A structure preserving model order reduction method for calcium homeostatic system.

Calcium Homeostasis is a complex physiological process. Its mathematical model results in high order differential equation. In this paper, a model order reduction technique, based on time scale separation is proposed for a 27th order Calcium Homeostasis and Bone Remodeling (CHBR) system. The original state-space model after linearization has been decoupled into three reduced order subsystems: "Very-Slow", "Slow" and "Fast", at the same time preserving the structure of the system. The time and frequency response of individual reduced order model has been compared with the response of the original system. Furthermore, the effect of administering a therapeutic daily moderate dose of PTH has been studied with the help of reduced order models.

Modulation-demodulation hypothesis of periodic breathing in human respiration.

Periodic breathing (PB) is a diseased condition of the cardiorespiratory system, and mathematically it is modelled as an oscillation. Modeling approaches replicate periodic oscillation in the minute ventilation due to a higher than normal gain of the feedback signals from the chemoreceptors coupled with a longer than normal latency in feedback, and do not consider the waxing-waning pattern of the oronasal airflow. In this work, a noted regulation model is extended by integrating respiratory mechanics and respiratory central pattern generator (rCPG) model, using modulation-demodulation1 hypothesis. This is a top-down modeling approach, and it is assumed that the sensory feedback signal from the chemoreceptors modulates the output of the rCPG model. It is also assumed that the brainstem network is responsible for the demodulation process. The respiratory mechanics is modeled as a multi-input multi-output (MIMO) system, where modulated and demodulated neural signals are applied as input and the minute ventilation and the oronasal airflow are specified as output. The minute ventilation signal drives the regulation model, completing the feedback loop. The proposed model is validated by comparing the model output with the clinical data. Using the modulation-demodulation hypothesis, a respiratory mechanics model is formulated in the form of a linear state-space model, which can be useful for providing assisted ventilation in clinical conditions.

Modeling of cardiovascular circulation for the early detection of coronary arterial blockage.

Coronary arteries are responsible for maintaining blood supply to the heart. When these arteries get blocked due to plaque deposition, the corresponding pathological condition is referred to as coronary artery disease. This disease develops gradually over the years and consequently, the function of the heart deteriorates, leading to a heart attack in many cases. As the symptoms manifest themselves only when it has become severe, detection of the disease often gets delayed. In order to detect it early and take preventive action, this work is aimed at detecting the arterial blockage in its early stage via cardiovascular modeling. To achieve this, the cardiovascular circulation has been modeled as a sixth order nonlinear system. Blood circulation in a body is viewed as an electrical system using the pressure-voltage analogy. In this case, the heart is considered as a self-excited generator. The rest of the body tissues form a systemic load. In the models reported in the literature, coronary circulation has been assumed to be a part of the systemic load. However, this circulation path has its own importance as it is responsible for the blood supply to the heart. Therefore, in our work, the coronary path is separated out from the rest of the body tissues. This enables us to explicitly model the coronary arterial resistance and thereby helps us to detect coronary arterial blockage condition by estimating this parameter from blood pressure measurements. Increase in the coronary resistance is found to reduce the left ventricular ejection fraction; this information can therefore be used as an index for coronary arterial blockage. It has been shown that the systolic function of the heart deteriorates when the resistance of the coronary path increases beyond a critical value; the situation can be related to a severe blockage condition. The model has been tested on a chosen sample of 20 subjects suffering from coronary artery disease and the results are found to be quite promising.

Oxygen therapy for management of periodic breathing : A theoretical approach.

A generalized framework for the generation of Periodic Breathing (PB), caused by delay variation, hypocapnia and sleep along with its management with oxygen therapy is presented. For this, a minimal model of respiratory regulation with cardiovascular component and two delays is proposed. This model is linearized and analyzed for stability by the proposed algorithms using Lyapunov-Krasovskii functional. Oscillation in this model is produced by the increase of delays, an increase of chemoreceptor gains (hypocapnia) and a decrease in minute ventilation (sleep induced PB). For delay variation, it is established that both the delays are responsible for oscillation in the system. However, maximum tolerable delay limit for the peripheral chemoreceptors is lower (0.3  min) compared to the central chemoreceptors (5.2  min). Stability analysis shows that application of additional oxygen is capable of suppressing the oscillation in the system by increasing the tolerable delay limit. Hypocapnia caused by hyperventilation is modeled by increased chemoreceptor gain. 50% increase in chemoreceptor gain along with 46% decrease in lung carbon dioxide storage makes the system oscillatory, which increases average minute ventilation by 19.42%. Application of additional oxygen makes the system stable. For sleep induced PB, it is shown that lowering minute ventilation causes oscillation in the system. A parameter is introduced to limit the minute ventilation in sleep, and its upper limit is calculated (8.7% drop in minute ventilation) for producing oscillation in the system. Application of higher oxygen makes the system stable by compensating for the reduction. Finally, two simulation studies are presented, showing the delay limits in hyperventilation and sleep condition. In these conditions, as the gains increase or minute ventilation decreases, tolerable delay limits become smaller.