# ABT 263 The value selected for the first were Q CT C

The value selected for the first were Q = CT C. The three differ-

when the drug concentration in the ABT 263 was over 5% above the
ent input signals Ui are performed by using different values of Ri ,

where A, B, and C are matrices that define the linearized state model.
2.2.2. Pharmacodynamical simulation
The Pharmacodynamical Simulation (PS) block has two main roles: choosing the least toxic therapy UT from the set of thera-pies U, and transforming it into a drug dose. To accomplish it, the block has to simulate pharmacodynamical processes of the patient before making any decision. Thus, one may consider the PS as a soft-ware that aims to approximate patient behavior, being possible to have some discrepancy with reality. The uncertainty between the
258 F.F. Teles, J.M. Lemos / Biomedical Signal Processing and Control 48 (2019) 255–264

Fig. 3. Controller architecture for a patient model.

Fig. 4. Composition of the Pharmacodynamical Simulation and Patient Model.

since decreasing Ri means increasing the power of the manipu-lated variable Ui . The vector Ui represents anti-angiogenesis and immunotherapy, hence a balance between both drugs can be made. The chosen matrices are

Since Ui = [Gi Ii ]T , the effect of the immunotherapy in U1 is smaller

angiogenesis in U3 is lower than in U2 .

the feedback gain with dimension [2 × 3], computed by

(10)
Fig. 5. Continuous therapy approximation of discrete bolus.

where Si is the only definite solution of the Riccati equation. It is

worth noticing that the signal Ui is limited between 0 and 1 by a
parameters of the PS and of the patient model is given byPS (in

saturation.

percentage) – see Section 3.

Aside from that, since the controller has a non-null reference,

The PS structure and its connection with the Patient Model are

another additional term that leads the system to follow the set point

The process of selecting the least toxic therapy is executed by

state estimation differential equation xˆ, that not only assures the
first transforming the effect vector U into a concentration vector

previous condition, but also allows the use of the tracking error e =

Cp , through the inverse of the PD, denoted PD−1 . The parame-

R − V in the controller. Therefore, the system controller is defined
ter C50 required for this transformation is calculated through an

by

approximation of the DR model, named DR’. After the concentration

(11)
calculation, it is possible to measure toxicity levels, as described in

Section xxx2.1.5. Therefore, the least toxic drug concentration is

chosen, by the block Tx .

(13)
In practice, it is desired that the Cp of the patient model fol-

lows the reference Cp∗ , selected by the PS block, since it is the least

toxic drug concentration. This is achieved by the PK Control block that uses linear feedback. However, since PK information cannot be directly accessed and Cp tends to be the same as Cp∗ , one may assume PK Control to be an unitary gain. The process is continuous but, in many cases, the therapy is applied in the form of a sequence of con-centrated actions that may be mathematically modelled as a train of varying amplitude Dirac-delta impulses. This work assumes that this application is such that it yields an approximation to the effect concentrations required by the controller continuous controller, as shown in Fig. 5.

Fig. 6. Simplified architecture of the MMAC.

2.3. Multiple model adaptive control

In oncology the uncertainty in the patient behavior is significant not only at the beginning of therapy, when the patient’s character-istics are unknown, but also during its course, since the organism response is time-variant [35].

MMAC is a modular technique, where the plant supervision is aside from control. It overcomes the poor performance problem of the linear control theories in environments with a low degree of accuracy, embodying the control system with adaptation features and improving the transient performance [36].

Assuming that the plant dynamics P is defined by a set of param-eters p, one can consider p ∈ S, being S a closed and bounded set
Fig. 7. Computer diagram of the decision logic sequential process.
of parameter space with finite dimension. The objective of MMAC

is to control the plant by switching between a finite set of con-
trollable and observable models M =
N

i=1 Mi , being each model Mi
where K is the memory length, ˛ and ˇ determine the importance

characterized by a set
of parameters
pˆ , that also respect pˆ
S.
of current and past data, respectively, and is the forgetting factor.