**5. Lung-status evaluation and indicators for extubation of mechanicallyventilated COPD patients**

### **5.1 Introduction**

In mechanically ventilated patients with chronic-obstructive-pulmonary-disease (COPD), elevated airway resistance and decreased lung compliance (i.e., stiffer lung) are observed with rapid breathing. The need for accurate predictive indicators of lung-status improvement is essential for ventilator discontinuation through stepwise reduction in mechanical support, as and when patients are increasingly able to support their own breathing, followed by trials of unassisted breathing preceding extubation, and ending with extubation.

For this reason, we have developed an easy-to-employ lung ventilatory index (*LVI*), involving the intrinsic parameters of a lung ventilatory model, represented by a first-order differential equation in lung-volume response to ventilator driving pressure. The *LVI* is then employed for evaluating lung-status of chronic-obstructive-pulmonary-disease (COPD) patients requiring mechanical ventilation because of acute respiratory failure.

## **5.2 Scope and methodology**

We recruited 13 mechanically ventilated patients with chronic obstructive pulmonary disease (COPD) in acute respiratory failure [3]. All patients met the diagnostic criterion of COPD. The first attempt of discontinuation (or weaning off the ventilator) for every patient was made within a short duration (not exceeding 88 hours). The patients in the study were between the ages of 54-83 years. All the patients were on synchronized intermittent mandatory ventilation (SIMV) mode with mandatory ventilation at initial intubation. Based on the physician's judgment, the modes were changed for eventual discontinuation of mechanical ventilation. The time period for recording observations was one hour. For all purposes in this study, a successful ventilator discontinuation is defined as the toleration to extubation for 24 hours or longer and a failed ventilator discontinuation is defined as either a distress when ventilator support is withdrawn or the need for reintubation. Our LVI was then employed to distinguish patients who could be successfully weaned off the mechanical ventilator.

based on a lung-model represented by a first-order differential equation in lung-volume dynamics to assess lung function and efficiency in the case of chronic-obstructive-pulmonarydisease (COPD) patients requiring mechanical ventilation because of acute respiratory failure. Herein, we have attempted to evaluate the efficacy of the *LVI* in identifying improving or deteriorating lung condition in such mechanically ventilated chronic-obstructive-pulmonarydisease (COPD) patients, and consequently if *LVI* can be used as a potential indicator to predict ventilator discontinuation. In our bioengineering study of 13 COPD patients who were mechanically ventilated because of acute respiratory failure, when their *LVI* was evaluated, it provided clear separation between patients with improving and deteriorating lung condition. Finally, we formulated a lung improvement index (*LII*) representative of the overall lung response to treatment and medication, and a parameter *m* that corresponds to the rate of lung improvement and reflects the stability of lung-status with time. This chapter is based on our previous chapter [3] in the book on Human Respiration (edited by V. Kulish and published by WIT Press) and other works on this subject [4-9].

### **5.3 Lung ventilation model**

From a ventilatory mechanics viewpoint, the lungs can be considered analogous to a balloon, which can be inflated and deflated (passively). The gradient between the mouthpressure (*Pmo*) and the alveolar pressure (*Pal*) causes respiration to occur. During inspiration, *Pm* **>** *Pal*, which causes air to enter the lungs. During expiration *Pal* increases, and is greater than *Pmo*; this causes the air to be expelled out of the lungs passively. These pressure differentials provide a force driving the gas flow. The pressure difference between the alveolar pressure (*Pal*) and pleural pressure (*Pp*) counter balances the elastic recoil. Thus the assessment of respiratory mechanics involves the measurement of flows, volumes (flow integrated over time) and pressure-gradients. The lung ventilation model (shown in Figure 1) is based on the same dynamic-equilibrium differential equation (Equation 1-b), expressing lung volume response to pressure across the lung, as:

$$R\,\dot{V} + \frac{V}{C} = P\_L(t) - P\_{el0} = B\sin(\omega t) \tag{31}$$

wherein:

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expect its value to be of the order of 30 for normal subjects, 300 for COPD patients, 5 for

Here again, we need to determine *LVI* for normal lung states as well as for different lung disease states. We can then compare which of the formulas (10) or (30) enable better

