3. Materials and methods

About 188 arterial blood gas sample data were utilized. Strict precautions were taken to avoid pre-analytical errors, and the consistency of the ABG report was checked by using the modified Henderson equation [2].

The main parameters like measured pH, pCO2, HCO3, standard HCO3, and standard base excess values were noted. Carbonic acid concentration was calculated from pCO2. The difference between bicarbonate and standard bicarbonate was calculated. The ratio of (HCO3 standard HCO3)/H2CO3 was calculated [1].

Calculation of H<sup>+</sup> :

and the ratio of (HCO3 standard HCO3)/H2CO3 in the two axes that demarcate

The aim of the manuscript is to increase in depth the understanding of the acidbase balance which is a challenging and at times an arduous task, yet it has immense

the various acid-base disturbances which are shown in Figure 3 [1].

Analysis of various acid-base disturbances using standard base excess (x-axis) and the ratio of

(HCO3 standard HCO3)/H2CO3 (y-axis) in the four-quadrant graph.

Figure 2.

Erythrocyte

Figure 3.

36

Relation between pCO2 and HCO3/Std HCO3.

H+ —hydrogen ion concentration at actual pH (Calculated using modified Henderson equation) H+ (hydrogen ion concentration) = {24 pCO2}/HCO3 pH = log[H<sup>+</sup> nanomoles/L] <sup>=</sup> log [H<sup>+</sup> <sup>10</sup><sup>9</sup> moles/L] <sup>=</sup> log [H<sup>+</sup> ] log [10<sup>9</sup> ] {nanomoles/L = 10<sup>9</sup> moles/L} pH <sup>=</sup> <sup>9</sup> log [H<sup>+</sup> ]

Calculation of NRH<sup>+</sup> (non-respiratory hydrogen ion concentration):

NRH<sup>+</sup> —hydrogen ion concentration at non-respiratory pH (At pCO2 of 40 mmHg)

This calculated hydrogen ion concentration equivalent of standard bicarbonate has thus been called the "non-respiratory" hydrogen ion concentration or NRH<sup>+</sup> [13, 14]. It has a unique value for a given standard bicarbonate concentration, and the relationship is clearly shown in Figure 4:

Figure 4. Relation between NRH<sup>+</sup> and Std HCO3.

NRH<sup>+</sup> = {24 pCO2}/Std HCO3 ={24 40}/Std HCO3 (pCO2 is 40 mmHg) NRH<sup>+</sup> = 960/Std HCO3 NRpH = 9 log [NRH<sup>+</sup> ]

Calculation of ΔRpH:

pH <sup>=</sup> <sup>9</sup> log [H<sup>+</sup> ] NRpH = 9 log [NRH<sup>+</sup> ] pH NRpH = 9 log [H<sup>+</sup> ] 9 + log [NRH<sup>+</sup> ] = log [NRH<sup>+</sup> /H+ ] or log [H<sup>+</sup> /NRH<sup>+</sup> ] H+ (hydrogen ion concentration) = {24 pCO2}/HCO3 NRH<sup>+</sup> (non-respiratory hydrogen ion concentration) ={24 40}/Std HCO3 [NRH<sup>+</sup> ]/[H<sup>+</sup> ] = {24 40}/Std HCO3/{24 pCO2}/HCO3 = 40 {(HCO3/Std HCO3)/pCO2} Or in terms of carbonic acid [pCO2 = H2CO3/0.03], this can be written as = 1.2 {(HCO3/Std HCO3)/H2CO3} pH NRpH = log [NRH<sup>+</sup> /H+ ] pH NRpH = log 40 + log (HCO3/Std HCO3) log(pCO2) [pH NRpH] = 1.6 + log{(HCO3/Std HCO3)/pCO2}

The predicted respiratory pH is the pH at which the changes in pH due to

] {9 log [40]

] 9 + log [40]

]/{[H<sup>+</sup>

= log {[NRH<sup>+</sup>

]/{[H+

the blood include both the changes due to respiratory (ΔRH+ = [H+

]/[H<sup>+</sup>

)/40

/40)}.

