# Topological Indices of Novel Drugs Used in Cardiovascular Disease Treatment and Its QSPR Modeling

Authors: Fozia Bashir Farooq; Nadeem Ul Hassan Awan; Saima Parveen; Nazeran Idrees; Salma Kanwal; Tarig A. Abdelhaleem
Journal: Journal of Chemistry
 (2022)

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## Abstract

A topological index is a score function that changes each molecular structure to a unique real number. It aids in determining the physicochemical and biological properties of a wide range of drugs, and it more accurately reflects the theoretical properties of drugs. The task is accomplished through the use of degree-based topological indices (TIs). Heart disease refers to a group of disorders that affect our hearts. Heart diseases include blood vessel disorders such as irregular heartbeat and heart muscle disease. In this article, Eliquis, metoprolol, valsartan, etc., and other drugs employed to treat cardiovascular disease are studied and the QSPR analysis goal will probe the mathematical relationship of properties such as (polarity, boiling point, enthalpy, etc.) and assorted descriptors associated to drug’s structure. The present study on TIs imposed on drugs was found to have a good correlation with physical properties.


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## Body

## 1. Introduction

The cardiovascular system is made up of the heart and its associated blood vessels. It is a group of illnesses that affect the heart. A buildup of fatty plaques in your arteries can harm your blood vessels and heart. Plaque blocks blood vessels, resulting in a heart attack and chest pain (angina). Cardiovascular disease, also known as heart disease, encompasses four distinct conditions: peripheral artery disease (PAD), coronary heart disease (CHD), coronary artery disease (CAD), and aortic atherosclerosis [1]. CAD is a result of decreased myocardial perfusion that causes angina and results in a heart attack or heart failure. It causes one-third to one-half of cardiovascular disease cases. Cerebrovascular disease is used to designate strokes and transient ischemic attacks (TIAs). Men and women experience shortness of breath, nausea, and extreme fatigue. Your heart beats slowly, too quickly, and irregularly. Heart infection signs are fever, fatigue, changes in your heart rhythm, skin rashes, and so on. Heart attacks, strokes, and other preventable cardiovascular diseases kill or have a significant impact on the population [2]. On a global scale, the disease kills a large number of people. Scientists create and study new drugs and their discovery is an uphill task since it is costly, time-consuming, and becomes incredibly hard in this field. Many drug trials are imposed to treat and halt this deadly disease, and many drug testing is performed to combat lethal disease [3]. It necessitates prompt finding and medication that will devise the disease. Nine drugs Eliquis, vericiguat, Pradaxa, ivabradine, dapagliflozin, empagliflozin, metoprolol, sacubitril, and valsartan are harmless and utmost effective medicines that are obligatory for well-being community. Figure 1 displays the aforementioned drugs.Figure 1
Molecular structure: (a) Eliquis; (b) vericiguat; (c) Pradaxa. (d) ivabradine; (e) dapagliflozin; (f) empagliflozin; (g) metoprolol; (h) sacubitril; (i) valsartan.
(a)(b)(c)(d)(e)(f)(g)(h)(i)TIs are unique numeric descriptors obtained from the graph and completely describe a chemical structure. These are employed efficiently to describe the physical properties of numerous drugs. Several types of TIs and polynomials are employed for this purpose and exactly depict the hidden information in graph theory [4–7]. All TIs are important and show a noteworthy role in chemical graphs. In the past few years, there has been a big interest in the use of graph invariants (TIs) in quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) studies. For a detailed review of QSPR studies, readers are offered to read [8–13]. Topological indices are widely used in the fields of cheminformatics, bioinformatics, and mathematics but they have the most substantial use in QSPR [14]. The ABC, Wiener, and Randic index can all be used to predict drug bioactivity. QSPR models support to decide the best relationship between TIs and drug properties. In the present paper, we calculated degree-based TIs for cardiovascular drugs. Correspondingly, cardiovascular disease drugs are thoroughly investigated with topological indices and imposed QSPR. It has been calculated with a linear regression model (RM) those TIs and drug properties have a good relation.


## 2. Material and Methods

Atoms denote vertices in drug structure, and the corresponding bonds are referred to as edges. GraphGV,E is thought to be simple and connected. The V and E are referred to as vertex and edge set, respectively. The degree of a vertex is denoted by du and is the number of vertices adjacent to it. We used the following TIs:Definition 1.
ABC index [15] G is given under(1)ABCG=∑uv∈EGdu+dv−2dudvDefinition 2.
Randic index [16] is given under(2)RAG=∑uv∈EG1dudvDefinition 3.
sum connectivity index [17] is given under(3)SG=∑uv∈EG1du+dvDefinition 4.
GA index [18] is given under:(4)GAG=∑uv∈EG2dudvdu+dvDefinition 5.
Zagreb indices [19] are given under(5)M1G=∑uv∈EGdu+dvM2G=∑uv∈EGdu+dvDefinition 6.
harmonic index [20] of G is given under:(6)HG=∑uv∈EG2du+dvDefinition 7.
hyper-Zagreb index [21] is given under(7)HMG=∑uv∈EGdu+dv2Definition 8.
forgotten index [22] is given under(8)FG=∑uv∈EGdu2+dv2
Theπ-electron energy of a molecule was calculated in [23]. ChemSpider is used to calculate the values of physical properties. As an outcome, the RM is preeminent to check and use for the aforementioned examination.
Sacubitril propionate has molecular formula C24H29 N O5. This is a neprilysin inhibitor used in conjunction with valsartan as an adjunct to decrease the risk of cardiovascular death. In Europe and Canada, medication is only sanctioned for adults with symptomatic chronic heart failure irrespective of ejection fraction. Dabigatran etexilate propionate has the molecular formula C34H41 N7O5. It is an anticoagulant that is used to prevent venous thromboembolic events or strokes in patients who have recently had hip or knee replacement surgery. The molecular formula for ivabradine is C27H36 N2O5. This medication is used to reduce the risk of hospitalization for exacerbating heart failure in adult patients and to treat stable symptomatic heart failure in pediatric patients due to dilated cardiomyopathy. The molecular formula of dapagliflozin propionate is C21H25 Cl O6. The medication is a sodium-glucose cotransporter inhibitor that is used to treat the disease. C15H25 N O3 is the molecular formula for metoprolol propionate. Valsartan was first approved in Europe in 1996 for the treatment of adult hypertension. This is commonly used to treat hypertension, heart failure, and diabetes.
Previous research on Covid-19, anticancer, blood cancer, and QSPR studies of various topological indices for various chemical structures motivated us to work on the current research problem. The purpose of this study is to look into the use of TIs in determining the physical properties and its QSPR modeling of cardiovascular disease drug regimens used in therapeutic management.


