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Automation and Control in Biomedical Systems 76.2 Theory and Tools 1365

Table 76.1 Summary of theory and tools by Section, topic(s), and advantages/disadvantages of the various methods

Section Topic(s) Pros (+) and cons (–)

76.2.1 A priori identiﬁability + Highlights parameter estimation concerns based on available data

− Theoretically and computationally challenging

(Weighted) least + Straightforward application, many tools available

squares − Weighting of points is subjective

Maximum likelihood + Robust and commonly employed

− Based on assumed error structure/distribution

76.2.2 Compartmental PK + Compact models, generally identiﬁable

− No relationship to mechanism or physiology

Population PK + Incorporates intra-/interpatient variability in model

(when justiﬁed by available data)

− Not straightforward to tailor to an individual

− Patient and data intensive

76.2.3 Physiological PK + Incorporates patient physiology explicitly

− Measurements of individual tissues are difﬁcult

to collect (limited to animal studies)

− Large number of equations makes parameter estimation

computationally challenging

76.2.4 Biochemical networks + May provide high-resolution mechanistic detail

− May be difﬁcult to resolve causality (cause versus effect)

− Semiquantitative (colorimetric)

76.2.5 Optimal control + Solves constrained dynamic optimization problem

− Formulation (two-point boundary-value problem, continuous

controls) must be reasonable for solution of corresponding

biomedical problem

Model predictive + Robust to mismatch between actual patient/process

control and mathematical model

+ Solves constrained dynamic optimization problem

− Suboptimal (relaxed) solution of problem

− Mathematical analysis of stability and performance

is theoretically challenging

zero mean and normally distributed with variance σ

While these may not be rigorously true of biomedi-

cal data sets, MLE has been shown to work well with

biomedical data, and packages are available that use

MLE for estimation [76.18, 19]. These packages also

return parameter information in the form of a conﬁ-

dence interval or coefﬁcient of variation. Large values

indicate poor parameter accuracy, and hence possible

structural parameter identiﬁability issues [76.20]orvi-

olations of the assumptions above as parameters may

not be Gaussian distributed in the modeling of multiple

individuals.

Part H 76.2

1366 Part H Automation in Medical and Healthcare Systems

76.2.2 Pharmacokinetics

PK is the study of drug administration to, distribution

in, and clearance from the body [76.4,5]. To capture the

dynamics observed after drug dosing, compartmental

models are often employed (Fig. 76.3). The adminis-

tered dose is given by D(t). Individual compartments

aremodeledasdrugmasses(x

and x

), with cor-

rection to concentration in the output equation (via

division by volume V). Clearance of the drug is from

the central compartment (rate k

). Additional dynamic

character is included by adding compartments and in-

tercompartment transfer rates (k

from compartment i

to compartment j). A two-compartment model can be

represented mathematically as

(t)

=−k

(t)−k

(t)+k

(t)+ D(t) ,

(76.3)

(t)

(t)−k

(t) , (76.4)

y(t) =

(t)

(76.5)

The output(s) of the model corresponds to measurable

concentrations of drug, as given by y(t). Additional

blocks can be added, as necessary, to capture observed

plasma dynamics related to dosing (for drugs not de-

livered intravenously) and/or absorption. The resulting

model is an empirical description of patient drug con-

centration as a function of time after administration.

These model structures are commonly employed using

available PK modeling tools such as ADAPT II [76.18],

and the FDA requires some pharmacokinetic informa-

tion for most new chemotherapeutics [76.7]. Parameters

in the model can be estimated from individual patient

data, when detailed pharmacokinetic measurements are

available. More often, models of this form are con-

structed from animal studies where multiple animals

D(t)

Fig. 76.3 Two-compartment mamillary model used in

pharmacokinetic analysis. Plasma dynamics are captured

by the central compartment (block 1) in Eq. (76.3)

(e.g., mice or rats) are euthanized at each measuredtime

point. The mean and standard deviation of measured

drug concentrations are used as the data to which a sin-

gle model is ﬁt. Low-order deterministic models may

not capture the observed drug concentration measure-

ments for a variety of reasons, including nonlinearity,

higher-order dynamics, and interindividual variability.

To address interindividual variability and data spar-

sity, population models are often developed [76.16,

21, 22]. In this case, a stochastic approach to model

parameterization is employed, where parameters are

composed [76.21]as

=θ

+η

+θ

. (76.6)

Parameters (p

) for patient i are a function of the

population mean value of the parameter θ

, interindi-

vidual variability in the parameter η

, and any known

correlative effects C

scaled by their population mean

correlation θ

. These parameter formulations are then

included in model structures akin to those in (76.3–

76.5), as replacements for the k

and k

parameters, for

example. Variances on the measurement noise (added

to (76.5)) and interpatient variability η

are speciﬁed as

part of the estimation. With this approach, it is possi-

ble to use a small number of output measurements from

a large number of individuals to characterize both the

underlying model structure (through the observed dy-

namics) andthe populationvariability(through the need

for η and θ

or C

to describe individual responses).