This new graphical tool developed for ABG interpretation contains four quadrants. In the x-axis, standard base excess values were taken, and in the y-axis, the ratio of (HCO3 standard HCO3)/H2CO3 values was taken to analyze the various acid-base disturbances which are clearly shown in the four-quadrant graph

In the first quadrant (both x- and y-axes are positive), if the plotted area is toward the x-axis, then it represents metabolic alkalosis, and if the area is toward the y-axis, then it represents respiratory acidosis. The plotted area in between and higher may represent combined acid-base disturbances (metabolic alkalosis and respiratory acidosis). The combined acid-base disturbances may be due to compen-

In the second quadrant (the x-axis is positive, and the y-axis negative), if the plotted area is toward the y-axis, then it represents respiratory alkalosis, and if the

non-respiratory (metabolic) components (ΔNRH<sup>+</sup> = [NRH<sup>+</sup>

The sum total changes in the hydrogen ion concentration (ΔH<sup>+</sup> = [H<sup>+</sup>

] or log {[NRH<sup>+</sup>

] [40]}

]/[H<sup>+</sup>

] = <sup>1</sup> {[NRH<sup>+</sup>

The hydrogen ion concentration is 40 at pH 7.4 which denotes the homeostatic set

] [40]}

]/[40]}

] 9 + log [NRH<sup>+</sup>

]}or log {[H<sup>+</sup>

]/[H<sup>+</sup> ]}

] 9 + log [NRH+

]

]/[NRH<sup>+</sup>

] [40]):

]}

] [NRH<sup>+</sup>

] [40]) in

]) and

]}

The difference between the predicted respiratory pH and actual pH denotes the changes in pH due to metabolic component. The magnitude and direction (positive or negative) of the changes in the parameter ΔNRpH (NRpH 7.4) are due to the accumulation of acids other than carbonic acid or bases. The value is negative for acidic effect and positive for alkaline effect. This is one of the postulates of the acidbase balance theory recently published. If the actual pH is less than the predicted respiratory pH, ΔNRpH is negative. If the actual pH is greater than the predicted

metabolic component are zero (ΔNRpH is zero).

Who Is Balancing: Is It RBC or Acid-Base Status? DOI: http://dx.doi.org/10.5772/intechopen.84768

respiratory pH, ΔNRpH is positive [15–18].

= 9 log [NRH+

= log {[40]/[NRH<sup>+</sup>

7.4 + <sup>Δ</sup>RpH = {9 log [40] + 9 log [H<sup>+</sup>

= 9 + log[NRH<sup>+</sup>

3.3 Net changes in total hydrogen ion concentration

{ΔRpH (pH NRpH) = 9 log [H<sup>+</sup>

] = [H<sup>+</sup> NRH<sup>+</sup>

point of acid-base balance [14, 18].

/40] = (NRH<sup>+</sup> 40)/40 or

= 1 {(NRH<sup>+</sup>

/40] = (40 NRH<sup>+</sup>

satory mechanism or mixed acid-base disorders.

NRPH-7.4 = 9 log [NRH<sup>+</sup>

Pr Resp Ph related to [NRH<sup>+</sup>

NRPH-7.4:

7.4 + ΔRpH:

[ΔRH<sup>+</sup>

(Figure 3).

39

[ΔNRH<sup>+</sup>

[ΔNRH<sup>+</sup>

/H<sup>+</sup>

4. New graphical tool

At pCO2 of 40 mmHg, pH NRpH is zero (because bicarbonate and standard bicarbonate values are equal, log 1 is zero, and log 40 is 1.6). At higher pCO2 levels (>40 mmHg), the value of [pH NRpH] is negative which denotes the acidic influence of increased pCO2. At lower pCO2 levels (<40 mmHg), the value of [pH NRpH] is positive which denotes the alkaline influence of decreased pCO2:

[pH NRpH] = 1.6 + log {(HCO3/Std HCO3)/pCO2} where NRpH denotes the non-respiratory pH. pH = 9 log [H+ ] NRpH = 9 log [NRH+ ] pH NRpH = 9 log [H<sup>+</sup> ] 9 + log [NRH<sup>+</sup> ] = log [NRH<sup>+</sup> ]/[H<sup>+</sup> ] or log [[H+ ]/[NRH<sup>+</sup> ]

The magnitude and direction (positive or negative) of the changes in the parameter ΔRpH (pH NRpH) denote the respiratory influence in causing changes in pH. The value is negative for acidic effect and positive for alkaline effect. At pCO2 of 40 mmHg, pH NRpH is zero [14].