## 3. Regression Model and Quantitative Structure Analysis

In this section, TIs are discussed as cardiovascular disease treatment drugs. Calculation between QSPR and TIs clearly depicts that these are vastly correlated for the aforementioned drugs of disease [24,25]. Nine medicines Eliquis, vericiguat, Pradaxa, ivabradine, dapagliflozin, empagliflozin, metoprolol, sacubitril, and valsartan are used in a mathematical analysis for cardiovascular disease. The drug structure is shown in Figure 1. The chemical structure of a drug is characterized by a graph and its elements denote vertices and bonds that represent edges. Regression analysis was used to find the best cardiovascular treatment options. In this article, nine TIs for QSPR modeling tenacity are performed and the following properties, molar refractivity (R), polarity (P), complexity (C), molar volume (MV) enthalpy (E) and boiling point (BP), and flash point (FP) for nine remedies used for cardiovascular treatment are listed in Table 1. The regression model (RM) imposed on drugs is tested by applying the following equation:(9)P=A+bTITable 1
physical properties of drugs.
DrugBoiling point (℃)Enthalpy (℃)Flash Point (℃)Molar Refractivity (cm3)Polarity (cm3)Molar Volume (cm3)ComplexityDensity (g/cm3)Polar surface area (A2)Eliquis770.5112.2419.8125.649.8323.47771.4111Vericiguat535.981.2277.941.5260.86221.6147Pradaxa827.9120.3454.5175.969.75049911.2154Ivabradine626.992.8332.9132.252.4408.76631.160Dapagliflozin60995.1322.1105.641.9303.14721.399Empagliflozin664102.7355.7114.445.4322.45581.4109Metoprolol398.668.5194.977.130.6258.72151.051Sacubitril656.9101.6351.1113.645357.45501.293Valsartan105.5368120.647.8359.16081.2112P denotes the property of the given drug. The TI is an independent variable, A stands for constant, andb stands for regression coefficient. Statistix, SageMath, and MATLAB are useful for determining the results. A linear QSPR model is used to analyze nine TIs for cardiovascular drugs and their properties. Equation (9) is pertinent for the aforementioned calculation.Theorem 1.
LetG1 be the graph of Eliquis, TIs of G1 are given as follows:(i)
ABCG1=46.80(ii)
RAG1=26.41(iii)
SG1=27.27(iv)
GAG1=58.10(v)
M1G1=346(vi)
M2G1=444(vii)
FG1=1086(viii)
HG1=23.84(ix)
HMG1=1974Proof.
LetG1 be the graph of Eliquis with edge set E and Em,n are edges in G1 with,E1,3=13,E1,4=15,E2,4=1,E3,3=23,E3,4=4,E4,4=4,E2,3=3. By applying Definitions 1–8 we obtain the following results:(i)
ABC(G1) = 131+3−2/1×3+151+4−2/1×4+32+3−2/2×3+12+4−2/2×4+233+3−2/3×3+43+4−2/3×4+44+4−2/4×4=46.80(ii)
RAGG1=131/1×3+151/1×4+31/2×3+11/2×4+231/3×3+41/3×4+41/4×4=46.41(iii)
SG1=131/1+3+151/1+4+31/2+3+11/2+4+231/3+3+41/3+4+41/4+4=27.27(iv)
GAG1=261×3/1+3+301×4/1+4+62×3/2+3+22×4/2+4+463×3/3+3+83×4/3+4+84×4/4+4=58.10(v)
M1G1=131+3+151+4+32+3+12+4+233+3+43+4+44+4=346(vi)
M2=G1131×3+151×4+32×3+12×4+233×3+43×4+44×4=444(vii)
HG1=131/1+3+151/1+4+31/2+3+11/2+4+231/3+3+41/3+4+41/4+4=23.84(viii)
HMG1=131+32+151+42+42+32+52+42+33+32+13+42+44+42=1974(ix)
FG1=131+9+151+16+34+9+14+16+239+9+49+16+416+16=1086Theorem 2.
LetG2 be the graph of dapagliflozin, TIs in G2 are given as follows:(i)
ABCG2=40.75(ii)
RAG2=23.70(iii)
SG2= 24.03(iv)
GAG2=50.45(v)
M1G2=302(vi)
M2G2=390(vii)
FG2=974(viii)
HG2=21.36(ix)
HMG2=1754Proof.
LetG2 be the graph of dapagliflozin with edge set E, let Em,n are edges of G2 with E1,2=4,E2,3=1,E2,4=7,E3,3=12,E3,4=3,E1,3=8,E1,4=14. By applying Definitions 1–8 we obtain the following results:(i)
ABC(G2) = = 4 1+2−2/1×2+81+3−2/1×3 + 141+4−2/1×4+12+3−2/2×372+4−2/2×4+123+3−2/3×3+33+4−2/3×4=22.04.(ii)
RAG2=41/1×2+81/1×3+141/1×4+11/2×3+71/2×4+121/3×3+31/3×4=13.12.(iii)
SG2=41/1+2+81/1+3+141/1+4+11/2+371/2+4+121/3+3+31/3+4=13.46.(iv)
GAG2=81×2/1+2+161×3/1+3+281×4/1+4+22×3/2+3+142×4/2+4+243×3/3+3+63×4/3+4=27.72(v)
M1G2=41+2+81+3+141+4+12+3+72+4+123+3+33+4=162.(vi)
M2G2=41×2+81×3+141×4+12×3+72×4+123×3+33×4=209.(vii)
HG2=41/1+2+81/1+3+141/1+4+11/2+3+71/2+4+121/3+3+31/3+4=11.95(viii)
HMG2=41+22+81+32+141+42+12+32+72+42+123+32+33+42=934(ix)
FG2=41+4+81+9+141+16+14+9+74+16+129+9+39+16=516.
Topological indices for other drugs can be premeditated via the equivalent procedure as in Theorems1 and 2 and Definitions 1–8. Table 2 includes estimates for drugs' TIs. Figures 2 and 3 depict a 2D and 3D graphical representation of calculated TIs for various medicines. Using (1), we calculated the following models of TIs and are given under:Table 2
TIs of drugs.
DrugS (G)ABC (G)RA (G)HM (G)GA (G)F (G)M2 (G)H (G)M1 (G)Eliquis27.2746.8026.41197458.10108644423.84346Vericiguat22.1836.7921.52139246.8675431919.84260Pradaxa38.6866.9837.98275181.20153760733.95485Ivabradine31.0955.6430.40240265.52137051626.67412Dapagliflozin24.0340.7523.70175450.4597439021.36302Empagliflozin26.4545.1225.90200455.93111244623.32340Metoprolol19.0133.7819.03141639.1981430116.61244Sacubitril26.1645.2625.99188654.45105641523.10328Valsartan27.4347.3127.03196857.49109843524.17344Figure 2
2D graph of medicines with TIs.Figure 3
3D graph of medicines with TI.