Software tools are available for constructing these mod-

els (including NONMEM [76.22] and SPK [76.23]).

A population model, once constructed, is representative

of the population response to a drug dose. Furthermore,

it can provide a characterization of both validated vari-

abilities (as a function of body weight, gender, race,

liver or kidney performance status, etc.) and the dis-

tribution of responses expected after dosing a group of

patients with the drug. However, it is not designed to

be predictive in the single-patient case; here it may be

of more use to couple the variabilities established in the

population model with the ability to tailor an individual

PK model.

76.2.3 Modeling Physiology

The potential of detailed physiological models was

recognized by Teorell when he began studying pharma-

cokinetics [76.4, 5], but calculational limitations made

physiological modeling of drug PK intractable in 1937.

With today’s desktop computational power, simulat-

ing physiological models of drug administration and

Part H 76.2

Automation and Control in Biomedical Systems 76.2 Theory and Tools 1367

distribution is straightforward. A physiologically-based

model for a cancer chemotherapy application is shown

in Fig.76.4. Each block in a physiologically-based

model represents an ordinary differential equation

that characterizes concentration in a particular tissue

or ﬂuid, with the volume of the compartment cor-

responding to the physiological volume into which

the compound distributes. Where necessary, subcom-

partments can be added to modify tissue dynamic

response, and these are often denoted as vascular (blood

space) and extravascular (interstitial space) compart-

ments (models may also include intracellular or tissue

binding spaces as well [76.8, 24]). Transfer between

vascular and extravascular space can be via gradient-

based diffusion or active transport, and may be uni-

or bidirectional. Unidirectional arrows between tissue

compartments denote the ﬂow of blood; the bidirec-

tional arrow pairs between red blood cells (RBCs)

and the plasma compartments represent equilibration

(transport is often fast in RBCs, such that they are of-

ten represented algebraically rather than differentially).

Metabolic elimination and clearance are shown as un-

connected arrows exiting particular (sub)compartments

(e.g., the arrow out of liver extravascular space), and

infusion into the system can be properly placed in

a physiological sense, e.g., the IV dose administered

to the venous blood compartment. Advantages of this

approach include the accuracy of the tissue connectiv-

ity and the availability of mean values for the ﬂow and

volume parameters [76.25]. Furthermore, knowledge of

the metabolic pathway of drug clearance (e.g., liver

metabolism or kidney excretion) can be included in the

physiologically correct location. This structure changes

the identiﬁcation burden to that of metabolic rates and

intratissue transport (plasma ↔interstitial ﬂuid ↔cell)

and dynamics. Resolution of these effects can be chal-

lenging (when feasible) as the necessary information

(e.g., arterio–venous differences in drug concentration)

for identiﬁcation is not typically available from in vivo

measurements. The result is that tissues are often as-

sumed to be well mixed if they are highly perfused

(e.g., kidney and liver), and only tissues where sig-

niﬁcant transport resistances are involved are modeled

using more detailed intratissue dynamics (and then of-

ten using a compartmental approach).

The utility of these structures is of more potential

beneﬁt when evaluating pharmacodynamic effects. Un-

like the compartmental or population models described

above, the physiological model also allows the effects

of the drug to be properly assigned to their physiologi-

cal sites of action. These outcomes can be positive (e.g.,

Lung

Brain

Heart

Liver

RBCs RBCs

IV dose

Spleen

Gut

Kidney

Venous blood

Arterial blood

Tumor

Other

Muscle

Fat

Fig. 76.4 Block structure schematic of a physiological model of

drug distribution

antitumor activity related to tumor concentration, not

plasma concentration, of an antineoplastic) or negative

(e.g., toxic side-effects of a drug affecting liver perfor-

mance status). This is a signiﬁcant advantage in the use

of in vitro information for the purposes of in vivo mod-

eling, as the concentration at the site of action (effect

or toxicity) is more accurately represented by a physio-

logical model than the plasma concentration estimate of

a compartmental model.

76.2.4 Biochemical Networks

Phenotype is related to genotype at some level, mean-

ing that macroscopic observables such as physiology,

PK, etc., are driven by biological networks at a vari-

ety of scales. The ﬁeld of systems biology is focused

on developing a systems-level description of biology

by studying the dynamics of cellular and organ func-

tion, rather than the traditional drill-down study of

increasingly highly resolved portions of a cell [76.26].