### 3.1 Net changes in total pH

The net changes in total pH (actual pH) include both the changes in respiratory and non-respiratory (metabolic) components affecting the pH [14]:

ΔpH = ΔRpH + ΔNRpH pH 7.4 = ΔRpH + NRpH 7.4

where ΔNRpH (NRpH 7.4) denotes the changes in pH due to metabolic component.

#### 3.2 Predicted respiratory pH

pH = 7.4 + ΔRpH + ΔNRpH 7.4 + ΔRpH pH = ΔNRpH Pr RpH pH = ΔNRpH {Pr RpH (predicted respiratory pH) = 7.4 + ΔRpH} Who Is Balancing: Is It RBC or Acid-Base Status? DOI: http://dx.doi.org/10.5772/intechopen.84768

The predicted respiratory pH is the pH at which the changes in pH due to metabolic component are zero (ΔNRpH is zero).

The difference between the predicted respiratory pH and actual pH denotes the changes in pH due to metabolic component. The magnitude and direction (positive or negative) of the changes in the parameter ΔNRpH (NRpH 7.4) are due to the accumulation of acids other than carbonic acid or bases. The value is negative for acidic effect and positive for alkaline effect. This is one of the postulates of the acidbase balance theory recently published. If the actual pH is less than the predicted respiratory pH, ΔNRpH is negative. If the actual pH is greater than the predicted respiratory pH, ΔNRpH is positive [15–18].

NRPH-7.4:

NRH<sup>+</sup> = {24 pCO2}/Std HCO3

]

= log [NRH<sup>+</sup>

NRH<sup>+</sup> = 960/Std HCO3 NRpH = 9 log [NRH<sup>+</sup>

Calculation of ΔRpH:

NRpH = 9 log [NRH<sup>+</sup>

={24 40}/Std HCO3

pH NRpH = log [NRH<sup>+</sup>

]/[H<sup>+</sup>

pH = 9 log [H+

NRpH = 9 log [NRH+

pH NRpH = 9 log [H<sup>+</sup>

40 mmHg, pH NRpH is zero [14].

3.1 Net changes in total pH

ΔpH = ΔRpH + ΔNRpH

3.2 Predicted respiratory pH

pH = 7.4 + ΔRpH + ΔNRpH 7.4 + ΔRpH pH = ΔNRpH

component.

38

pH 7.4 = ΔRpH + NRpH 7.4

]

= log [NRH<sup>+</sup>

[NRH<sup>+</sup>

Erythrocyte

pH NRpH = 9 log [H<sup>+</sup>

pH <sup>=</sup> <sup>9</sup> log [H<sup>+</sup>

={24 40}/Std HCO3 (pCO2 is 40 mmHg)

] 9 + log [NRH<sup>+</sup>

] = {24 40}/Std HCO3/{24 pCO2}/HCO3 = 40 {(HCO3/Std HCO3)/pCO2}

= 1.2 {(HCO3/Std HCO3)/H2CO3}

Or in terms of carbonic acid [pCO2 = H2CO3/0.03], this can be written as

At pCO2 of 40 mmHg, pH NRpH is zero (because bicarbonate and standard bicarbonate values are equal, log 1 is zero, and log 40 is 1.6). At higher pCO2 levels (>40 mmHg), the value of [pH NRpH] is negative which denotes the acidic influence of increased pCO2. At lower pCO2 levels (<40 mmHg), the value of [pH NRpH] is positive which denotes the alkaline influence of decreased pCO2:

] 9 + log [NRH<sup>+</sup>

] or log [[H+

The magnitude and direction (positive or negative) of the changes in the parameter ΔRpH (pH NRpH) denote the respiratory influence in causing changes in pH. The value is negative for acidic effect and positive for alkaline effect. At pCO2 of

The net changes in total pH (actual pH) include both the changes in respiratory

where ΔNRpH (NRpH 7.4) denotes the changes in pH due to metabolic

Pr RpH pH = ΔNRpH {Pr RpH (predicted respiratory pH) = 7.4 + ΔRpH}

]

]/[NRH<sup>+</sup>

]

] or log [H<sup>+</sup>

]

/NRH<sup>+</sup> ]

]

]

/H+

H+ (hydrogen ion concentration) = {24 pCO2}/HCO3 NRH<sup>+</sup> (non-respiratory hydrogen ion concentration)

/H+ ] pH NRpH = log 40 + log (HCO3/Std HCO3) log(pCO2)

[pH NRpH] = 1.6 + log{(HCO3/Std HCO3)/pCO2}

[pH NRpH] = 1.6 + log {(HCO3/Std HCO3)/pCO2} where NRpH denotes the non-respiratory pH.