### 3.1. Regression Models for ABC (G)

(i)
BP = 171.475 + 10.018 [ABC (G)](ii)
EP = 41.507 + 1.210 [ABC (G)](iii)
FP = 59.120 + 6.082 [ABC (G)](iv)
M = −10.427 + 2.747 [ABC (G)](v)
P = −0.273 + 1.019 [ABC (G)](vi)
MV = −7.037 + 7.554 [ABC (G)](vii)
C = −221.857 + 17.811 [ABC (G)]


### 3.2. RM for RA (G)]

(i)
BP = 136.030 + 18.971 [RA (G)](ii)
E = 36.702 + 2.310 [RA (G)](iii)
FP = 37.149 + 11.525 [RA (G)](iv)
R = −3.007 + 1.896 [RA (G)](v)
P = -21.820 + 13.843 [RA (G)](vi)
MV = 212.050 + 9.447 [RA (G)](vii)
C = −227.825 + 33.436 [RA (G)]


### 3.3. RM for S (G)

(i)
BP = 134.715 + 18.672 [S (G)](ii)
E = 36.901 + 2.261 [S (G)](iii)
FP = 36.666 + 11.337 [S (G)](iv)
R = -13.430 + 4.872 [S (G)](v)
P = −2.758 + 1.853 [S (G)](vi)
MV = −15.044 + 13.343 [S (G)](vii)
C = −286.200 + 33.148 [S (G)]


### 3.4. RM for GA (G)

(i)
BP = 132.919 + 8.914 [GA (G)](ii)
E = 36.896 + 1.076 [GA (G)](iii)
FP = 35.837 + 5.409 [GA (G)](iv)
R = -11.830 + 2.289 [GA (G)](v)
P = −2.372 + 0.875 [GA (G)](vi)
MV = −8.142 + 6.227 [GA (G)](vii)
C = −289.368 + 15.830 [GA (G)]


### 3.5. RM for M1 (G)

(i)
BP = 170.708 + 1.371 [M1 (G)](ii)
EP = 41.290 + 0.166 [M1 (G)](iii)
FP = 59.202 + 0.831 [M1 (G)](iv)
R = −11.830 + 0.378 [M1 (G)](v)
P = 0.702 + 0.136 [M1 (G)](vi)
MV = −0.381 + 1.013 [M1 (G)](vii)
C = −199.614 + 2.369 [M1 (G)]


### 3.6. RM for HM (G)

(i)
BP = 90.149 + 0.229 [HM (G)](ii)
E = 43.148 + 0.028 [HM (G)](iii)
FP = 71.169 + 0.039 [HM (G)](iv)
R = −14.022 + 0.067 [HM (G)](v)
P = 3.155 + 0.023 [HM (G)](vi)
MV = 10.033 + 0.171 [HM (G)](vii)
C = −134.240 + 0.380 [HM (G)]


### 3.7. RM for M2 (G)

(i)
BP = 156.992 + 1.115 [M2 (G)](ii)
E = 39.081 + 0.361 [M2 (G)](iii)
FP = 50.928 + 0.676 [M2 (G)](iv)
R = −14.688 + 0.305 [M2 (G)](v)
P = 1.255 + 0.107 [M2 (G)](vi)
MV = 6.006 + 0.786 [M2 (G)](vii)
C = −190.310 + 1.851 [M2 (G)]


### 3.8. RM for F (G)

(i)
BP = 219.223 + 0.383 [F (G)](ii)
EP = 46.714 + 0.047 [F (G)](iii)
FP = 88.903 + 0.232 [F (G)](iv)
R = −12.042 + 0.117 [F (G)](v)
P = 5.016 + 0.039 [F (G)](vi)
MV = 16.534 + 0.301 [F (G)](vii)
C = −85.217 + 0.635 [F (G)]


### 3.9. RM for H (G)

(i)
BP = 117.355 + 21.998 [H (G)](ii)
E = 34.520 + 2.674 [H (G)](iii)
FP = 243.838 + 13.363 [H (G)](iv)
R = -15.356 + 5.636 [H (G)](v)
P = -4.046 + 2.163 [H (G)](vi)
MV = -20.739 + 15.429 [H (G)](vii)
C = -315.098 + 38.955 [H (G)]Tables3–11 are statistical parameters in QSPR models of TIs.Table 3
RM of ABC (G).
PropertyNAbrr2FpEnthalpy941.5071.2100.7680.59010.0560.016Flash Point959.1206.0820.8010.64212.5510.009Molar Refractivity8−10.4272.7470.9800.961147.449≤ 0.001Polarity9−0.2731.0190.9670.936101.578≤ 0.001Molar Volume9−7.0377.5540.9840.968210.248≤ 0.001Complexity9−221.85717.8110.8410.70716.9000.005Boiling Point8171.47510.0180.8050.64711.0170.016Table 4
RM of RA (G).
PropertyNAbrr2FpEnthalpy936.7022.3100.7980.63712.3040.010Flash Point937.14911.5250.8270.68415.1640.006Molar Refractivity8−15.7275.0400.9900.979285.580≤ 0.001Polarity9−3.0071.8960.9800.960169.494≤ 0.001Molar Volume9−21.82013.8430.9820.964189.488≤ 0.001Complexity9−227.82533.4360.8600.74019.8740.003Boiling Point8136.03018.9710.8300.68813.2590.011Table 5
RM of S (G).
PropertyNAbrr2FpEnthalpy936.9012.2610.8040.64712.817.009Flash Point936.66611.3370.8270.70116.413.005Molar Refractivity8−13.4304.8720.9920.985388.144≤ 0.001Polarity9−2.7581.8530.9850.971235.553≤ 0.001Molar Volume9−15.04413.3430.9740.949129.876≤ 0.001Complexity9−286.20033.1480.8770.77023.3970.002Boiling Point8134.71518.6720.8410.70714.4520.009Table 6
RM of GA (G).
PropertyNAbrr2FpEnthalpy936.8961.0760.8130.66113.6250.008Flash Point935.8375.4090.8480.72017.9800.004Molar Refractivity8−11.6362.2890.9940.988477.849≤0.001Polarity9−2.3720.8750.9880.976290.534≤0.001Molar Volume9−8.1426.2270.9650.93296.106≤0.001Complexity9−289.36815.8300.8900.79226.5940.001Boiling Point8132.9198.9140.8520.72715.9410.007Table 7
RM of M1 (G).
PropertyNAbrr2FpEnthalpy941.2900.1660.7780.60610.7670.013Flash Point959.2020.8310.8090.65413.2540.008Molar Refractivity8−11.8300.3780.9780.957132.373≤ 0.001Polarity90.7020.1360.9570.91575.687≤ 0.001Molar Volume9−0.3811.0130.9750.950133.079≤ 0.001Complexity9−199.6142.3690.8260.68315.0820.006Boiling Point8170.7081.3710.8140.66211.7440.014Table 8
RM of M2 (G).
PropertyNAbrr2FpEnthalpy939.0810.1360.8110.65813.4760.008Flash Point950.9280.6760.8350.69716.1240.005Molar Refractivity8−14.6880.3050.9790.959139.905≤ 0.001Polarity91.2550.1070.9480.89962.189≤ 0.001Molar Volume96.0060.7860.9590.92080.997≤ 0.001Complexity9−190.3101.8510.8190.67114.2890.007Boiling Point8156.9921.1150.8400.70514.3690.009Table 9
RM of HM (G).
PropertyNAbrr2FpEnthalpy943.1480.0280.7690.59110.1060.016Flash Point971.1690.1390.7910.62611.6950.011Molar Refractivity8−14.0220.0670.9660.93484.254≤ 0.001Polarity93.1550.0230.9250.85641.582≤ 0.001Molar Volume910.0330.1710.9650.93194.877≤ 0.001Complexity9−134.2400.3800.7750.60110.5470.014Boiling Point8190.1490.2290.7960.63310.3580.018Table 10
RM of H (G).
PropertyNAbrr2FpEnthalpy934.5202.6740.8180.67014.2020.007Flash Point925.83813.3630.8490.72118.0850.004Molar Refractivity8−15.3565.6360.9950.989563.243≤ 0.001Polarity9−4.0462.1630.9900.980346.941≤ 0.001Molar Volume9−20.73915.4290.9690.939108.128≤ 0.001Complexity9−315.09838.9550.8870.78725.8440.001Boiling Point8117.35521.9980.8520.72615.8750.007Table 11
RM of F (G).
PropertyNAbrr2FpEnthalpy946.7140.0470.7320.5368.0910.025Flash Point988.9030.2320.7530.5679.1820.019Molar Refractivity8−12.0420.1170.9510.90456.541≤ 0.001Polarity95.0160.0390.9030.81530.9150.001Molar Volume916.5340.3010.9640.93093.089≤ 0.001Complexity9−85.2170.6350.7380.5448.3650.023Boiling Point8219.2230.3830.7580.5758.1060.029


