Traffic noise modelling on urban arterial roads using mathematical and machine-learning techniques

Abstract

Simultaneous measurements of main arterial roads inside the urban perimeter of Kurukshetra City (Haryana, India) regarding noise levels, traffic flow, and vehicle composition were taken and then used to develop some Traffic Noise Models (TNMs) to predict equivalent noise levels ( $L_{e q}$ ) from traffic flow per hour. The performance of the developed mathematical model was compared with four widely used TNMs. The potential of machine-learning techniques (M5 model tree, random forest and support vector machines) was also explored and their performance was compared with the developed mathematical TNM. Finally, the versatility of the developed mathematical model was examined for predicting the standard noise descriptors ( $L_{D}$ , $L_{N}$ and $L_{D N}$ ). The model required tuning for enhanced performance in predicting $L_{D N}$ , which was achieved by introducing a model coefficient ( $P_{n}$ = 1.05) to compensate for the night-time penalty. The study exhibited the potential application of machine-learning techniques in developing TNMs. However, the developed mathematical TNM allows a simple representation of a mathematical formula for the determination of $L_{e q}$ for any time-duration from the corresponding traffic flow per hour.

Keywords

Noise level traffic flow traffic noise model M5 model tree random forest support vector machines

Introduction

Excessive noise can be annoying and increase the risk of various health problems, such as ischemic heart disease (IHD), hypertension, sleep disturbance, headache, vertigo, bowel disturbances, hearing impairment, speech impediments, tinnitus, cognitive impairment, mental health problems, and adverse birth outcomes.^1–3 Increasing road traffic in urban areas globally has become a serious noise pollution issue affecting the health and quality of life of urban residents.^4–6 According to an estimate, about one million healthy years of life are being lost annually to ill health, disability or early death in Western European countries due to traffic noise.⁷ This necessitates periodic evaluation and 24-h monitoring of urban traffic noise. However, the measurement surveys are time and cost-intensive, and can only be performed on existing roads. In such a scenario, the development of a Traffic Noise Model (TNM) for the prediction of noise levels for urban areas has become necessary for the traffic management on the existing arterial road network of the city as well as in the designing of new road infrastructure so that the wellbeing of the residents be maintained. A well-developed model not only minimizes the measurement surveys but it can also be used in varying traffic conditions by just tuning or calibrating the model.⁸ Several TNMs have been developed and reported from all over the world representing and accounting for the peculiarities of the area, such as traffic volume, vehicle typologies, carriageway width, features of urban roads, queue length, the distance between the carriage and receivers, human behaviour, traffic regulations, honking, weather features, etc.⁹ However, all the TNMs have usually taken into account traffic flow, with or without vehicle typologies, for predicting noise levels in terms of equivalent noise levels ( $L_{e q}$ ) specific to the case study and the simplest functional form is logarithmically based as represented by the following mathematical formula:¹⁰

L_{e q} (f) = C_{1} \cdot \log_{10} f \pm C_{2}

(1)

where

C_{1}

and

C_{2}

are the constants or coefficients of the model to be evaluated making an analysis of experimental data and

\log_{10} f

is the functional transformation that plays the major role in calculation wherein

f

is the homogenized traffic flow (vehicles per hour). Then there are models that include the distance of the receiver from the carriage/source (or road width) within the formula, and/or other parameters such as heavy vehicles’ percentage in the total vehicles per hour to extend the application of the model to other contexts or uses.^8,11–15 Recently, some researchers have also proposed machine learning techniques (such as artificial neural networks, multiple linear regression and genetic algorithms) for the development of TNMs^9,16–20 and compared their results with analytical methods.

India is a fast urbanizing country, with the third largest road network globally, had 326.3 million vehicles on its roads in 2022, increasing by over 7% annually.^21,22 As a consequence, traffic noise has significantly increased in Indian cities in the past decade. An increase of 5-6 db(A) from 2012 to 2019 has been reported in Nagpur City (India).²⁰ This motivates the authors to develop TNMs in the context of a mid-sized developing city in India and also to employ advanced machine-learning models for the development of TNMs. Thus, the objectives of this study are: (i) to develop a mathematical TNM and investigate its adequacy to predict equivalent noise levels due to urban traffic flow through, taking as a case study of four urban arterial roads of a medium-sized city in India, (ii) to compare the developed mathematical model to four other well-known and widely used TNMs to verify its applicability to the Indian conditions, (iii) to use three machine-learning based TNMs (namely M5 model tree, random forest and support vector machines), and (iv) to explore the versatility of developed mathematical TNM in predicting standard noise descriptors used in national and international standards. The novelty of the present study is that the traffic flow with simultaneous traffic noise data used in the development and validation of TNMs represents the whole day (24 hours), and the vehicle typology/class has been as per the Indian Road Congress (IRC) guidelines.²³

Materials and methods

Kurukshetra – a mid-sized city spread over an area of about 48 km² with an estimated population of about 0.113 million has been selected for the present work. The data set of a recently conducted traffic assessment study of four arterial roads of Kurukshetra City from August 2023 to January 2024²⁴ has been used in this work. The contents related to the study area, materials and computations summarized below.