]/[H<sup>+</sup>

and non-respiratory (metabolic) components affecting the pH [14]:

]

NRPH-7.4 = 9 log [NRH<sup>+</sup> ] {9 log [40] = 9 log [NRH+ ] 9 + log [40] = log {[40]/[NRH<sup>+</sup> ] or log {[NRH<sup>+</sup> ]/[40]} 7.4 + ΔRpH:

7.4 + <sup>Δ</sup>RpH = {9 log [40] + 9 log [H<sup>+</sup> ] 9 + log [NRH<sup>+</sup> ] = 9 + log[NRH<sup>+</sup> ]/{[H<sup>+</sup> ] [40]} {ΔRpH (pH NRpH) = 9 log [H<sup>+</sup> ] 9 + log [NRH+ ]} = log {[NRH<sup>+</sup> ]/[H<sup>+</sup> ]}or log {[H<sup>+</sup> ]/[NRH<sup>+</sup> ]} Pr Resp Ph related to [NRH<sup>+</sup> ]/{[H+ ] [40]}

#### 3.3 Net changes in total hydrogen ion concentration

The sum total changes in the hydrogen ion concentration (ΔH<sup>+</sup> = [H<sup>+</sup> ] [40]) in the blood include both the changes due to respiratory (ΔRH+ = [H+ ] [NRH<sup>+</sup> ]) and non-respiratory (metabolic) components (ΔNRH<sup>+</sup> = [NRH<sup>+</sup> ] [40]):

[ΔRH<sup>+</sup> /H<sup>+</sup> ] = [H<sup>+</sup> NRH<sup>+</sup> ]/[H<sup>+</sup> ] = <sup>1</sup> {[NRH<sup>+</sup> ]/[H<sup>+</sup> ]} [ΔNRH<sup>+</sup> /40] = (NRH<sup>+</sup> 40)/40 or [ΔNRH<sup>+</sup> /40] = (40 NRH<sup>+</sup> )/40 = 1 {(NRH<sup>+</sup> /40)}.

The hydrogen ion concentration is 40 at pH 7.4 which denotes the homeostatic set point of acid-base balance [14, 18].

#### 4. New graphical tool

This new graphical tool developed for ABG interpretation contains four quadrants. In the x-axis, standard base excess values were taken, and in the y-axis, the ratio of (HCO3 standard HCO3)/H2CO3 values was taken to analyze the various acid-base disturbances which are clearly shown in the four-quadrant graph (Figure 3).

In the first quadrant (both x- and y-axes are positive), if the plotted area is toward the x-axis, then it represents metabolic alkalosis, and if the area is toward the y-axis, then it represents respiratory acidosis. The plotted area in between and higher may represent combined acid-base disturbances (metabolic alkalosis and respiratory acidosis). The combined acid-base disturbances may be due to compensatory mechanism or mixed acid-base disorders.

In the second quadrant (the x-axis is positive, and the y-axis negative), if the plotted area is toward the y-axis, then it represents respiratory alkalosis, and if the area is in between and lower, then it may represent combined acid-base disturbances (metabolic alkalosis and respiratory alkalosis).

In the third quadrant (both x- and y-axes are negative), if the plotted area is toward the x-axis, then it represents metabolic acidosis, and if the area is in between and lower, then it represents both metabolic acidosis and respiratory alkalosis. In the fourth quadrant (the x-axis is negative and the y-axis is positive), if the area is toward the y-axis, then it represents respiratory acidosis, and if the area is in between and higher, then it may represent both metabolic acidosis and respiratory acidosis [1].