### 3.10. Comparison between TIs and Correlation Coefficient of Properties

Table1 shows the properties of nine cardiovascular disease drugs, and Table 2 shows their TIs computed using molecules. Table 12 lists correlation coefficients between seven physical properties and TIs. Figure 4 depicts the graph between TIs and physical properties.Table 12
Correlation coefficients.
Correlation coefficientTopological IndexBoiling pointEnthalpyFPrefractivityPolarityMolar volumeCABC(G)0.8050.7680.8010.980.9670.9840.841RA(G)0.8300.7980.8270.990.980.9820.86S(G)0.8410.8040.8370.9920.9850.9740.877GA(G)0.8520.8130.8480.9940.9880.9650.89M1(G)0.8140.7780.8090.9780.9570.9750.826M2(G)0.840.8110.8350.9790.9480.9590.819HM(G)0.7960.7690.7910.9660.9250.9650.775F(G)0.7580.7320.7530.9510.9030.9640.738H(G)0.8520.8180.8490.9950.9900.9690.887Figure 4
Properties and Tis: (a) complexity on TI; (b) enthalpy on TI; (c) enthalpy on TI; (d) molar refractivity on TI; (e) MV on TI; (f) polarity on TI; (g) boiling point on TI.
(a)(b)(c)(d)(e)(f)(g)


