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University: Politecnico di Milano
Degree programme: Biomedical Engineering
Subject: Bioengineering of Physiological Control Systems
Material language: English
Classification: Notes · Complete set
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Complete course materials for Bioengineering of Physiological Control Systems in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: PHYSIOLOGICAL CONTROL SYSTEM SOME FUNDAMENTAL DEFINITIONS A control system may be defined as a collection of interconnected components that can be made to achieve a desired response in the face of external disturbances. - The “desired response” could be the tracking of a

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PHYSIOLOGICAL CONTROL SYSTEM SOME FUNDAMENTAL DEFINITIONS A control system may be defined as a collection of interconnected components that can be made to achieve a desired response in the face of external disturbances. - The “desired response” could be the tracking of a specified dynamic trajectory, (servomechanism, e.g. a robot arm that moves objects). - The “desired response” could be to maintain a certain physical quantity within specified limits (regulator, e.g. thermostat). There are two basic ways in which a control system can be made to operate: in open-loop or close-loop mode. OPEN-LOOP VS CLOSED-LOOP SYSTEM AN EXAMPLE OF OPEN-LOOP SYSTEM A fan-heater heats up and circulates the air within the room. By setting the temperature control to “medium”, we should be able to get the room temperature to settle down to an agreeable level. However, if the external environment becomes warmer, the room temperature becomes much higher than desired, because the rate at which heat is added by the fan-heater exceeds the rate at which heat is dissipated from the room. Open-loop system can perform satisfactorily as long as the external conditions do not affect the system much. A physical analogue is the thermoregulatory control in “cold-blooded” animals. The design of the thermoregulatory processes in these animals do not allow core body temperature to be maintained at a level independent of external conditions; as a consequence, the animal’s metabolism also becomes a function of external temperature. AN EXAMPLE OF CLOSE-LOOP SYSTEM If the external temperature varies in a roughly predictable pattern, we need to make the heater “aware” of changes in the room temperature to respond accordingly. We can measure the room temperature, compare the measured temperature with the desired…

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At the equilibrium, the increment in pressure corresponding to the sudden dumping of the stroke volume on the capacitor must be equal to the pressure drop during the diastolic period of length T: The exponential decay during diastole is a realistic representation of the pressure in the human aorta. Using typical values of Ra ≈ 1 mmHg/ml/sec and Ca ≈ 2 ml/mmHg, the time constant for the decay is about 2 sec. The envelope of systolic, mean, and diastolic pressure over several beats is governed by the same time constant τ = RaCa so after 5τ the system reaches steady state. The arterial blood pressure and flow measured in a rabbit aorta. At t = 2.5 sec the heart is stopped with vagal stimulation, and the blood pressure falls exponentially, consistent with the Windkessel model. 48

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We can observe that although the model contained three physiological parameters (L, C and R), these parameters always appeared in combination with one another, for example, LC and RC. Indeed, the transfer function contains only two free parameters for a given value of k, the feedback gain. We can thus extend the system equations for a generalized second-order model that is characterized by the same dynamics as the lung mechanics model. In the generalized second-order model dynamics are governed by two independent parameters. A third parameter, the steady-state gain GSS is also introduced. In the lung mechanics model GSS was equal to 1. We generalize the input and output variables as We can generalized further the model by introducing two new parameters to substitute the three redundant parameters: L, C and R. As we had shown earlier, in the undamped behavior the responses to unit impulse or step took the form of a sustained oscillation at frequency equal to This frequency is commonly referred to as the natural frequency A second parameter is the damping factor or damping ratio Rearranging terms, it can be easily shown that the overall transfer function for the model now becomes 96

Page 144

Let’s see now the example of the linear lung mechanics model with integral feedback: We’re approaching the value of k=100 (instability) so we’re reducing the margin of stability. STABILITY ANALYSIS OF PUPILLARY REFLEX The pupillary light reflex is a classic example of a negative feedback control system. In response to a decrease in light intensity, for example, receptors in the retina transmit neural impulses at a higher rate to the pretectal nuclei in the midbrain and, subsequently, to the Edinger–Westphal nuclei. A change in neural traffic down the efferent nerves back to the eyes then leads to the relaxation of the sphincter muscles and the contraction of the radial dilator muscles. These changes together produce an increase in pupil area, thereby increasing the total flux of light falling on the retina. When radial muscle of iris contracts pupil enlarges, when circular muscle of iris contracts pupil reduces in size. Light strikes the retinae and is channelled back via the optic nerves, cranial nerve CN2, to the midbrain. (We only show one optic tract leading to the midbrain so that we can see that each side produces a bilateral response.) The optic tract then triggers the pretectal olivary nucleus, which activates the oculomotor nerve CN3 bilaterally. Each CN3 then activates the ciliary ganglia. These ciliary ganglia then send short ciliary nerves to the iris sphincter muscles, producing pupillary constriction. 144

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Impulse responses estimated from normal controls (open circles) and subjects with obstructive sleep apnea (OSA) (filled circles) are here illustrated. Significantly lower ABR and RCC gains (e.g. 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝑅𝑅𝑅𝑅𝑅𝑅 = ∑ ℎ𝑅𝑅𝑅𝑅𝑅𝑅 ) in subjects with sleep disorders indicate that these pathologies lead to impaired autonomic nervous system control mechanisms. 192

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