlinear

responses

of

CO

and

MAP

in

acute

heart

failure

using

DBT

and

SNP

under

unexpected

changes

of

patient

sensitivities

to

drugs

drug

interactions

acute

disturbances

and

time-variant

responses

to

therapeutic

agents

The

MAPCNN

showed

robust

control

performance

irrespective

of

various

unexpected

responses

to

drugs

over

actual

physiological

responses

-LRB-

Fig.

-RRB-

and

actual

response

of

a

dog

in

heart

failure

Flexibility

of

a

NN

coupled

with

an

adaptive

control

mechanism

will

enable

the

regulation

of

various

physiological

responses

to

drugs

with

heart

failures

cardiac output
mean arterial pressure
therapeutic agents