### 3.11. Standard Error of Estimate (SEE) and Statistical Parameters

A measure of variation for an observation calculated around the computed regression line is said to be the standard error estimate. This will be helpful in calculating the range of accuracy to predict around the regression line in Table13. In Table 14 correlation determination describes the percentage of relationship that provides additional info about the association between variables. It is calculated by squaring the value of r. Tables 15–21 associate properties, theoretical, and experimental estimated values that are found with the models.Table 13
coefficient of determination.
Coefficient of determinationTopological IndexBPEnthalpyFPrefractivityPolarityMolar volumeComplexityABC (G)0.6470.590.6420.9610.9360.9680.707RA (G)0.6880.6370.6840.9790.9600.9640.74S (G)0.7070.6470.7010.9850.9710.9490.77GA (G)0.7270.6610.7200.9880.9760.9320.792M1 (G)0.6620.6060.6540.9570.9150.9500.683M2 (G)0.7050.6580.6970.9590.8990.9200.671HM (G)0.6330.5910.6260.9340.8560.9310.601F (G)0.5750.5360.5670.9040.8150.9300.544H (G)0.7260.6700.7210.9890.9800.9390.787Table 14
Standard error of the estimate.
SeeTopological IndexBPEnthalpyFPRefractivityPolarityMolar volumeComplexityABC (G)85.131610.768148.443415.944452.8542814.7016122.262RA (G)80.02210.121845.498554.312352.2387315.4588115.298S (G)77.65439.9898144.268473.709081.9097018.5216108.411GA (G)74.97289.7922842.856833.347641.7242521.3403103.123M1 (G)83.369610.550447.595316.259903.2707618.3087127.196M2 (G)77.81249.8277444.543436.096183.5756023.0998129.542HM (G)86.828410.752519.540677.751064.2670721.4687142.686F (G)93.503411.447853.247349.311334.8301621.6596152.484H (G)75.08479.6581142.767573.086341.5808920.1954104.295Table 15
Comparision.
DrugPolarityPolarity computed from RMABCRSGAM1M2FHHMEliquis49.8±0.5cm342.213442.170142.177642.152542.20941.99642.30342.185341.18Vericiguat41.5±0.5cm336.779836.447636.496136.654237.35837.75637.88336.258536.98Pradaxa69.7±0.5cm346.175546.382146.329546.145545.67444.91145.36346.560244.07Ivabradine52.4±0.5cm340.410740.217640.526640.863141.13141.51941.38340.426540.47Dapagliflozin41.9±0.5cm341.742041.629841.619241.612941.82441.67842.00341.579340.88Empagliflozin45.4±0.5cm322.568322.47322.547322.550822.4222.17422.32322.542721.96Metoprolol30.6±0.5cm322.568322.915022.668722.465622.4222.33322.44322.897422.09Sacubitril45.00±0.5cm344.532144.773444.909144.731244.51944.32844.46344.978743.33Valsartan47.8±0.0cm319.593519.206519.305919.483620.1120.58420.52319.025020.31Table 16
Comparison.
DrugMolar volumeMolar volume computed from RMABRSGAM1M2FHHMEliquis323.4±7.0cm3344.058343.528343.406343.508343.293343.034343.097343.143341.924Vericiguat260.875.0cm3294.874292.133292.413293.917298.941303.514302.433290.324301.919Pradaxa504±7.0cm3379.923381.357380.670379.523374.973370.204371.249382.132369.539Ivabradine408.7±3.0cm3327.741325.992328.588331.879333.437338.588334.633327.469335.204Dapagliflozin303.1±3.0cm3339.791338.675338.394338.641339.773340.07340.337337.743339.089Empagliflozin322.4±3.0cm3166.235166.623167.218166.713162.365158.278159.281168.087158.489Metoprolol258.7±3.0cm3166.235170.593168.307165.945162.365159.76160.385171.249159.749Sacubitril357.4±3.0cm3365.047366.909367.922366.766364.413364.77362.969368.038362.504Valsartan359.1±3.0cm3139.308137.285138.125139.049141.245143.458142.721136.738142.739Table 17
Comparison.
DrugEnthalpyEnthalpy computed from RMABCRSGAM1M2FHHMEliquis112.2±3.0℃99.752599.666899.680899.698699.5899.44198.93499.6577100.626Vericiguat81.2±3.0℃92.851792.467192.511092.719493.40694.00193.40992.223294.911Pradaxa120.3±3.0℃104.784104.966104.920104.767103.99103.181102.759105.145104.571Ivabradine92.8±3.0℃97.463097.210297.597398.062098.20898.82997.78497.451599.666Dapagliflozin95.1±3.0℃99.153898.98798.976199.013799.0999.03398.55998.8976100.221Empagliflozin102.7±3.0℃74.802974.88574.908474.816974.39474.00973.95975.018174.421Metoprolol68.5±3.0℃74.802975.441275.061674.708874.39474.21374.10975.463074.601Sacubitril101.6±3.0℃102.697102.942103.127102.972102.52102.433101.634103.161103.566Valsartan105.5±3.0℃71.024970.775370.817970.923571.45471.96971.70970.605572.171Table 18
Comparison.
DrugMolar refractivityMolar refractivity computed from RMABCRSGAM1M2FHHMEliquis125.6±5.0cm3119.352119.326119.342119.277119.06118.509118.659119.309117.44Vericiguat104.168103.296103.444103.905105.578106.749106.504102.719105.63Pradaxa175.9±5.0cm3130.423131.125130.96130.441128.69126.594127.074131.554125.59Ivabradine132.2±3.0cm3114.314113.857114.722115.672116.064117.186116.129114.386115.45Dapagliflozin105.6±3.0cm3118.035117.813117.78117.768117.99117.627117.834117.613116.6Empagliflozin114.4±3.0cm364.45764.14964.412764.475464.06263.53163.71464.328563.28Metoprolol77.1±3.0cm364.45765.387464.752464.237264.06263.97264.04465.321463.652Sacubitril113.6±3.0cm3125.831126.619126.985126.486125.48124.977124.599127.128123.51Valsartan120.6±3.0cm356.144454.998655.342755.900257.64259.12158.76454.482458.63Table 19
Comparison.
DrugComplexityComplexity computed from RMABCRSGAM1M2FHHMEliquis777918.993916.572916.631917.327916.775914.103915.126915.531916.04Vericiguat622754.040744.744745.703750.715768.032782.023779.211738.678781.54Pradaxa9911039.271043.041041.541038.321023.021004.901009.221046.071008.9Ivabradine663864.267857.944866.96878.256883.721899.244886.836863.048893.44Dapagliflozin472904.683900.348899.830900.976904.97904.197905.901897.449906.5Empagliflozin558322.609325.13326.054323.341309.998296.629300.741329.402299.34Metoprolol215322.609338.404329.706320.759309.998301.582304.431339.987303.58Sacubitril550989.384994.743998.808995.470987.605986.747981.546998.886985.22Valsartan608232.301227.047228.537230.396239.168247.099245.391224.437246.39Table 20
Comparison.
DrugBoiling point of the drugBoiling point computed from RMABCRSGAM1M2FHHMEliquis770.5±6.0℃640.3174637.0541643.9677.9733645.074652.052635.161641.7873642.2Vericiguat535.9±5.0℃540.0372544.2859548.86621.6272527.168512.677508.005553.7953508.92Pradaxa827.9±75℃842.4806856.5486856.948793.7736835.643833.797807.894864.1871820.13Ivabradine626.9±55℃728.8765712.7484715.227715.1698735.56732.332743.933704.0417740.21Dapagliflozin609±55℃579.7085585.6427583.403639.6239584.75591.842592.265587.2323591.82Empagliflozin664.5±55℃623.4872627.3789628.589667.0951636.848654.282645.119630.3484649.07Metoprolol398.6±37℃509.883497.0481489.67583.1775505.232492.607530.985482.7418514.41Sacubitril656.9±55℃624.8897629.0863623.175659.6759620.396619.717623.671625.5088622.04Valsartan645.4266648.8161646.888674.9154642.332642.017639.757649.0467640.82Table 21
Comparison.
DrugFlash pointFlash point computed from RMABCRSGAM1M2FHHMEliquis419±32℃343.7576341.5243345.826350.0999346.728351.072340.855344.4119148.155Vericiguat277.9±30℃282.8768285.167288.1207289.3027275.262266.572263.831290.9599125.457Pradaxa454.5±3℃466.4924474.8685475.1812475.0478462.237461.26445.487479.5119178.458Ivabradine332.9±31.5℃397.5225387.509389.1333390.2347401.574399.744406.743382.2292164.847Dapagliflozin322.±31.5℃306.9615310.2915309.0941308.7211310.164314.568314.871311.2717139.575Empagliflozin355.7±31.5℃333.5398335.6465336.5297338.3624341.742352.424346.887337.4632149.325Metoprolol194.9±26.5℃264.57256.4698252.1824247.8157261.966254.404277.751247.7974126.393Sacubitril351.1±31.5℃334.3913336.6838333.2419330.3571331.77331.468333.895334.5233144.723Valsartan368±34.3℃346.8594348.6698347.6399346.8004345.066344.988343.639348.8217147.921In this section, we find the relation of TIs with the properties of aforementioned drugs of said disease, such as Eliquis, vericiguat, Pradaxa, ivabradine, dapagliflozin, empagliflozin, metoprolol, sacubitril, and valsartan, and it will best be calculated with the aid of QSPR modeling, whereas TIs,b, r, and N are independent variables, RM constant, correlation coefficient, and sample size, respectively. This test can associate and decide the enhancement of the model. The observations evaluate that p should be less than 0.05 and r is greater than 0.6. Therefore, based on the calculating procedure used above, it is clearly shown that the features listed in Tables 3–11 are important.


