Mathematical model of the human respiratory system in chronic obstructive pulmonary disease

Non‐invasive ventilation treatment for patients with chronic obstructive pulmonary disease

“…In COPD, the bicarbonate levels of the arterial blood and the CSF are elevated to compensate for chronic hypercapnia [2]. The following equations are used in the model [19] to find the hydrogen ion concentration of the arterial blood (H’ a + ), the hydrogen ion concentration of the CSF (H CSF + ), and the hydrogen ion concentration of the blood at the site of the central receptors (H C + ): $$$$\begin{equation}{H^{\prime}_{\rm{a}}} = \frac{{\left[ {0.65. {{P^{\prime}}_{{\rm{aCO}}2\left( {{\rm{mean}}} \right)}} + 13.5} \right]}}{{{\gamma}}}\end{equation}$$$$ $$$$\begin{equation}H_{{\rm{CSF}}}^ + = \left[ {\frac{{{{\alpha}} \cdot {{\beta}}}}{{{{\left( {{\rm{BHCO}}3} \right)}_{{\rm{CSF}}}}}}} \right] \cdot \frac{{{P_{{\rm{CSFCO}}2}}}}{{{\gamma}}}\end{equation}$$$$ $$$$\begin{equation}H_{\rm{C}}^ + = \left[ {\frac{{{{\alpha}} \cdot {{\beta}}}}{{{{\left( {{\rm{BHCO}}3} \right)}_{{\rm{CSF}}}}}}} \right] \cdot \frac{{{P_{{\rm{CCO}}2}}}}{{{\gamma}}}\end{equation}$$$$…”

“…The controller equations of the model are modified to include the effects of a major shift in the acid–base balance that occurs under prolonged disease conditions. The detailed description of this model and the mathematical equations of its plant and the controller can be found elsewhere [19] and, for the sake of brevity, are not given here. However, the ventilation controller equation that includes the COPD effects is the following: $$$$\begin{eqnarray}{\rm{AVR}} &=& \left[ {0.131 + \frac{{0.0715}}{{{\gamma}}}} \right] \cdot {\rm{P}}{{\rm{\rm{^{\prime}}}}}_{{\rm{aCO}}2\left( {{\rm{mean}}} \right)} + \left[ {0.131 + \frac{{0.10227}}{{{\gamma}}}} \right]\nonumber\\ && \cdot {{\rm{P}}}_{{\rm{CCO}}2} + {\rm{FACTV}} + \left[ { - K + \frac{{1.485}}{{{\gamma}}}} \right] + {\rm{MRV}}\end{eqnarray}$$$$…”

Self Adaptive Fuzzy Controller for Supplementary Oxygen Supply to the Respiratory Distress Patients

“…The human respiratory system is highly non-linear and dynamic and its functioning is governed by numerous factors, be it within the body or outside the body of the individual [1]. From the knowledge of control systems, the human respiratory system can be considered to be a regulatory one and under certain conditions can behave in an oscillatory manner exhibiting both damped and sustained oscillations [2].…”

System Modeling and Prediction of Respiratory Diseases using Machine Learning

“…In this model the trachea-bronchial tree is divided into 24 generations (Table 1), where generation '0' is the trachea, the generation from 1 to 19 is counted for bronchi and the generation 20 to 23 corresponds to alveolar sacs. Starting from the trachea, considering each branch of a given generation divides into two identical daughters; therefore generation 'n' has 2n branches [1][2][3][4][5]. Each section have their characteristics Resistance, Inertance and Compliance due to the obstruction offered by the section, obstruction to the change in airflow through the section and expansion or contraction of the concerned section respectively [6][7][8].…”

“…The Transfer Function (TF) of each section is determined by considering Fig. 1 which comes out to be in this form after executing Laplace transform, with all initial conditions to zero [1/(s 2 LC+sRC+1)], where R, L, and C are the characteristic values of Resistance, Inductance and Capacitance of the section concerned [1][2][3][4][5]. The necessary calculations of R, L, and C to reflect it for the different generations of the respiratory system are shown in Table 1.…”