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Medical Automation and Robotics 78.5 Emerging Trends in Medical Robotics Systems 1405

have been identiﬁed as appropriate at this stage include

orthopedic surgery, cutting and joining of bones at ex-

act optimal location, laparoscopic surgical procedures,

and accurate maneuvering of laparoscopic camera and

tools in a constrained environment.

In light of this, the advantages of using a medical

robotic system can be divided into two categories: those

related to the beneﬁts to the surgeon and those related

to the beneﬁts to the patient when using robotic tech-

nology. Medical robotics enable the surgeon to perform

new percutaneous procedures that could not have been

executed before, improve the surgeon’s ergonomics, en-

hance the surgical result (MIS), shorten the surgical

procedure, reduce radiationexposure,providebetter im-

age visualization, and enable extension of the operation

theater to remote locations usingtelesurgery techniques.

For the patient, there are few advantages due to the

use of medical robotic technology during the procedure,

mainly since the surgical procedure is performed min-

imally invasively. This results in faster recovery time,

less pain, less postoperative complications, better cos-

metic results, and cost reduction.

78.5 Emerging Trends in Medical Robotics Systems

Robots complement the trend in surgical procedures

toward minimal invasiveness. Robots serve as remote

hands for the surgeon and can deliver his/her motions

to the patient through miniature incisions. In order to

be able to mimic the surgeon’s hand adequately and

even achievesuperiority in terms of accuracy andminia-

ture motions, it is important to integrate force feedback

capabilities into the system as well as tactile feed-

back. However today even the best systems still suffer

from inaccurate forces and insufﬁcient tactile feed-

back, which are essential in several medical procedures.

Fig. 78.10 CardioArm – a hyper redundant snake like

robot for cardiac surgery

Hence, this is an area for future research and develop-

ment.

Making medical robots more friendly and intu-

itive is essential for the introduction of robots into

operating rooms. One of the lessons that robot devel-

opers can learn from the two decades of application

of surgical robots is that it is of utmost importance

to make robots friendlier to the operating-room en-

vironment. Moreover, even though the technology is

here, almost no new surgical procedures have been

developed based on robotic technology that cannot

be performed otherwise. It is therefore expected that,

in order to penetrate the operating-room environment,

new surgical technologies have to be developed based

on robotic technology, and even more importantly,

robots must become much more friendly to this unique

atmosphere.

An even more intriguing approach to medical robots

is miniature robots that canmoveinside the human body

(Fig.78.10). Several laboratories around the world are

pursuing this research with very few (like the passive

Given Imaging’s pillCam) in clinical use.

The area of medical robots is still in its infancy,

with applications with great potential not yet explored.

The trends are surgical robots with high accuracy,

robotically operated minimally invasive approaches,

miniature robots that move inside the human body, and

rehabilitation robotics.

Part H 78.5

1406 Part H Automation in Medical and Healthcare Systems

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Part H 78

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1409

Rotary Heart

79. Rotary Heart Assist Devices

Marwan A. Simaan

The left ventricular assist device (LVAD)isame-

chanical device implanted in patients with

congestive heart failure to assist the heart in

pumping blood through the circulatory system.