## 3.1. Regression Models for ABC (G)

(i)
BP = 171.475 + 10.018 [ABC (G)](ii)
EP = 41.507 + 1.210 [ABC (G)](iii)
FP = 59.120 + 6.082 [ABC (G)](iv)
M = −10.427 + 2.747 [ABC (G)](v)
P = −0.273 + 1.019 [ABC (G)](vi)
MV = −7.037 + 7.554 [ABC (G)](vii)
C = −221.857 + 17.811 [ABC (G)]


## 3.2. RM for RA (G)]

(i)
BP = 136.030 + 18.971 [RA (G)](ii)
E = 36.702 + 2.310 [RA (G)](iii)
FP = 37.149 + 11.525 [RA (G)](iv)
R = −3.007 + 1.896 [RA (G)](v)
P = -21.820 + 13.843 [RA (G)](vi)
MV = 212.050 + 9.447 [RA (G)](vii)
C = −227.825 + 33.436 [RA (G)]


## 3.3. RM for S (G)

(i)
BP = 134.715 + 18.672 [S (G)](ii)
E = 36.901 + 2.261 [S (G)](iii)
FP = 36.666 + 11.337 [S (G)](iv)
R = -13.430 + 4.872 [S (G)](v)
P = −2.758 + 1.853 [S (G)](vi)
MV = −15.044 + 13.343 [S (G)](vii)
C = −286.200 + 33.148 [S (G)]


## 3.4. RM for GA (G)

(i)
BP = 132.919 + 8.914 [GA (G)](ii)
E = 36.896 + 1.076 [GA (G)](iii)
FP = 35.837 + 5.409 [GA (G)](iv)
R = -11.830 + 2.289 [GA (G)](v)
P = −2.372 + 0.875 [GA (G)](vi)
MV = −8.142 + 6.227 [GA (G)](vii)
C = −289.368 + 15.830 [GA (G)]


## 3.5. RM for M1 (G)

(i)
BP = 170.708 + 1.371 [M1 (G)](ii)
EP = 41.290 + 0.166 [M1 (G)](iii)
FP = 59.202 + 0.831 [M1 (G)](iv)
R = −11.830 + 0.378 [M1 (G)](v)
P = 0.702 + 0.136 [M1 (G)](vi)
MV = −0.381 + 1.013 [M1 (G)](vii)
C = −199.614 + 2.369 [M1 (G)]


## 3.6. RM for HM (G)

(i)
BP = 90.149 + 0.229 [HM (G)](ii)
E = 43.148 + 0.028 [HM (G)](iii)
FP = 71.169 + 0.039 [HM (G)](iv)
R = −14.022 + 0.067 [HM (G)](v)
P = 3.155 + 0.023 [HM (G)](vi)
MV = 10.033 + 0.171 [HM (G)](vii)
C = −134.240 + 0.380 [HM (G)]


## 3.7. RM for M2 (G)

(i)
BP = 156.992 + 1.115 [M2 (G)](ii)
E = 39.081 + 0.361 [M2 (G)](iii)
FP = 50.928 + 0.676 [M2 (G)](iv)
R = −14.688 + 0.305 [M2 (G)](v)
P = 1.255 + 0.107 [M2 (G)](vi)
MV = 6.006 + 0.786 [M2 (G)](vii)
C = −190.310 + 1.851 [M2 (G)]


## 3.8. RM for F (G)

(i)
BP = 219.223 + 0.383 [F (G)](ii)
EP = 46.714 + 0.047 [F (G)](iii)
FP = 88.903 + 0.232 [F (G)](iv)
R = −12.042 + 0.117 [F (G)](v)
P = 5.016 + 0.039 [F (G)](vi)
MV = 16.534 + 0.301 [F (G)](vii)
C = −85.217 + 0.635 [F (G)]


## 3.9. RM for H (G)

(i)
BP = 117.355 + 21.998 [H (G)](ii)
E = 34.520 + 2.674 [H (G)](iii)
FP = 243.838 + 13.363 [H (G)](iv)
R = -15.356 + 5.636 [H (G)](v)
P = -4.046 + 2.163 [H (G)](vi)
MV = -20.739 + 15.429 [H (G)](vii)
C = -315.098 + 38.955 [H (G)]Tables3–11 are statistical parameters in QSPR models of TIs.Table 3
RM of ABC (G).
PropertyNAbrr2FpEnthalpy941.5071.2100.7680.59010.0560.016Flash Point959.1206.0820.8010.64212.5510.009Molar Refractivity8−10.4272.7470.9800.961147.449≤ 0.001Polarity9−0.2731.0190.9670.936101.578≤ 0.001Molar Volume9−7.0377.5540.9840.968210.248≤ 0.001Complexity9−221.85717.8110.8410.70716.9000.005Boiling Point8171.47510.0180.8050.64711.0170.016Table 4
RM of RA (G).
PropertyNAbrr2FpEnthalpy936.7022.3100.7980.63712.3040.010Flash Point937.14911.5250.8270.68415.1640.006Molar Refractivity8−15.7275.0400.9900.979285.580≤ 0.001Polarity9−3.0071.8960.9800.960169.494≤ 0.001Molar Volume9−21.82013.8430.9820.964189.488≤ 0.001Complexity9−227.82533.4360.8600.74019.8740.003Boiling Point8136.03018.9710.8300.68813.2590.011Table 5
RM of S (G).
PropertyNAbrr2FpEnthalpy936.9012.2610.8040.64712.817.009Flash Point936.66611.3370.8270.70116.413.005Molar Refractivity8−13.4304.8720.9920.985388.144≤ 0.001Polarity9−2.7581.8530.9850.971235.553≤ 0.001Molar Volume9−15.04413.3430.9740.949129.876≤ 0.001Complexity9−286.20033.1480.8770.77023.3970.002Boiling Point8134.71518.6720.8410.70714.4520.009Table 6
RM of GA (G).
PropertyNAbrr2FpEnthalpy936.8961.0760.8130.66113.6250.008Flash Point935.8375.4090.8480.72017.9800.004Molar Refractivity8−11.6362.2890.9940.988477.849≤0.001Polarity9−2.3720.8750.9880.976290.534≤0.001Molar Volume9−8.1426.2270.9650.93296.106≤0.001Complexity9−289.36815.8300.8900.79226.5940.001Boiling Point8132.9198.9140.8520.72715.9410.007Table 7
RM of M1 (G).
PropertyNAbrr2FpEnthalpy941.2900.1660.7780.60610.7670.013Flash Point959.2020.8310.8090.65413.2540.008Molar Refractivity8−11.8300.3780.9780.957132.373≤ 0.001Polarity90.7020.1360.9570.91575.687≤ 0.001Molar Volume9−0.3811.0130.9750.950133.079≤ 0.001Complexity9−199.6142.3690.8260.68315.0820.006Boiling Point8170.7081.3710.8140.66211.7440.014Table 8
RM of M2 (G).
PropertyNAbrr2FpEnthalpy939.0810.1360.8110.65813.4760.008Flash Point950.9280.6760.8350.69716.1240.005Molar Refractivity8−14.6880.3050.9790.959139.905≤ 0.001Polarity91.2550.1070.9480.89962.189≤ 0.001Molar Volume96.0060.7860.9590.92080.997≤ 0.001Complexity9−190.3101.8510.8190.67114.2890.007Boiling Point8156.9921.1150.8400.70514.3690.009Table 9
RM of HM (G).
PropertyNAbrr2FpEnthalpy943.1480.0280.7690.59110.1060.016Flash Point971.1690.1390.7910.62611.6950.011Molar Refractivity8−14.0220.0670.9660.93484.254≤ 0.001Polarity93.1550.0230.9250.85641.582≤ 0.001Molar Volume910.0330.1710.9650.93194.877≤ 0.001Complexity9−134.2400.3800.7750.60110.5470.014Boiling Point8190.1490.2290.7960.63310.3580.018Table 10
RM of H (G).
PropertyNAbrr2FpEnthalpy934.5202.6740.8180.67014.2020.007Flash Point925.83813.3630.8490.72118.0850.004Molar Refractivity8−15.3565.6360.9950.989563.243≤ 0.001Polarity9−4.0462.1630.9900.980346.941≤ 0.001Molar Volume9−20.73915.4290.9690.939108.128≤ 0.001Complexity9−315.09838.9550.8870.78725.8440.001Boiling Point8117.35521.9980.8520.72615.8750.007Table 11
RM of F (G).
PropertyNAbrr2FpEnthalpy946.7140.0470.7320.5368.0910.025Flash Point988.9030.2320.7530.5679.1820.019Molar Refractivity8−12.0420.1170.9510.90456.541≤ 0.001Polarity95.0160.0390.9030.81530.9150.001Molar Volume916.5340.3010.9640.93093.089≤ 0.001Complexity9−85.2170.6350.7380.5448.3650.023Boiling Point8219.2230.3830.7580.5758.1060.029