In order to rigorously integrate the complex behaviors

taking place at the genetic level with the macroscopic

(whole-organism) response, and to ground these hy-

Part H 76.2

1368 Part H Automation in Medical and Healthcare Systems

potheses in experimental data, requires a computational

model [76.27].

Due to the scales spanned in network analysis (from

the gene regulatory [76.28] to the metabolic [76.29]), it

is infeasible in this space to review the plethora of tools

employed. Ordinary differential equations, due to their

simplicity, are popular, and compartmental approaches

(such as those in Sect.76.2.2) are also used to sim-

plify the model structures. The systems biology markup

language (SBML) is one tool for representing biochem-

ical networks, both qualitative and quantitative [76.30].

AreviewofSBML, along with two other data rep-

resentation standards (PSI MI (Proteomics Standards

Initiative Molecular Interaction) and BioPAX), can be

found in[76.31]. The strengths of thesepackages can be

seen in the complexity of the models that are generated,

and can be simulated, as a result of complex network

modeling (see [76.29] and models at www.systems-

biology.org and www.biopax.org).

76.2.5 Model-Based Control

and Optimization

A commonly employed tool in model-based treatment

design for biomedical systems is optimal control. Math-

ematically, optimal control problems can be formulated

as follows [76.32]

min

u(t)

J(y(t), u(t), r(t)) , (76.7)

subject to:

x = f(x(t), u(t), p) , (76.8)

y(t) =h(x(t), u(t), p) , (76.9)

min

≤u(t) ≤u

max

, (76.10)

y(t

) = y

ﬁn

. (76.11)

The objective function (76.7) often takes the form of

a least-squares deviation of y(t) from some desired

trajectory r(t), and the decision variable is the u(t)

proﬁle over 0 ≤t ≤ t

; for example, in the diabetes ex-

ample introduced later in this chapter, the measured

variable would be plasma glucose concentration (y(t)),

r(t) would be the desired glucose concentration (e.g.,

90mg/dl), and u(t) would be the insulindelivery proﬁle

(or delivery rate) from the present time t to t +t

. Feasi-

ble system trajectories are governed by the dynamics of

the model (states x(t), parameters p), and these are in-

corporated as constraints (76.8)and(76.9). Continuing

the diabetes example, the states characterize the patient;

in a physiological model context, these states would be

the glucose and insulin concentrations in the various

physiological tissues (not all of which are measurable).

Constraints on the input magnitude can be enforced, as

in (76.10); other input constraints can also be included,

though they are not explicitly described here. Finally,

a desired ﬁnal value for the controlled variable y(t

)

is included. The identiﬁcation of a feasible treatment,

an input sequence that drives y(0) to y(t

), involves

the solution of a constrained two-point boundary-value

problem. Control vector parameterization [76.33]is

a common method of computer implementation, where

the timeaxis is discretized into k equal-length steps, and

the series of input levels over each of the steps become

the decision variables of the optimization problem. The

resulting input proﬁle generally has a characteristic

bang–bang shape, switching from full on to full off at

one or more points along the time axis. The strength

of optimal control is the ability to solve nonlinear

control problems in the presence of input constraints.

A key shortcoming is the formulation of optimal control

versus the practice of medicine. The former speciﬁes

an endpoint constraint and has no mechanism for the

inclusion of information that becomes available at in-

termediate time points. Clinical practice, on the other

hand, does not generally have an a priori speciﬁed end

time of treatment and routinely takes measurements of

patient performance status and incorporates these into

treatment decisions.

One way to take advantage of model-based control

and optimization techniques while retaining the advan-

tages of the optimal control formulation is to use reced-

ing horizon control, also referred to as model predictive

control [76.34,35]. Recedinghorizon controlis an open-

loop optimization posed and solved for a sequence of

input move changes at each time step; a typical model

predictive control formulation may be posed as

min

Δu(k|k)

Γ

(r(k +1|k)−y(k +1|k))

+Γ

Δu(k|k)

(76.12)

subject to: x(k +1|k) = f(x(k|k), u(k|k), p)

(76.13)

y(k|k) =h(x(k|k), u(k|k), p) (76.14)

min

≤u(k|k) ≤u

max

(76.15)

|Δu(k|k)|≤u

rate

. (76.16)

Because the model is used to predict output responses

at future times (up to N

steps in the future), statisti-

cal notation is employed, where y(k +1|k) is the vector

of N

predicted outputs at time k+1 given information

up to time k. The corresponding vector of desired out-

put values is r(k+1|k), and the degrees of freedom are

the N

input moves Δu(k|k). The matrices Γ

and Γ

Part H 76.2

Automation and Control in Biomedical Systems 76.3 Techniques and Applications 1369

are weights to trade off tracking error (large Γ

)ver-

sus input move suppression (large Γ

). The underlying

model dynamics of (76.13)and(76.14) can be continu-

ous or discrete, as they are simulated at each time step,

but the output values employed in the calculation of

the objective correspond to the N

future step times.