The latest generation of this device is comprised

of a rotary pump which is generally much smaller,

lighter, and quieter than the ﬁrst-generation con-

ventional pulsatile-type pump. The rotary pump is

controlled by varying the rotor (or impeller) speed

to adjust the amount of blood ﬂow through the

LVAD. If the patient is in a health care facility, the

pump speed can be adjusted manually by a trained

clinician to meet the patient’s blood needs. How-

ever, an important challenge facing the increased

use of these devices is the desire to allow the

patient to return home. The development of an

appropriate feedback controller that is capable of

automatically adjusting the pump speed is there-

fore a crucial step in meeting this challenge. In

addition to being able to adapt to changes in the

patient’s daily activities by automatically regu-

lating the pump speed, the controller must also

be able to prevent the occurrence of excessive

pumping. This dangerous phenomenon, known as

suction, may cause collapse of the ventricle and

damage to the heart muscle. In order to be able to

develop such a controller based on modern con-

trol theory an appropriate mathematical model of

a combined cardiovascular system and LVAD must

ﬁrst be developed. In this chapter, we develop

79.1 The Cardiovascular Model ..................... 1410

79.2 Cardiovascular Model Validation ........... 1414

79.3 LVAD Pump Model ................................ 1415

79.4 Combined Cardiovascular

and LVAD Model................................... 1416

79.5 Challenges in the Development

of a Feedback Controller

and Suction Detection Algorithm .......... 1418

79.6 Conclusion .......................................... 1420

References ................................................. 1420

such a model. The model is dynamic, time-varying,

and consists of six coupled nonlinear differential

equations. The time variation occurs over four

consecutive intervals representing the contraction,

ejection, relaxation, and ﬁlling phases of the left

ventricle. The LVAD in the model along with its inlet

and outlet cannulae are represented by a nonlin-

ear differential equation which relates the pump

rotational speed and pump ﬂow to the pressure

difference across the pump. Suction is accounted

for by adding a nonlinear resistance in the LVAD

model when the pressure in the left ventricle drops

below a speciﬁed threshold. Using this model we

discuss some of the challenges faced in the devel-

opment of: (1) an appropriate feedback controller

for the LVAD, and (2) an effective algorithm for

detection of suction in the left ventricle.

Heart transplantation has now been recognized as the

best therapy for patients withend-stage congestive heart

failure. However, potential recipients often wait long

periods of time (300 days or more on the average) be-

fore a suitable donor heart becomes available,and many

of these candidates, 20–30%, will die while awaiting

heart transplantation. Consequently, the medical com-

munity has placed increased emphasis on the use of

mechanical circulatory assist devices that can substitute

for, or enhance, the function of the natural heart while

the patient is waiting for the heart transplant [79.1,2].

A left ventricular assist device (LVAD) is such a de-

vice. There are two different types of LVADs. The ﬁrst

is a pulsatile pump producing pulsatile pressures and

Part H 79

1410 Part H Automation in Medical and Healthcare Systems

ﬂowssimilar to those produced by thenatural heart. The

second, and more recent, is a rotary pump that operates

continuously attempting to draw blood out of the left

ventricle and into the circulation. Rotary pumps are typ-

ically, quieter, smaller, and more efﬁcient than pulsatile

pumps, and consequently have received considerable

acceptance in recent years. Generally speaking, the goal

of the LVAD is to assist the native heart in pumping

blood so as to provide the patient with as close to a nor-

mal lifestyle as possible until a donor heart becomes

available or, in some cases, until the patient’s heart

recovers. In many situations, this means allowing the

patient to return home and/or to the workforce.

An important engineering challenge facing the in-

creased use of the rotary LVAD is the development of

an appropriate controller for the speed of the rotor (or

pump impeller). Such a controller, in addition to be-

ing robust and reliable, must be able to adapt to the

daily activities and physiological changes of the pa-

tient by regulating the pump speed in order to meet

the body’s requirements for cardiac output (CO)and

mean arterial pressure (MAP) [79.3, 4]. Since the ro-

tary pump does not use valves, if its speed is too low,

blood may regurgitate back from the aorta to the left

ventricle through the pump, resulting in what is known

as backﬂow. If the pump speed is too high, the pump

will attempt to draw more blood from the ventricle than

available, which may cause collapse of the ventricle

resulting in a dangerous phenomenon called suction.

The occurrence of suction must be detected quickly

and the pump speed reduced before the heart muscle

is damaged. While avoiding these two extremes, the

pump speed must also be adjusted continuously, up and

down to meet the patient’s varying levels of physical

activity and emotional changes [79.5–10]. The eventual

goal of a pump speed controller is therefore to meet all

these requirements so that an LVAD recipient patient

could potentially leave the hospital and return home

to a normal lifestyle. Given that the pump is contin-

uously interacting with the cardiovascular system, the

development of a speed controller that meets the above

objectives must therefore be done using tools developed

in modern control theory. This cannot be done without

ﬁrst having an appropriate mathematical model for this

complex system. The model must be simple enough to

be tractable and yet it must be comprehensive enough

to capture the essential relationships between the hemo-

dynamic variables and provide the important input and

output boundary conditions without the ambiguity of

unnecessary state variables. In this chapter, we discuss

the development of such a model. We ﬁrst present and

validate an autonomous ﬁfth-order model of the cardio-

vascularsystem which emphasizes the pressure–volume

relationship of the left ventricle. We then present a ﬁrst-

order model of a rotary LVAD along with its inlet and

outlet cannulae and with the pump rotational speed as

its control variable. We account for the phenomenon

of suction by adding a nonlinear resistance to the in-

let cannula model which becomes active when the left

ventricular pressure drops below a certain threshold. Fi-

nally, we combine these two models into a sixth-order

time-varying nonlinear model with the rotational speed

of the pump being the only control variable. The time

variations in this model are due to the cyclical nature

of the ventricle elastance and its changes as a function

of time within one cardiac cycle. The nonlinearities are

due to the mitral and aortic valves in the cardiovascular

model and the suction resistance in the LVAD model.