## 3.10. Comparison between TIs and Correlation Coefficient of Properties

Table1 shows the properties of nine cardiovascular disease drugs, and Table 2 shows their TIs computed using molecules. Table 12 lists correlation coefficients between seven physical properties and TIs. Figure 4 depicts the graph between TIs and physical properties.Table 12
Correlation coefficients.
Correlation coefficientTopological IndexBoiling pointEnthalpyFPrefractivityPolarityMolar volumeCABC(G)0.8050.7680.8010.980.9670.9840.841RA(G)0.8300.7980.8270.990.980.9820.86S(G)0.8410.8040.8370.9920.9850.9740.877GA(G)0.8520.8130.8480.9940.9880.9650.89M1(G)0.8140.7780.8090.9780.9570.9750.826M2(G)0.840.8110.8350.9790.9480.9590.819HM(G)0.7960.7690.7910.9660.9250.9650.775F(G)0.7580.7320.7530.9510.9030.9640.738H(G)0.8520.8180.8490.9950.9900.9690.887Figure 4
Properties and Tis: (a) complexity on TI; (b) enthalpy on TI; (c) enthalpy on TI; (d) molar refractivity on TI; (e) MV on TI; (f) polarity on TI; (g) boiling point on TI.
(a)(b)(c)(d)(e)(f)(g)