Because the solution methodology includes the use of

an optimization routine at each time step, constraint

incorporation is straightforward, and input constraints

can be included in magnitude-constrained (76.15)and

rate-constrained (76.16) forms. Output constraints can

be included, but these may lead to infeasibilities in the

optimization problem, much as state constraints do in

optimal control. One option is to soften the constraints

by including them as additional weighted terms in the

objective function [76.36]. At each sample time, mea-

surements from the system are used to update the states

or outputs of the model, and the optimization problem

is solved. The ﬁrst input move change is implemented,

and the process repeats at each following sample time

(as shown schematically in Fig.76.5). In the case that

measurable quantities are sampled at different intervals,

the update rate of the model can be variable (this is

referred to as a multirate MPC formulation [76.37]).

When measurements are not collected at each sample

time, multiple inputs in the sequence Δu(k|k) can be

implemented. The structural advantages of MPC,in-

cluding the online solution of an optimization problem

that incorporates available patient information, are sig-

niﬁcant, but a key drawback of this control structure is

k+1 k+2 k+N

–1

u(k+N

–1|k)

k+N

Past Future

Current output

measurement

y(k)

Past

output

measurements

Model-predicted

future output values

(k+1|k)

Optimal

input profile

u(k|k)

Reference r(k+1|k)

Horizon

Fig. 76.5 Receding horizon (model predictive) control implemen-

tation schematic. Model-predicted deviations from the desired

reference are minimized over a future horizon

the challenging analysis of algorithm performance. Sta-

bility guarantees, which may be required by the FDA

before an algorithm can be deployed in an ambulatory

setting, often require the use of endpoint constraints

or long prediction horizons (i.e., large N

or inﬁnite-

horizon formulations), which may limit the achievable

performance.

76.3 Techniques and Applications

The potential scope for automation and control in

biomedical problems precludes a canonical review here.

Entire journals are focused on biomedical problems

from the engineering perspective (e.g., IEEE Transac-

tions on Biomedical Engineering, Annals of Biomedical

Engineering, IET Systems Biology), and mainstream

control journals (e.g., Automatica, Journal of Process

Control, Control Engineering Practice) also publish

biomedical control papers. There are also journals fo-

cused on the tools as they apply to classes of problems

(e.g., Journal of Pharmacokinetics and Pharmaco-

dynamics for PK and PD modeling tools). Beyond

the diabetes and cancer case studies discussed below,

a wide variety of problems have been addressed, such

as human immunodeﬁciency virus (HIV)/acquired im-

munodeﬁciency syndrome (AIDS), blood pressure, and

anesthesia, among others (some recent review articles

include [76.9,38,39]).

76.3.1 Type I Diabetes Modeling and Control

Diabetes has been a popular biomedical modeling and

controller design case study for almost 50years [76.40–

44]. The development of models of glucose–insulin

interaction, sometimes including additional hormones,

substrates, or contributions, has an equally long his-

tory [76.40–42, 45–56]. In order to estimate the

parameters in these models, tools from Sect. 76.2.1

are employed, and the model structures can be

of either compartmental (Sect. 76.2.2) or physiologic

(Sect.76.2.3) form. With a model in place to represent

the patient (i.e., patient=model), for use in con-

Part H 76.3

1370 Part H Automation in Medical and Healthcare Systems

troller design (i. e., model-based optimal control using

tools from Sect.76.2.5), or both (i. e., patient =model),

a control problem can be formulated. One option

is to pose a single-input single-output control prob-

lem, the formulation of which is quite similar to the

continuous processes seen in the chemical industry

for decades: a manipulated variable (insulin delivery),

with a steady-state value (pancreatic insulin release

in a healthy patient), is altered to maintain a con-

trolled variable (glucose concentration) within a small

range of its nominal value. Normoglycemia is generally

taken as circulating glucose concentrations in the range

70–120 mg/dl [76.57], with a nominal value between

80 and 100mg/dl. Insulin delivery for type I diabetic

patients, who have no insulin release from the β-cells

of the pancreas, is altered in order to control glucose

concentration. Clinical approaches at present involve

intensive subcutaneous insulin therapy [76.57, 58]or

continuous subcutaneous insulin infusion via mechan-

ical pump [76.59].