The acid-base disorders can be classified and plotted in the four-quadrant graph by using the values of standard base excess and the ratio of (HCO3 standard HCO3)/ H2CO3. Each acid-base disorder will occupy any of the four quadrants, and the normal ABG analysis reports will be seen around the center of the graph. ABG interpretation is very essential for critically ill patients. Immediate analysis, interpretation, and prompt treatment may reduce the morbidity and mortality of the patients. [1] This newer graphical tool may provide a rough guide and help in easier and quicker interpretation of ABG reports. A minor drawback of this graphical tool is that, as the pCO2 increases, the ratio of (HCO3 standard HCO3)/H2CO3 also increases and afterward the curve flattens. This may not clearly demarcate the different higher levels of pCO2 values. Although the ratio of (HCO3 standard HCO3)/H2CO3 differentiates the respiratory acidosis and respiratory alkalosis, it may not clearly differentiate the different pCO2 levels. But this can be corrected (rectified) in a three-dimensional graph if pCO2 values are included in the third axis (z-axis). The parameter (pCO2 40 mmHg) should be taken in the third axis, because the ratio (HCO3 standard HCO3)/H2CO3 is zero at pCO2 of 40 mmHg, so that the zero central point is common to all the three parameters of the three axes [18].

Figure 6.

Figure 7.

Figure 8.

41

X-axis pCO2 vs. y-axis [NRH]/[H].

X-axis ΔRpH vs. y-axis [NRH]/[H].

Relation between [40 NRH<sup>+</sup>

Who Is Balancing: Is It RBC or Acid-Base Status? DOI: http://dx.doi.org/10.5772/intechopen.84768

] and Std base excess.

Arterial blood gas reports should be interpreted with clinical correlation. This newer graphical tool clearly demonstrates that the different acid-base disorders in a four-quadrant graph method may provide a rough guide to interpret the results quickly and easily. The current research study tries to emphasize the clinical significance of this newer diagnostic tool, which, used along with other ABG parameters and proper clinical correlation, may help in better interpretation of ABG reports.

The concept of non-respiratory hydrogen ion concentration plays a key role in understanding of ABG interpretation, yet often it is not discussed in detail during

Figure 5. Relation between NRH<sup>+</sup> and Std base excess.

Figure 6.

area is in between and lower, then it may represent combined acid-base distur-

In the third quadrant (both x- and y-axes are negative), if the plotted area is toward the x-axis, then it represents metabolic acidosis, and if the area is in between and lower, then it represents both metabolic acidosis and respiratory alkalosis. In the fourth quadrant (the x-axis is negative and the y-axis is positive), if the area is toward the y-axis, then it represents respiratory acidosis, and if the area is in between and higher, then it may represent both metabolic acidosis and respiratory

The acid-base disorders can be classified and plotted in the four-quadrant graph by using the values of standard base excess and the ratio of (HCO3 standard HCO3)/ H2CO3. Each acid-base disorder will occupy any of the four quadrants, and the normal ABG analysis reports will be seen around the center of the graph. ABG interpretation is very essential for critically ill patients. Immediate analysis, interpretation, and prompt treatment may reduce the morbidity and mortality of the patients. [1] This newer graphical tool may provide a rough guide and help in easier and quicker interpretation of ABG reports. A minor drawback of this graphical tool is that, as the pCO2 increases, the ratio of (HCO3 standard HCO3)/H2CO3 also increases and afterward the curve flattens. This may not clearly demarcate the different higher levels of pCO2 values. Although the ratio of (HCO3 standard HCO3)/H2CO3 differentiates the respiratory acidosis and respiratory alkalosis, it may not clearly differentiate the different pCO2 levels. But this can be corrected (rectified) in a three-dimensional graph if pCO2 values are included in the third axis (z-axis). The parameter (pCO2 40 mmHg) should be taken in the third axis, because the ratio (HCO3 standard HCO3)/H2CO3 is zero at pCO2 of 40 mmHg, so that the zero central point is common to all the three parameters of the three

Arterial blood gas reports should be interpreted with clinical correlation. This newer graphical tool clearly demonstrates that the different acid-base disorders in a four-quadrant graph method may provide a rough guide to interpret the results quickly and easily. The current research study tries to emphasize the clinical significance of this newer diagnostic tool, which, used along with other ABG parameters and proper clinical correlation, may help in better interpretation of ABG reports. The concept of non-respiratory hydrogen ion concentration plays a key role in understanding of ABG interpretation, yet often it is not discussed in detail during

bances (metabolic alkalosis and respiratory alkalosis).

acidosis [1].

Erythrocyte

axes [18].

Figure 5.

40

Relation between NRH<sup>+</sup> and Std base excess.