The binary state of each of these valves yield four con-

secutive phases within one cardiac cycle during which

the ventricle contracts, ejects, relaxes, and then ﬁlls de-

pending on which valve is open and which is closed.

As a result, the mathematical description of the entire

model changes as the ventricle crosses from one phase

to the next. We will conclude this chapter by outlin-

ing some of the challenges in the development of both

a feedback speed controller and a suction detection al-

gorithm that need to be overcome before the ultimate

goal of the LVAD becomes a reality and LVAD patients

are able to return to a normal lifestyle.

79.1 The Cardiovascular Model

A cross-section schematic of the heart illustrating its

various components is shown in Fig.79.1. Each side of

the heart has its own atrium and ventricle, and each side

controls a different blood circulation path. The left side

of the heart controls the systemic circulation of blood

throughout the body while the right side controls the

pulmonary circulation of blood to the lungs [79.11]. Af-

ter the blood picks up oxygen in the lungs it returns to

the heart entering through the left atrium. The left ven-

tricle pumps the oxygen-rich blood through the aorta to

the rest of the body. The blood returns to the heart de-

pleted of oxygen, this time through the right atrium. It

Part H 79.1

Rotary Heart Assist Devices 79.1 The Cardiovascular Model 1411

Aorta

Left atrium

Right atrium

Mitral valve

Aortic valve

Left ventricle

Right ventricle

Fig. 79.1 Cross-section of a beating heart

is then pumped to the lungs by the right ventricle. The

blood receives oxygen in the lungs, and returns to the

left atrium of the heart. Upon entering the left atrium,

the two circulatory paths are then repeated. The blood

path through the heart and both circulation systems can

be seen in Fig.79.2 [79.12]. Due to the different nature

of the two circulation paths, each side of the heart has

a different workload. The systemic circulation is much

longer than the pulmonary one, and encounters consid-

erable more resistance [79.11]. To handle the longer

path, the left ventricle is more elastic than the right,

givingit thestrength topump bloodat ahigher pressure.

The heart is a very complex system that is very dif-

ﬁcult to model mathematically. Numerous dynamical

state-space models of varying degrees of complexity

have been developed in the past ﬁfteen years or so.

For example, an eighth-order hybrid model of the heart

which subdivides the human circulatory system into

a number of lumped parameter blocks that include the

pulmonary arterial and venous systems as well as both

ventricles has been developed in [79.13]. An 11th-order

model which includes the resistance of peripheral blood

vessels has been developed in [79.14]. Although a com-

plete heart model can be supplemented with a model

of an LVAD, in this chapter we assume that the right

ventricleand pulmonarycirculation are healthy and nor-

mal and as a result their effect on the LVA D,which

is connected from the left ventricle to the ascending

aorta, can be neglected [79.1, 6]. A ﬁfth-order lumped

parameter electric circuit model which can reproduce

the left ventricle hemodynamics of the heart [79.15,16]

is shown in Fig.79.3. In this model, the behavior of the

left ventricle is modeled by means of a time-varying ca-

pacitance (or compliance) C(t), which is the reciprocal

of the ventricle’s elastance function E(t). The elastance

represents the contractual state of the left ventricle. It

relates to the ventricle’s pressure and volume [79.17]

according to an expression of the form

E(t) =

LVP( t)

LVV(t)−V

, (79.1)

where LVP(t) is the left ventricular pressure, LVV(t)is

the left ventricular volume, and V

is a reference vol-

ume, which corresponds to the theoretical volume in the

ventricle at zero pressure. Several mathematical expres-

sions have been derived to approximate the elastance

function E

(t) of a healthy heart. In our work, we use

the expression

(t) =(E

max

−E

min

)+E

min

, (79.2)

Capillary beds of

lungs where gas

exchange occurs

Capillary beds of

all body tissues

where gas

exchange occurs

Oxygen rich,

-poor blood

Pulmonary

veins

Pulmonary

arteries

Aorta and

branches

Left

atrium

Right

atrium

Left

ventricle

Right

ventricle

Heart

Systemic circuit

Key:

Pulmonary circuit

Venae

cavae

Oxygen poor,

-rich blood

Fig. 79.2 Diagram of systemic and pulmonary circulatory systems

(after [79.12])

Part H 79.1

1412 Part H Automation in Medical and Healthcare Systems

C(t)

LAP(t)

LVP(t)AoP(t)

AP(t)

–

Fig. 79.3 Cardiovascular circuit model

where E

) is the so-called double hill function repre-

sented by the expression [79.18]

) =1.55





0.7



1.9



0.7



1.9







1.17



21.9



(79.3)