Based on this traditional control conﬁguration and

the control schemes introduced in Sect. 76.2.5,the

glucose control problem can be posed in the model-

predictive control framework [76.42, 43], as shown

in Fig. 76.6. Using glucose concentration measure-

ments (at 10 min or faster intervals), insulin delivery

rate would be changed in order to regulate ambu-

latory diabetic patient glucose levels in response to

meal disturbances. Controller tuning would require

rapid rejection of meal disturbances (to keep glucose

levels below 120 mg/dl), but also aggressive down-

regulation of the controller so that post-meal glucose

concentrations remain above the hypoglycemic level of

Controller Patient

Patient

model

Glucose

sensor

Insulin

pump

Glucose concentrationInsulin delivery

Meals, exercise, etc.

Measurement device

Disturbances

Desired

glucose

concentration

Reference Manipulated

variable

Controlled variable

Model predicted glucose concentration

Controlled variable (model-predicted)

Fig. 76.6 Block diagram structure for model predictive control, as applied to the diabetic patient control problem

60mg/dl, which can be dangerous to patients [76.57,

58]. Furthermore, signiﬁcant levels of measurement

noise accompany each glucose observation. The poten-

tially conﬂicting objectives of aggressive response and

noise suppression challenge model-based algorithm de-

signers. Simulation studies of control algorithms have

focused on the type of control needed [76.60], pro-

viding upper bounds on achievable control [76.42],

or evaluating the potential effects of measurement or

other disturbances on closed-loop performance [76.43].

A key hurdle atpresent isthe glucosesensor,as the FDA

has not approved any real-time glucose sensor for use in

a closed-loop control algorithm.

One focus of improving diabetes treatment via

automation is the use of run-to-run control (com-

monly deployed in the batch processing literature) in

designing insulindosing protocols[76.61,62]. Here, pa-

tient glucose concentrations are not sampled at ﬁxed

short intervals, but instead the measurements taken by

patients over a typical day are used to improve day-

to-day performance of their glucose control. In the

context of Fig.76.6, the controller and insulin pump

are replaced by the patient (who will determine in-

sulin delivery amount) and their delivery mechanism

(pump, subcutaneous injection, etc.); Fig. 76.7 shows

a potential conﬁguration of a wireless sensor commu-

nicating with the combination data storage device and

insulin pump. By reformulating this problem, the use

of advanced control and automation techniques has the

potential to make a rapid contribution to the treatment

of diabetic patients instead of suffering from the crit-

ical ﬂaw in artiﬁcial pancreas deployment highlighted

above: the lack of FDA acceptance of a glucose sensing

Part H 76.3

Automation and Control in Biomedical Systems 76.3 Techniques and Applications 1371

Fig. 76.7 Diabetic patient using a wireless subcutaneous

glucose sensor communicating the measurement to the

data storage device. This device also includes the insulin

pump mechanism; note that the pump is notaltering insulin

delivery rate based on the glucose measurement unless

commanded to do so by the patient (courtesy of Dr. Cesar

Palerm, Medtronic Diabetes)

device for use in the closed loop. In fact, the run-to-run

algorithm can provide robustness to interpatient differ-

ences [76.62], which is important given the span of

patients that such an algorithm could encounter.

Changing the focus from ambulatory diabetes to

the critical-care setting, the potential for impact is sig-

niﬁcant [76.63–65]. In postsurgical patients, glucose

control via insulin administration can dramatically re-

duce morbidity and mortality. The altered metabolic

state in thesepatients issimilar to the diabeticcondition,

in that patients are hyperglycemic with low insulin sen-

sitivity. Hence, the automated administration of insulin

to regulate glucose concentration could assist in pa-

tient recovery. Whilemeasurement noise and rate would

(likely) be unchanged from the ambulatory setting,

other challenges manifest. First, individual models of

patients are not available a priori, and population mod-

els are insufﬁcient for use on speciﬁc patients because

individual insulin sensitivity will vary widely. Further-

more, the dynamic state of recovering patients would

lead to time-varying insulin sensitivity requiring time-

varying model parameters. A patient model updating

mechanism, such as recursive least squares (assuming

a linear parameterization of the model), is required.

Given the present legal and regulatory climate, a high-

level safety and fault-detection layer for the algorithm

would need to be developed. Alternatively, the algo-

rithm could be implemented as a semiclosed decision

support system with medical professionals afﬁrming or

declining the recommendation of the updating algo-

rithm. In the context of bringing an automated system

to market, the decision support system in critical care

could be the most rapid approach because collecting

a nonautomated measurement and allowing medical

professionals to intervene in therapy has the lowest en-

ergy barrier to review board approval.