## 3.11. Standard Error of Estimate (SEE) and Statistical Parameters

A measure of variation for an observation calculated around the computed regression line is said to be the standard error estimate. This will be helpful in calculating the range of accuracy to predict around the regression line in Table13. In Table 14 correlation determination describes the percentage of relationship that provides additional info about the association between variables. It is calculated by squaring the value of r. Tables 15–21 associate properties, theoretical, and experimental estimated values that are found with the models.Table 13
coefficient of determination.
Coefficient of determinationTopological IndexBPEnthalpyFPrefractivityPolarityMolar volumeComplexityABC (G)0.6470.590.6420.9610.9360.9680.707RA (G)0.6880.6370.6840.9790.9600.9640.74S (G)0.7070.6470.7010.9850.9710.9490.77GA (G)0.7270.6610.7200.9880.9760.9320.792M1 (G)0.6620.6060.6540.9570.9150.9500.683M2 (G)0.7050.6580.6970.9590.8990.9200.671HM (G)0.6330.5910.6260.9340.8560.9310.601F (G)0.5750.5360.5670.9040.8150.9300.544H (G)0.7260.6700.7210.9890.9800.9390.787Table 14
Standard error of the estimate.
SeeTopological IndexBPEnthalpyFPRefractivityPolarityMolar volumeComplexityABC (G)85.131610.768148.443415.944452.8542814.7016122.262RA (G)80.02210.121845.498554.312352.2387315.4588115.298S (G)77.65439.9898144.268473.709081.9097018.5216108.411GA (G)74.97289.7922842.856833.347641.7242521.3403103.123M1 (G)83.369610.550447.595316.259903.2707618.3087127.196M2 (G)77.81249.8277444.543436.096183.5756023.0998129.542HM (G)86.828410.752519.540677.751064.2670721.4687142.686F (G)93.503411.447853.247349.311334.8301621.6596152.484H (G)75.08479.6581142.767573.086341.5808920.1954104.295Table 15
Comparision.
DrugPolarityPolarity computed from RMABCRSGAM1M2FHHMEliquis49.8±0.5cm342.213442.170142.177642.152542.20941.99642.30342.185341.18Vericiguat41.5±0.5cm336.779836.447636.496136.654237.35837.75637.88336.258536.98Pradaxa69.7±0.5cm346.175546.382146.329546.145545.67444.91145.36346.560244.07Ivabradine52.4±0.5cm340.410740.217640.526640.863141.13141.51941.38340.426540.47Dapagliflozin41.9±0.5cm341.742041.629841.619241.612941.82441.67842.00341.579340.88Empagliflozin45.4±0.5cm322.568322.47322.547322.550822.4222.17422.32322.542721.96Metoprolol30.6±0.5cm322.568322.915022.668722.465622.4222.33322.44322.897422.09Sacubitril45.00±0.5cm344.532144.773444.909144.731244.51944.32844.46344.978743.33Valsartan47.8±0.0cm319.593519.206519.305919.483620.1120.58420.52319.025020.31Table 16
Comparison.
DrugMolar volumeMolar volume computed from RMABRSGAM1M2FHHMEliquis323.4±7.0cm3344.058343.528343.406343.508343.293343.034343.097343.143341.924Vericiguat260.875.0cm3294.874292.133292.413293.917298.941303.514302.433290.324301.919Pradaxa504±7.0cm3379.923381.357380.670379.523374.973370.204371.249382.132369.539Ivabradine408.7±3.0cm3327.741325.992328.588331.879333.437338.588334.633327.469335.204Dapagliflozin303.1±3.0cm3339.791338.675338.394338.641339.773340.07340.337337.743339.089Empagliflozin322.4±3.0cm3166.235166.623167.218166.713162.365158.278159.281168.087158.489Metoprolol258.7±3.0cm3166.235170.593168.307165.945162.365159.76160.385171.249159.749Sacubitril357.4±3.0cm3365.047366.909367.922366.766364.413364.77362.969368.038362.504Valsartan359.1±3.0cm3139.308137.285138.125139.049141.245143.458142.721136.738142.739Table 17
Comparison.
DrugEnthalpyEnthalpy computed from RMABCRSGAM1M2FHHMEliquis112.2±3.0℃99.752599.666899.680899.698699.5899.44198.93499.6577100.626Vericiguat81.2±3.0℃92.851792.467192.511092.719493.40694.00193.40992.223294.911Pradaxa120.3±3.0℃104.784104.966104.920104.767103.99103.181102.759105.145104.571Ivabradine92.8±3.0℃97.463097.210297.597398.062098.20898.82997.78497.451599.666Dapagliflozin95.1±3.0℃99.153898.98798.976199.013799.0999.03398.55998.8976100.221Empagliflozin102.7±3.0℃74.802974.88574.908474.816974.39474.00973.95975.018174.421Metoprolol68.5±3.0℃74.802975.441275.061674.708874.39474.21374.10975.463074.601Sacubitril101.6±3.0℃102.697102.942103.127102.972102.52102.433101.634103.161103.566Valsartan105.5±3.0℃71.024970.775370.817970.923571.45471.96971.70970.605572.171Table 18
Comparison.
DrugMolar refractivityMolar refractivity computed from RMABCRSGAM1M2FHHMEliquis125.6±5.0cm3119.352119.326119.342119.277119.06118.509118.659119.309117.44Vericiguat104.168103.296103.444103.905105.578106.749106.504102.719105.63Pradaxa175.9±5.0cm3130.423131.125130.96130.441128.69126.594127.074131.554125.59Ivabradine132.2±3.0cm3114.314113.857114.722115.672116.064117.186116.129114.386115.45Dapagliflozin105.6±3.0cm3118.035117.813117.78117.768117.99117.627117.834117.613116.6Empagliflozin114.4±3.0cm364.45764.14964.412764.475464.06263.53163.71464.328563.28Metoprolol77.1±3.0cm364.45765.387464.752464.237264.06263.97264.04465.321463.652Sacubitril113.6±3.0cm3125.831126.619126.985126.486125.48124.977124.599127.128123.51Valsartan120.6±3.0cm356.144454.998655.342755.900257.64259.12158.76454.482458.63Table 19
Comparison.
DrugComplexityComplexity computed from RMABCRSGAM1M2FHHMEliquis777918.993916.572916.631917.327916.775914.103915.126915.531916.04Vericiguat622754.040744.744745.703750.715768.032782.023779.211738.678781.54Pradaxa9911039.271043.041041.541038.321023.021004.901009.221046.071008.9Ivabradine663864.267857.944866.96878.256883.721899.244886.836863.048893.44Dapagliflozin472904.683900.348899.830900.976904.97904.197905.901897.449906.5Empagliflozin558322.609325.13326.054323.341309.998296.629300.741329.402299.34Metoprolol215322.609338.404329.706320.759309.998301.582304.431339.987303.58Sacubitril550989.384994.743998.808995.470987.605986.747981.546998.886985.22Valsartan608232.301227.047228.537230.396239.168247.099245.391224.437246.39Table 20
Comparison.
DrugBoiling point of the drugBoiling point computed from RMABCRSGAM1M2FHHMEliquis770.5±6.0℃640.3174637.0541643.9677.9733645.074652.052635.161641.7873642.2Vericiguat535.9±5.0℃540.0372544.2859548.86621.6272527.168512.677508.005553.7953508.92Pradaxa827.9±75℃842.4806856.5486856.948793.7736835.643833.797807.894864.1871820.13Ivabradine626.9±55℃728.8765712.7484715.227715.1698735.56732.332743.933704.0417740.21Dapagliflozin609±55℃579.7085585.6427583.403639.6239584.75591.842592.265587.2323591.82Empagliflozin664.5±55℃623.4872627.3789628.589667.0951636.848654.282645.119630.3484649.07Metoprolol398.6±37℃509.883497.0481489.67583.1775505.232492.607530.985482.7418514.41Sacubitril656.9±55℃624.8897629.0863623.175659.6759620.396619.717623.671625.5088622.04Valsartan645.4266648.8161646.888674.9154642.332642.017639.757649.0467640.82Table 21
Comparison.
DrugFlash pointFlash point computed from RMABCRSGAM1M2FHHMEliquis419±32℃343.7576341.5243345.826350.0999346.728351.072340.855344.4119148.155Vericiguat277.9±30℃282.8768285.167288.1207289.3027275.262266.572263.831290.9599125.457Pradaxa454.5±3℃466.4924474.8685475.1812475.0478462.237461.26445.487479.5119178.458Ivabradine332.9±31.5℃397.5225387.509389.1333390.2347401.574399.744406.743382.2292164.847Dapagliflozin322.±31.5℃306.9615310.2915309.0941308.7211310.164314.568314.871311.2717139.575Empagliflozin355.7±31.5℃333.5398335.6465336.5297338.3624341.742352.424346.887337.4632149.325Metoprolol194.9±26.5℃264.57256.4698252.1824247.8157261.966254.404277.751247.7974126.393Sacubitril351.1±31.5℃334.3913336.6838333.2419330.3571331.77331.468333.895334.5233144.723Valsartan368±34.3℃346.8594348.6698347.6399346.8004345.066344.988343.639348.8217147.921In this section, we find the relation of TIs with the properties of aforementioned drugs of said disease, such as Eliquis, vericiguat, Pradaxa, ivabradine, dapagliflozin, empagliflozin, metoprolol, sacubitril, and valsartan, and it will best be calculated with the aid of QSPR modeling, whereas TIs,b, r, and N are independent variables, RM constant, correlation coefficient, and sample size, respectively. This test can associate and decide the enhancement of the model. The observations evaluate that p should be less than 0.05 and r is greater than 0.6. Therefore, based on the calculating procedure used above, it is clearly shown that the features listed in Tables 3–11 are important.


## 4. Conclusions

The statistical parameters applied to the models and TIs that: H(G) delivers maximum correlation of molar polarityr = 0.990. ABC(G) delivers highly correlated worth for molar volume r = 0.984. H(G) index offers a maximum correlated value of flash point i.e., r = 0.849. GA (G) and H (G) index describe the extreme correlation coefficient of BP r = 0.852. H(G) delivers the ultimate correlated value of molar refractivity r = 0.995. Tables 3–11 display various statical parameters of correlation between seven physical properties of medicine and the values of nine degree-based topological indices. There was no correlation between TIs and density and between polar surface area and surface tension.In this paper, we calculated TIs and compared them to the QSPR model for drugs employed in cardiovascular disease. In the pharmaceutical industry, the calculated value gained through this will be useful in designing novel drugs that will obviously be helpful in obtaining preventive measures for the aforementioned disease. The correlation coefficient subsidizes meaningfully with many TIs for the drugs. Drugs calculated values are eye-opening to chemists deployed on drug discovering phenomenon in the pharmaceutical industry. They deliver methods for the estimation of properties for new exposures to other specific diseases.



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*Source: 9749575-2022-11-04.xml*