Relation between [40 NRH<sup>+</sup> ] and Std base excess.

Figure 7. X-axis pCO2 vs. y-axis [NRH]/[H].

Figure 8. X-axis ΔRpH vs. y-axis [NRH]/[H].

#### Figure 9.

X-axis ΔRpH vs. y-axis 1 {[NRH]/[H]}.

ABG interpretation because it is not routinely applied at the clinical practice due to the lack of simple formulae to calculate the same and nonavailability of its interrelationship with the other acid-base parameters. In the recently published research study, calculation of non-respiratory hydrogen ion concentration from standard bicarbonate and its relationship with other commonly utilized ABG parameters were discussed with the postulates of the acid-base balance theory and shown in

Examples of ABG data showing metabolic and respiratory components involved in net changes in total pH.

S. no pH pCO2 HCO3 Std HCO3 pH-7.4 ΔRpH ΔNRpH NRPH-7.4 Pr RpH 7.4 + ΔRpH

7. 7.5 57 44.5 39.3 0.1 0.10 0.20 7.30 Comment: changes in net pH (alkaline) are mainly due to metabolic component, partly opposed by

8. 7.4 72 44.6 36.1 0 0.17 0.17 7.23 Comment: changes in net pH are zero. The changes in pH due to metabolic and respiratory component are

9. 7.17 76 27.7 23.3 0.23 0.21 0.02 7.19

10. 7.6 12 11.8 19.5 0.2 0.30 0.10 7.70 Comment: changes in net pH (alkaline) are mainly due to respiratory component, partly opposed by

11. 7.02 14 3.6 4.1 0.38 0.40 0.78 7.80 Comment: changes in net pH (acidic) are mainly due to metabolic component, partly opposed by

equal and opposite. So, they cancelled out each other and the net change is zero

Comment: changes in net pH (acidic) are mainly due to respiratory component

The predicted respiratory pH is usually calculated by pCO2 variance. This calculation is slightly different for higher (>40 mmHg) and lower (<40 mmHg) pCO2

Figures 5–10 and tabulated in Table 1 [14, 18].

X-axis predicted respiratory pH vs. y-axis [NRH]/{[40]\*[H]}.

5. Predicted respiratory pH

respiratory component (acidic effect)

Who Is Balancing: Is It RBC or Acid-Base Status? DOI: http://dx.doi.org/10.5772/intechopen.84768

metabolic component (acidic effect)

respiratory component (alkaline effect)

Table 1.

Figure 11.

43

Figure 10. X-axis (pCO2 40 mmHg) vs. y-axis 1 {[NRH]/[H]}.



#### Table 1.

Figure 9.

Erythrocyte

Figure 10.

X-axis ΔRpH vs. y-axis 1 {[NRH]/[H]}.

X-axis (pCO2 40 mmHg) vs. y-axis 1 {[NRH]/[H]}.

respiratory component (alkaline effect)

Comment: changes in net pH are normal

respiratory component

42

S. no pH pCO2 HCO3 Std HCO3 pH-7.4 ΔRpH ΔNRpH NRPH-7.4 Pr RpH 7.4 + ΔRpH

1. 7.26 31 13.9 15.5 0.14 0.06 0.20 7.46 Comment: changes in net pH (acidic) are mainly due to metabolic component, partly opposed by

2. 7.5 37 28.9 29.2 0.1 0.03 0.07 7.43 3. 7.48 43 32 30.9 0.08 0.02 0.10 7.38

4. 7.41 37 23.5 24.3 0.01 0.02 0.01 7.42 5. 7.39 38 23 23.6 0.01 0.01 0.02 7.41

6. 7.02 61 15.8 12.5 0.38 0.08 0.30 7.32 Comment: changes in net pH (acidic) are mainly due to metabolic component and partly due to

Comment: changes in net pH (alkaline) are mainly due to metabolic component

Examples of ABG data showing metabolic and respiratory components involved in net changes in total pH.

ABG interpretation because it is not routinely applied at the clinical practice due to the lack of simple formulae to calculate the same and nonavailability of its interrelationship with the other acid-base parameters. In the recently published research study, calculation of non-respiratory hydrogen ion concentration from standard bicarbonate and its relationship with other commonly utilized ABG parameters were discussed with the postulates of the acid-base balance theory and shown in Figures 5–10 and tabulated in Table 1 [14, 18].