In the above expression, E

) is the normalized elas-

tance, t

= t/T

max

, T

max

= 0.2+0.15t

,andt

is the

cardiac cycle interval, i. e., t

=60/HR, where HR is

the heart rate. Notice that E

(t) is a rescaled version

of E

) and the constants E

max

and E

min

are related to

the end-systolic pressure–volumerelationship (ESPVR)

and the end-diastolic pressure–volume relationship

(EDPVR), respectively. Figure 79.4 shows a plot of

(t) for a healthy heart with E

max

= 2 mmHg/ml,

min

= 0.06 mmHg/ml, and a heart rate of 60bpm

0 0.2 0.4 0.6

Cardiac cycle

min

0.8 1

Time (s)

(mmHg/ml)

1.5

0.5

max

Fig. 79.4 Elastance function E

(t) =

C(t)

of a healthy

heart (cardiac cycle =60 /HR)

(beats per minute). For a heart with cardiovascular dis-

ease, the elastance expression used in our model is

modiﬁed according to E(t) =δE

(t). That is, the elas-

tance E

(t) is scaled with a factor 0 < δ ≤ 1, where

δ =1 represents a healthy heart and smaller values of δ

are used to represent cardiovascular disease. The more

severe the disease, the smaller the value of δ. Also in

the model, preload and pulmonary circulations are rep-

resented by the capacitance C

; the aortic compliance is

represented by the capacitance C

, and afterload is rep-

resented by the four-element Windkessel model [79.19]

comprising R

, L

, C

,andR

. Preload, or venous

blood returning to the heart, is closely related to the

cardiac output (CO) produced by the heart for a given

level of contractility. Afterload can be described as the

pressure that the left ventricle has to generate in or-

der to eject blood. It refers to the vascular resistance

that the heart sees as it pumps blood. The mitral and

aortic valves (Fig.79.1) are represented by two non-

ideal diodes consisting of a resistance R

and ideal

diode D

for the mitral valve, and resistance R

and

ideal diode D

for the aortic valve. In this representa-

tion, we have kept the number of model parameters to

a minimumwhile maintainingenough complexity in the

model so that it can reproduce the hemodynamics of the

left ventricle. Table 79.1 lists the various system param-

eters and their typical associated values [79.20–22].

Obviously the circuit model in Fig.79.3 is time-

varying because of the capacitance C(t) and nonlinear

because of the two diodes. Since each ideal diode has

two states: open-circuit (O/C) and short-circuit (S/C),

Table 79.1 Model parameters

Parameters Value Physiologicalmeaning

Resistances (mmHgs/ml)

1.0000 Systemic vascular resistance

(SVR)

0.0050 Mitral valve resistance

0.0010 Aortic valve resistance

0.0398 Characteristic resistance

Compliances (ml/mmHg)

C(t) Time-varying Left ventricular compliance

4.4000 Left atrial compliance

1.3300 Systemic compliance

0.0800 Aortic compliance

Inertances (mmHgs

/ml)

0.0005 Inertance of blood in aorta

Val ve s

Mitral valve

Aortic valve

Part H 79.1

Rotary Heart Assist Devices 79.1 The Cardiovascular Model 1413

Table 79.2 Phases of the cardiac cycle

Modes Valves Phases

Mitral Aortic

1 Closed Closed Isovolumic relaxation

2 Open Closed Filling

1 Closed Closed Isovolumic contraction

3 Closed Open Ejection

– Open Open Not feasible

Table 79.3 State variables in the cardiovascular model

Variables Name Physiologicalmeaning (unit)

(t) LV P(t) Left ventricular pressure (mmHg)

(t) LAP(t) Left atrial pressure (mmHg)

(t) AP(t) Arterial pressure (mmHg)

(t) AoP(t) Aortic pressure (mmHg)

(t) Q

(t) Total ﬂow (ml/s)

four different circuits representing different phases of

the ventricular function can therefore be modeled.

When D

is S/C and D

is O/C (i.e., the mitral valve is

open and aortic valve is closed) the circuit in Fig.79.3

represents the phase when the left ventricle is ﬁlling.