*Comments related to values of the ranges of the parameters:* Before proceeding to the next section, let us address the basis of providing the above indicated ranges of parameters. The lung ventilation volume and driving pressure curves in Figure 3 are for a normal case. By carrying out this procedure for other normal subjects, we can define and confirm the above

Now then how do we distinguish subjects with disorders, such as obstructive lung disease (with increased value of *Ra*), emphysema (with enhanced value of *Ca*), lung fibrosis (with decreased value of *Ca*)? This can be made out from the shape and values of the lung ventilation volume curve. So then by repeating this procedure for subjects with these disorders, we will be able to characterize the shapes of the lung ventilation curves for normal subjects and for prescribing appropriate ranges of the parameters, for obtaining the

**5. Lung-status evaluation and indicators for extubation of mechanically-**

In mechanically ventilated patients with chronic-obstructive-pulmonary-disease (COPD), elevated airway resistance and decreased lung compliance (i.e., stiffer lung) are observed with rapid breathing. The need for accurate predictive indicators of lung-status improvement is essential for ventilator discontinuation through stepwise reduction in mechanical support, as and when patients are increasingly able to support their own breathing, followed by trials of unassisted breathing preceding extubation, and ending with

For this reason, we have developed an easy-to-employ lung ventilatory index (*LVI*), involving the intrinsic parameters of a lung ventilatory model, represented by a first-order differential equation in lung-volume response to ventilator driving pressure. The *LVI* is then employed for evaluating lung-status of chronic-obstructive-pulmonary-disease (COPD)

We recruited 13 mechanically ventilated patients with chronic obstructive pulmonary disease (COPD) in acute respiratory failure [3]. All patients met the diagnostic criterion of COPD. The first attempt of discontinuation (or weaning off the ventilator) for every patient was made within a short duration (not exceeding 88 hours). The patients in the study were between the ages of 54-83 years. All the patients were on synchronized intermittent mandatory ventilation (SIMV) mode with mandatory ventilation at initial intubation. Based on the physician's judgment, the modes were changed for eventual discontinuation of mechanical ventilation. The time period for recording observations was one hour. For all purposes in this study, a successful ventilator discontinuation is defined as the toleration to extubation for 24 hours or longer and a failed ventilator discontinuation is defined as either a distress when ventilator support is withdrawn or the need for reintubation. Our LVI was then employed to distinguish

patients requiring mechanical ventilation because of acute respiratory failure.

patients who could be successfully weaned off the mechanical ventilator.

mentioned normal ranges for these parameters, for obtaining their best values.

emphysema patients, and 100 in the case of lung fibrosis.

separation of lung disease states from the normal state.

best values of these parameters.

**ventilated COPD patients** 

**5.2 Scope and methodology** 

**5.1 Introduction** 

extubation.


Let *B* be the amplitude of the net pressure wave form applied by the ventilator, *Ca* be the averaged dynamic lung compliance, *Ra* the averaged dynamic resistance to airflow, the driving pressure *PL* be given as *PL* = *Pel*<sup>0</sup> + *B*sin(*ωt*), and the net pressure *PN* be given by *PN* = *B*sin(*ωt*), as depicted in Figure 4. The governing equation (31) then becomes:

$$R\_a \dot{V} + \frac{V}{C\_a} = P\_N = B \sin(\alpha t) \tag{32}$$

Fig. 4. Lung ventilatory model data shows air-flow (*V* ) and volume (*V*) and net pressure (*PN*). Pause pressure (*P*0) occurs at *tv*, at which the volume is maximum (TV = tidal volume). Δ*t* is the phase difference between the time of maximum volume and peak pressure (*Pm*). It is also the time lag between the peak and pause pressures. *B* is the amplitude of the net pressure waveform *PN* applied by the ventilator. This *PN* oscillates about *Pel0* with amplitude of *B*. The difference between peak pressure *Pm* and pause pressure *P*0 is Δ*p*. This figure is adopted from our work in Ref [3].