A concern with any insulin delivery system is the

potential for overadministration, as this could lead to

hypoglycemia and possibly death. Adding a second

channel to the closed-loop system could alleviate some

of these issues. A model-based structure using both in-

sulin and glucose has been proposed [76.66,67], where

insulin is added to reduce glucose levels, and glucose

infusion is used to elevate glucose. To keep glucose

from being administered continuously, an output reg-

ulator formulation is employed (a modiﬁcation of the

MPC scheme in Fig.76.6 and Sect. 76.2.5), such that

positive glucose infusion rates are penalized at a lower

level than deviations in glucose concentration from

the reference value. The result is that glucose is in-

fused only when predicted glucose levels drop below

the basal level. While numerically superior, this ap-

proach is more relevant to use in a clinical, rather than

ambulatory, setting, as patients are unlikely to desire

a two-pump/two-needle (or two-infusion-line) device.

Also, a high-dextrose solution is an excellent culture

medium for bacteria, so sterility in the nonhospital

setting would become an even greater issue for these

patients.

As McGarry highlighted in the 2001 Banting lec-

ture, glucose and insulin are not the only important

endogenous compounds in diabetes. Type 2 diabetes

typically involves the dysregulationof fatty acids (FAs);

there is also signiﬁcance of FAs in insulin-dependent di-

abetes as metabolic interactions exist with insulin and

glucose. Using the minimal model [76.41] as a basis, an

extendedminimal model ofglucose/insulin/FA has been

constructed [76.55] using data from the literature and

the tools of Sects. 76.2.1 and 76.2.2 (see the schematic

in Fig.76.8). While this model is not mechanistic, it

does capture the interactions of glucose, insulin, and

FAs; furthermore this model is a low-order parameteri-

zation, which would facilitate tailoring to an individual

patient.

Finally, meal disturbances are not the sole chal-

lenge to diabetic patients, and hence automated insulin

delivery systems. Exercise alters glucose and insulin ki-

netics [76.68,69], and models of these processes have

been proposed in both physiologic[76.54] (Sect.76.2.3)

and minimal [76.56] (Sects. 76.2.1 and 76.2.2)forms.

Part H 76.3

1372 Part H Automation in Medical and Healthcare Systems

Adipose

tissue

Liver Periphery

Periphery

Insulin

administration

Meal

(fats)

Meal

(glucose)

Fig. 76.8 Schematic of interactions between insulin (I),

glucose (G), and fatty acids (F). Peripheral tissues con-

sume glucose and fats, while the liver and adipose tissue

serve dual source/sink roles for G and F, respectively.

Meal consumption increases glucose and fatty-acid levels,

and insulin administration drives circulating insulin level.

Dashed lines represent the effect of one compound on an-

other (G on F dynamics, for example). The X

blocks

represent additional dynamics (equations) that alter the ex-

tent and duration of effect of i on j (e.g., insulin on glucose

through X

)

Again, these models are more macroscopic than mech-

anistic, but they are able to capture the important

responses for the purposes of glucose regulation in di-

abetic patients. While the population-level variability

of the model parameters remains to be characterized

(which is also true of the FA models, above), the

proposed structure does allow preliminary analysis of

control structures to establish feasibility and potential

performance of automated glucose control systems.

76.3.2 Cancer Radio- and Chemotherapy

Cancer is a collection of diseases resulting from a series

of genetic mutations and characterized by an imbal-

ance between cell proliferation and apoptosis, or pro-

grammed cell death [76.71]. Ifuntreated, cancerleads to

organ failure and the death of the host organism. One in

four deathsin the USA in 2008was projectedto be from

cancer, claiming over 565650 lives [76.72]. In addition,

the total disease burden, including treatment costs and

loss of productivity, was estimated at US$ 219.2 billion

in 2007, providing both societal and monetary reasons

for improving cancer treatment [76.72]. Unlike insulin-

dependent diabetes, cancer is not a single disease, and

therefore, no silver bullet (i. e., insulin) exists. Hence,

cancers must be addressed individually; e.g., pancreatic

and breast cancers are separate diseases with different

treatment options and chemotherapeutic choices.

Accessible cancers are removed surgically. Alter-

natives or complements to surgery include systemic

chemotherapy and targeted site-speciﬁc treatment,

such as photodynamic therapy (PDT) or radiotherapy

(RT) [76.73, 74]. RT is often used in place of surgery

because the tissue surrounding the tumor is too sen-

sitive to permit surgical excision (e.g., tumors located

near the spinal column). PDT is used alone, or as an

intrasurgical procedure, to kill tumor cells located at

the tumor margin that are invisible to the human eye.

All cancer treatments are usually complemented by sys-

temic chemotherapy for two reasons: (i) small remote

metastases are often present by the time cancer is de-

tected; and (ii) chemotherapy is the only treatment that

is whole body in nature, thereby giving it the ability

to indiscriminately attack metastatic lesions before they

are clinicallydiagnosed. Hence, automation advances in

this area address targeted therapies and chemotherapy.