When D

is O/C and D

is S/C (i.e., the mitral valve is

closed and the aortic valve is open)the circuitrepresents

the phase when the ventricle is ejecting. The circuit in

which bothdiodes are O/C (i.e., boththe mitral andaor-

0 0.2 0.4 0.6 0.8 1

Time (s)

–C(t)/C(t) (s

–1

)

–10

–20

–30

–40

Fig. 79.5 Plot of

−

C(t)

for a healthy heart over one cardiac

cycle

tic valves are closed) will occur twice and represents

the phase when the ventricle is undergoing isovolumic

contraction and relaxation. Finally, the circuit in which

both diodes are S/C (i.e., both the mitral and aortic

valves are open) is clearly not feasible. The three dif-

ferent phases of operation of the left ventricle over four

consecutive different time intervals within the cardiac

cycle are summarized in Table 79.2. Every phase within

the cardiac cycle is therefore modeled by a different

equivalent circuit and hence a different set of linear

time-varying differential equations. However, by appro-

priately modeling the diodes as nonlinear elements, it

is possible to write only one set of differential equa-

tions, which describes the behavior of the entire model

for all three phases. Selecting the state variables as the

hemodynamic variables listed in Table 79.3 (and shown

on the circuit in Fig.79.2), and using basic circuit anal-

ysis methods [79.23] such as Kirchhoff’s voltage and

current laws (KVL and KCL), we can derive the state

equations for the cardiovascular circuit model shown

in Fig.79.2 as

⎛

⎜

⎝

⎞

⎟

⎠

⎛

⎜

⎝

−

C(t)

0000

−1

0000

−1

−R

⎞

⎟

⎠

⎛

⎜

⎝

⎞

⎟

⎠

⎛

⎜

⎝

C(t)

−1

C(t)

−1

⎞

⎟

⎠



r(x

−x

)

r(x

−x

)



(79.4)

In (79.4)

C(t) = dC(t)/ dt and r(x) represents the ramp

function

r(ξ) =

⎧

⎨

⎩

ξ if ξ ≥0 ,

0ifξ<0 .

(79.5)

We note that the model described above is an au-

tonomous switched linear time-varying system over

four different phases within the cardiac cycle [79.15,

16]. Its solution is oscillatory due to the cyclic nature

of the terms

C(t)and1/C(t) in the matrices in (79.4).

A plot of the expression −

C(t)/C(t) over one cardiac

cycle for a healthy heart is shown in Fig.79.5. The term

1/C(t) represents the elastance function E

(t) whose

plot is shown in Fig.79.4.

Part H 79.1

1414 Part H Automation in Medical and Healthcare Systems

79.2 Cardiovascular Model Validation

The ability of the ﬁfth-order model described in the pre-

vious section to emulate the hemodynamics of the left

ventricle is demonstrated by simulating the model for

both nominal steady-state conditions, and in response

to perturbations of preload and afterload. Figure 79.6

shows the simulation waveforms of the hemodynamics

for an adult with heart rate of 75bpm. In this particu-

lar case, systolic and diastolic pressure were 117 and

77mmHg, mean aortic pressure (MAP) was 99 mmHg,

cardiac output (CO) (i.e., the blood pumped by the ven-

tricle in 1min) was 5.21l/min and stroke volume (SV)

(i.e., the volume of blood pumped by the ventricle in

one cardiac cycle) was 69.5ml/beat. These numbers

and waveforms are all consistent with hemodynamic

data in normal subjects described in [79.24].

A second method to validate the model and verify

that it can reproduce the human left ventricle behavior

is to vary the preload and afterload conditions, while

keeping the left ventricle parameters (E

max

, E

min

,and

) constant. If the model behaves as expected, we

should have an approximately linear relationship be-

tween end-systolic pressure and left ventricle volume

0 0.5 1 1.5 2 2.5 3

AoP

LAP

LVP

Pressure (mmHg)

Time (s)

150

100

0 0.5 1 1.5 2 2.5 3

Aortic flow (ml/s)

600

400

200

0 0.5 1 1.5 2 2.5 3

LVV (ml)

150

100

Fig. 79.6 Simulated hemodynamic waveforms for a normal heart

(known as end-systolic pressure–volume relationship,

or ESPVR), in spite of changes in preload and af-

terload. A total of four preload and four afterload

conditions were simulated using E

max

=2mmHg/ml,

min

= 0.05 mmHg/ml, and V

= 10 ml. The result-

ing pressure and volume of the ventricle are typically

plotted in the form of pressure–volume (PV-)loops.

The PV-loops in Fig. 79.7a, represent the result of

changing afterload conditions by selecting different val-

ues of systemic vascular resistance (R

in Fig.79.3),

while keeping end-diastolic volume (EDV) constant.

050

ESPVR

=0.005

=0.08

=0.8

=0.32

ESPVR

=1.5

=0.5

100 150

a) LVP (mmHg)

LVV (ml)

180

160

140

120

100

0 50 100 150

b) LVP (mmHg)

LVV (ml)

180

160

140

120

100

Fig. 79.7a,b PV-loops for different values of (a) afterload

resistance, and

(b) preload volume

Part H 79.2