The volume response to *PN* (the solution to Equation (32)) is given by:

$$V(t) = \frac{BC\_a[\sin(\alpha t) - \alpha k\_a \cos(\alpha t)]}{1 + \alpha^2 k\_a^{-2}} + He^{\left(\frac{-t}{k\_a}\right)}\tag{33}$$

wherein:

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Lung Volume (liters) TV = 0.5

(FRC)

0

0.3

0

− 0.3

*Pm*

*P*0

*Pel*<sup>0</sup>

Fig. 4. Lung ventilatory model data shows air-flow (*V* ) and volume (*V*) and net pressure (*PN*). Pause pressure (*P*0) occurs at *tv*, at which the volume is maximum (TV = tidal volume). Δ*t* is the phase difference between the time of maximum volume and peak pressure (*Pm*). It is also the time lag between the peak and pause pressures. *B* is the amplitude of the net pressure waveform *PN* applied by the ventilator. This *PN* oscillates about *Pel0* with amplitude of *B*. The difference between peak pressure *Pm* and pause pressure *P*0 is Δ*p*. This figure is

0 5

*tv*

Δ*t*

Δ*P*

*t* (seconds)

*B*

adopted from our work in Ref [3].

*PN*, Net Applied Pressure (cmH2O)

*V*, Lung Air Flow (liters/sec)

i. *ka* (= *RaCa*) is the averaged time constant,

ii. the integration constant *H* is determined from the initial conditions,

iii. the model parameters are *Ca* and *ka* (i.e., *Ca* and *Ra*), and

iv. *ω*is the frequency of the oscillating pressure profile applied by the ventilator

An essential condition is that the flow rate is zero at the beginning of inspiration and end of expiration. Hence, the flow rate *dV/dt* = 0 at *t* = 0. Applying this initial condition to our differential Equation (33), the constant *H* is obtained as:

$$H = \frac{BC\_a a \phi k\_a}{1 + a^2 k\_a^{-2}}\tag{34}$$

Then, from Equations (33) and (34), we obtain:

$$V(t) = \frac{BC\_a[\sin(\alpha t) - \alpha k\_a \cos(\alpha t)]}{1 + \alpha^2 k\_a^{\;\;2}} + \frac{BC\_a \alpha k\_a}{1 + \alpha^2 k\_a^{\;\;2}} e^{\left(\frac{-t}{k\_a}\right)}\tag{35}$$

For *t* = *tv*, *V*(*t*) is maximum and equal to the tidal volume (TV). Now in a normal person, *ka* is of the order of 0.1 and 0.5 in ventilated patients with respiratory disorders, which is relevant to our study of COPD patients. At *t* = *tv* at which the lung volume is maximum, we note from Figure 4 that *tv* is of the order of 2 s. Hence *tv/ka* is of the order 20-4, so that / *<sup>a</sup> t k e* <sup>−</sup> is of the order of *e -20* to *e -4*, which is very small and hence negligible. Hence, in Equation (35), we can neglect the exponential term so that,

$$V(t) = \frac{BC\_a[\sin(\alpha t) - \alpha k\_a \cos(\alpha t)]}{1 + \alpha^2 k\_a^{-2}}\tag{36}$$

Figure 4 illustrates a typical data of *V*, *V* and *PN*. For evaluating the parameter *ka*, we will determine the time at which *V*(*t*) is maximum and equal to the tidal volume (TV), Hence, putting *dV/dt* = 0 in Equation (36), we obtain:

$$
\cos(\alpha t) + \alpha k\_d \sin(\alpha t) = e^{\left(\frac{-t}{k\_s}\right)}, \text{ for } t = t\_v \tag{37}
$$

Hence from Equation (37), we obtain the following expression for *ka*:

$$
\tan(\alpha t) = -1 \;/\; \alpha k\_{a'} \; \text{for } t = t\_v \tag{38-a}
$$

or,

$$k\_a = -(1 \;/\; \alpha) \tan(\alpha t\_v) \tag{38.4}$$

Since both ω and *tv* are known, we can evaluate *ka* from Equation (38-b). Now from Equation (38-b), we can put down:

$$\text{TV} = \frac{\text{BC}\_a[\sin(\alpha t\_v) - \alpha k\_a \cos(\alpha t\_v)]}{1 + \alpha^2 k\_a^{'2}} \tag{39}$$

Since ω, *tv* and *ka* are known, we can now determine *Ca* in terms of TV and applied pressure amplitude *B*.