AkeyadvanceinRT, which requires a signif-

icant automation component, was intensity modula-

tion (IMRT) [76.75, 76]. A linear accelerator source

(Fig.76.9) provides radiation that has its ﬂuence mod-

Fig. 76.9 IMRT gantry and linear accelerator source (ﬁg-

ure originally published in [76.70])

Part H 76.3

Automation and Control in Biomedical Systems 76.4 Emerging Areas and Challenges 1373

ulated across the beam width, thereby providing pre-

scribed radiation doses to a target tissue volume. By

using a rotating beam gantry and placing the patient

on an actuated table, critical tissues can be delivered

lower doses through optimization of radiation dose to

a particular planning volume. Mathematical models are

constructed based on fundamental physics of radiation,

with reﬁnements basedon the interactionof endogenous

absorbers and scatterers with the administered radia-

tion beam(s). Collaborative work between engineers

and clinicians (such as [76.76]) has provided advanced

ofﬂine algorithms for optimizing the treatment dose.

The state of the art in RT is image-guided radiation

therapy (IGRT) [76.73, 74]. This extends IMRT tech-

niques to include real-time adjustment of the planned

dose in order to reduce interfraction (positional changes

of anatomical objects between the fractions of a ra-

diation dose) and intrafraction (real-time motion of

tissues in response to actions such as breathing) spa-

tial uncertainties. From a calculational perspective, this

changes a mixed-integer programming (MIP) prob-

lem, as solved in [76.76], into either a mixed-integer

dynamic optimization problem [76.77, 78] or a dy-

namic control problem using the MIP solution as

a reference.

Model-based approaches to cancer chemotherapy

treatment design are an active area of research. Core

to this approach is the existence of models describing

PK (the effect of the body on the drug), untreated tumor

growth (generally using the Gompertz model [76.79],

which has been shown to capture solid-tumor progres-

sion in human patients), and pharmacodynamics (the

effect of the drug on the body, including both antitumor

effect [76.80, 81] and toxicity [76.82]). These mod-

els are constructed using compartmental (Sect.76.2.2)

or physiological (Sect. 76.2.3) approaches, depending

on the amount of data available. Population tools

(Sect.76.2.2) are also important, as the cancer-affected

population is heterogeneous. A common solution tech-

nique for the chemotherapy dosing problem is optimal

control [76.33, 83, 84] (Sect. 76.2.5), where the fol-

lowing two-point boundary-value problem is posed:

minimize tumor volume at the end of a ﬁxed time pe-

riod subject to constraints on drug dose (magnitude),

path constraints (states, as governed by the model dy-

namics), and in some cases explicit representations

of toxicity (e.g., neutrophils [76.85]). An alternative

formulation and solution method uses mixed-integer

programming [76.86–88]; advantages of this approach

include path constraint satisfaction and extensibility of

the framework to additional constraints. The existence

of nonlinearities (beyond the bilinear kill term) in the

PK or PD models causes additional challenges for their

solution, requiring either parameterization [76.87]or

mixed-integer nonlinear programming techniques (for

details on these methods, see [76.89,90]). A key change

in formulation introduced in [76.87] is the use of a re-

ceding horizon strategy instead of the ﬁxed ﬁnal time

(as in the latter part of Sect.76.2.5). This is consistent

with clinical practice: the patient is treated until dis-

ease progression or cure, thereby making the ﬁnal time

formulation clinically irrelevant.

76.4 Emerging Areas and Challenges

In a 2001 perspectives article [76.91], Morari and Gen-

tilini describe the state of process control, and in a larger

context, automation, as “... a victim of [its past suc-

cess]: it has reached a plateau and turning point.” The

remainder of their article highlights biomedical pro-

cesses as an area where, “...control engineers [can]

have signiﬁcant impact,” because automation and au-

tomatic control were not commonly employed. While

there have been some changes since 2001, the potential

impact of automation and engineering on biomedical

practice remains signiﬁcant. In this regard, this chapter

has introduced a set of challenges and tools for use in

melding systems engineering techniques with biomed-

ical problems. The case studies are areas in which

the author is active; additional opportunities abound

for those motivated to: (i) learn the biology, medical

practice, and automation need of a disease (e.g., inﬂam-

mation, infection, regenerative medicine), and (ii) work

closely with collaborators in complementary ﬁelds to

address the disease of interest (e.g., clinicians, biolo-

gists, engineers, mathematicians, etc.). Related to some

of the challenges that began this chapter, the emerg-

ing areas and challenges below represent areas where

systems engineering and automation can be employed

to advance science and disease treatment. These ar-

eas align along a key principle of model-based control:

model quality dictates theoretically achievable control

system performance [76.92]. Hence, the biomedical

goal is to construct mechanistic models, when possible,

and to understand the context of the model, which may

serve to limit the prospective use of the model to certain

scenarios.

Part H 76.4

1374 Part H Automation in Medical and Healthcare Systems

76.4.1 in vitro Physiological Systems

The basic science of biomedicine often begins with cell

culture and in vitro experiments. However, a key is-

sue in translating cell-only experimental results to live

animals is the disconnect between cells in a dish and

cells interacting. One approach to this problem has

been coculturing of cells to allow cellular crosstalk

and to allow the development of three-dimensional

structure that better mimics physiology. This is a tech-

nique used in blood–brain barrier research [76.93]to

develop in vitro tests for neurotoxicity. For PK anal-

ysis, many drugs are cleared by the cytochrome P450

enzymes in the liver but cause toxicities or effects else-

where in the body. Hence, an in vitro liver cell culture

could be used to analyze drug kinetics; one such op-

tion, although the cells are encapsulated in a polymeric

coating, is described in [76.94]. A secondary concern

beyond three-dimensional (3-D) structure is spatial het-

erogeneity, which may be more difﬁcult to recreate

in vitro [76.95].

A potential system for in vitro testing of drug PK

would be a fully integrated physiologically motivated

cell culture system: cells of different types growing in

culture, with ﬂuid volumes for each cell type corre-

sponding to in vivo physiological volume; ﬂuid ﬂow

and connectivity allowing intercell crosstalk within

and between cell types (simulated physiology); rele-

vant compartments for evaluating effect, as appropriate

(e.g., tumor cells in culture for cancer PD analysis);

and the entire system automated for sensing and con-

trol. In the context of cancer drug PK and PD,the

incorporation of tumor cells would alleviate two short-

comings commonly present in current in vitro analysis:

(i) clinicallyinvalidpharmacokinetic proﬁles,where the

tumor cells are bathed in a constant concentration of

drug for a period of time, and (ii) cell kill analysis

based on the aforementioned pharmacokinetic proﬁle.

While the mathematical analysis of tumor cell kill un-

der time-dependent pharmacokinetic proﬁles is more

complicated than the constant-concentration approach

used presently, the use of in vitro physiological systems

could serve to reduce the number of animal studies nec-

essary in drug development while also improving the

translation of in vitro results to the toxicity and efﬁcacy

studies that have to be performed.

76.4.2 Translating in vitro to in vivo

The transition from in vitro to in vivo provides a serious

challenge to modelers and treatment designers. Phys-

iology may provide an advantage, as the connectivity

between organs in animals is well understood. Organ

weights and blood ﬂow rates to individual organs are

available in the literature for a variety of species, in-

cluding toxicologic man [76.96]. However, this detailed

approach assumes a model of physiological structure,

which is not the generally applied practice in clini-

cal drug development. As described in Sects. 76.2.2

and 76.2.3, compartmental models are more commonly

employed in the (pre)clinical setting due to the smaller

number of parameters, reduced mathematical complex-

ity, and the relative ease of parameter estimation. In

this less detailed structure, however, the method for

incorporating in vitro information is ad hoc. Hence,

a more mechanisticapproach is desiredwhen signiﬁcant

in vitro information is available because the mapping to

the in vivo situation will be improved.

As discussed above, animals are not humans.

The compartmental and population-based PK models

often developed in animals rely upon allometric scal-

ing [76.97, 98] to address the interspecies differences

in dynamic proﬁle. While imperfect (as witnessed by

the dearth of PK-driven model-based treatment designs

deployed in the clinic), this scaling principle can pro-

vide useful insight for selecting ﬁrst-in-human doses

and times to sample during phase I trials. Translat-

ing information relies to some degree on mechanistic

accuracy at the cellular level, thereby limiting the

unknown factors to the physiologically connected tis-

sues. In some cases, carefully constructed physiological

models can be successfully scaled from animals to hu-

mans by accounting for changes in physiology, such

as body fat percentage, as seen for the lipophilic an-

ticancer drug Docetaxel [76.10]. Often this requires

assumptions, such as equivalent plasma protein binding

characteristics (potentially based on binding informa-

tion from in vitro studies), and similar mechanisms of

clearance (liver metabolism, elimination in urine, etc.).

Under these assumptions, the human physiologically

based pharmacokinetic (PBPK) model (Fig.76.4) can

be successfully constructed by using the metabolic and

clearance parameters as thedegrees of freedom in ﬁtting

human plasma data. When inconsistencies between the

scaled PBPK model and human data manifest, relaxing

the assumptions and ﬁtting novel mechanistic behaviors

to the human plasma proﬁle is required. The resulting

model at the human scale can provide information that

would otherwise be unattainable in humans, such as es-

timated drug concentrations in key tissues (e.g., brain)

or those prone to toxic side-effects (e.g., liver, kidney,

white blood cells).

Part H 76.4