Then knowing *ka* and *Ca*, we can determine

$$R\_a = k\_a \;/\mathbb{C}\_a \tag{40}$$

For our COPD patients, the ranges of the computed values of these parameters are:

$$\text{l}R\_a = 9 \text{--} 43 \text{(cmH}\_2\text{O)} \text{sL}^{-1}; \text{C}\_a = 0.020 \text{--} 0.080 \text{ L} \text{(cmH}\_2\text{O)}^{-1} \tag{41}$$

Now that we have determined the expressions for the parameters *Ra* and *Ca*, the next step is to develop an integrated index lung ventilatory incorporating these parameters.

### **5.4 Formulating a Lung Ventilatory Index (***LVI***) incorporating** *Ra* **and** *Ca*

We believe that the correlations between average airflow-resistance (*Ra*), average lungcompliance (*Ca*), tidal volume (TV), respiratory rate (*RF*), and maximum inspiratory pressure or peak pressure (*Pm*) can be used as a possible indicator for determining lungstatus in a mechanically ventilated COPD patient with acute respiratory failure. We hence propose that a composite index (*LVI*), incorporating these isolated parameters, can have a higher predictive power for assessing lung status and determining when a patient on a mechanical ventilator.

For this purpose, we note that COPD patients have higher *Ra*, lower *Ca*, lower TV, higher *Pm* and higher respiratory rate (or breathing frequency) *RF*. If we want the non-dimensional lung-ventilatory index (*LVI*) to have a high value for a COPD patient, further increasing *LVI* for deteriorating lung-status and decreasing *LVI* for improving lung-status in a mechanically ventilated COPD patient in acute respiratory failure, then the non-dimensional lung-ventilatory index (*LVI*) can be expressed, as given by Equation (30):

$$LVI\_2 = \left[\frac{R\_d \text{(TV)}^2 \text{(RF)}}{C\_a \text{(}P\_m\text{)}^2}\right] \times \text{(60)}^2\tag{42}$$

where *RF* is the respiratory-rate frequency.

Let us obtain the order-of-magnitude values of this *LVI*2 index for a mechanically ventilated COPD patient in acute respiratory failure (by using representative computed values of the parameters *Ra, Ca, RF,* TV*,* and *Pm*), in order to verify that the formula for *LVI*2 (given by Equation (42)) can enable distinct separation of COPD patients in acute respiratory failure from patients ready to be weaned off the respirator. For an intubated COPD patient, we have

$$LVI\_2 \text{ (Intubated COPD)} = \frac{[15 \text{(cmH}\_2\text{O)sL}^{-1}][0.5 \text{ L}]^2 [0.33 \text{ s}^{-1}]}{[0.035 \text{ L} (cmH\_2\text{O)}^{-1}][20 \text{ cmH}\_2\text{O}]^2} \times (60)^2 = 318 \tag{43}$$

wherein *Ra* = 15 (cmH2O)sL-1, *Ca* = 0.035 L(cmH2O)-1, *RF* = 0.33 s-1, TV = 0.5 L and *Pm* = 20 cmH2O.

Now, let us obtain the order-of-magnitude of *LVI* (by using representative computed values of *Ra, Ca, RF,* TV*,* and *Pm*) for a COPD patient with improving lung-status just before successful discontinuation. For a successfully weaned COPD patient (examined in an outpatient clinic), we have

$$LVI\_2 \text{ (Output COP)} = \frac{[5(\text{cmH}\_2\text{O})\text{s} \text{L}^{-1}][0.35 \text{ L}]^2 [0.33 \text{ s}^{-1}]}{[0.10 \text{ L} (\text{cmH}\_2\text{O})^{-1}][12 \text{ cmH}\_2\text{O}]^2} \times (60)^2 = 50.5 \tag{44}$$

wherein *Ra* = 5 (cmH2O)sL-1, *Ca* = 0.10 L(cmH2O)-1, *RF* = 0.33 s-1, TV = 0.35 L and *Pm* = 12 cmH2O.

Hence for *LVI*2 to reflect lung status improvement in a mechanically ventilated COPD patient in acute respiratory failure, there should be a pronounced decrease in the value of *LVI*2. This shows that the *LVI* given by Equation (42) can enable effective decision making to wean off a COPD patient from mechanical ventilator.