Study area

Kurukshetra is a historical and holy city in the state of Haryana (India) located in the Indo-Gangetic plains with a flat terrain at an elevation of around 250 m above mean sea level. Its climate falls under the ‘Cwa’ category as per the Koppen-Geiger classification.²⁵ The city is well connected to other parts of the state and country through railway and roadway networks. National Highway-44 (NH44) passes along the eastern periphery of the city, and State Highway-6 (SH6) passes right through the heart of the city and crosses the NH44 at the eastern side of the city. Due to SH6, vehicular traffic through the city is very high due to inter-city and inter-state road traffic augmenting the city traffic. The city has experienced substantial population, economic and infrastructural growth in the last few years, which is adversely impacting the vehicular traffic emissions leading to increased traffic flow, traffic congestion, and non-uniform and heterogeneous traffic flow patterns. The vehicle typology includes bicycles, cycle-rickshaws, E-rickshaws, motorized 2-wheelers, motorized 3-wheelers (auto-rickshaws), cars, vans, jeeps, buses, trucks, tractor-trailers, horse-driven carts (tonga), etc. Monitoring locations with varying traffic flow properties are selected for the data collection on the four arterial roads of the City, namely State Highway-6 (SH6), Railway Road (RR), KDB Road (KDB) and Brahmsarovar-NIT Road (BN) having nine, three, five and two monitoring locations respectively as shown in Figure 1. All the arterial roads have flexible pavement with smooth texture at all the monitored locations, and are 4-lanes 2-way divided roads having road width or distance of observation point to center of the road/carriageway ( $L$ ) as 15 $m$ , except a small stretch ( $L$ = 7.0 $m$ ) on which monitoring location B2 is located.

Figure 1.

Layout of studied arterial roads of Kurukshetra City depicting monitored locations.

Data collection and organization

A Class-1 Casella CEL-620B1 sound level meter (SLM), with a range of 0 to 140.2 dB(A), was used to measure sound levels using “A” frequency weighting and “Fast” time mode. To ensure accuracy, the SLM was calibrated at 94 dB(A) before and after each day’s work, using a Casella CEL-120/1 Class-1 acoustic calibrator, as per the instrument’s handbook. Traffic flow data, volume and composition, were measured simultaneously using a Handycam. The vehicle counts and composition were done manually based on Indian Roads Congress (IRC) guidelines provided in IRC:106-1990,²³ as reproduced in Table 1. At each monitoring site, well-spread and representative three sets of measurements were taken during morning hours (06 am to 12 noon), three sets during afternoon hours (12 noon to 06 pm), two sets during evening hours (06 pm to 10 pm) and four sets during night hours (10 pm to 06 am). Each set of measurements (traffic noise as well as traffic flow) was carried out continuously for ten minutes. All the measured noise and vehicle data are then extracted from SLM and Handycam respectively and represented on an hourly basis. Thus, accounting for twelve observations of equivalent noise levels (

L_{e q}

) with corresponding traffic flow per hour (

Q

) at each of the monitored locations. Therefore, a total of 228 (19 × 12) data samples are used for analysis and development of TNMs for the mid-sized cities in this study. For details of the procedure and protocol followed during the measurements, refer to the study conducted by Bhardawaj and Deswal.²⁴

Table 1.

Classification of vehicles on urban roads, as per IRC:106-1900.

Class	Vehicle type
$A$	Two-wheeler motor cycle or scooter, etc
$B$	Passenger car, pickup van
$C$	Light commercial vehicle (SUVs) auto-rickshaw
$D$	Heavy commercial vehicles (truck or bus)
Other ( $O$ )	Slow vehicles (cycle rickshaw, Tonga, etc.)

Selection of input variables

For model development, the data set is divided randomly to include around 70% for training (i.e. 168 samples) whereas the rest (i.e. 60) is for testing the developed models. The test data comprised of monitored noise levels ( $L_{e q}$ ) and corresponding traffic flow per hour ( $Q$ ) for the five sites, namely S3 and S7 on SH6, R2 on RR, K2 on KDB, and B1 on MN roads accounting for 60 numbers of observations. The data of the remaining sites is used as a training data set for model formulation.

Three machine-learning algorithms namely M5 model tree, random forest (RF) and support vector machines (SVM) were used to predict the noise levels. In the case of machine-learning models, optimal values of user-defined parameters are obtained by trial and error method. The performance of the model is evaluated for each iteration based on statistical parameters, namely correlation coefficient ( $r$ ), mean absolute error ( $e$ ) and root mean square error ( $r m s e$ ). The iteration process is repeated until the best statistical output (higher $r$ value with corresponding lower $e$ and $r m s e$ values) is identified.

Results and discussion

This section primarily focuses on – variation of equivalent noise levels ( $L_{e q}$ ) with corresponding traffic flow or total number of vehicles per hour ( $Q$ ); development and testing of mathematical TNM for predicting $L_{e q}$ from $Q$ ; comparison with well-known and widely used TNMs, namely Calixto et al. model,²⁶ Fagotti-Poggi model,²⁷ Josse model¹² and Burgess model¹¹; results of machine-learning based TNMs of all three techniques; and analysis of the limitations and versatility of mathematical TNM’s in estimating other standard noise indices are discussed.

Variation of noise levels with traffic flow

The measured $L_{e q}$ and the corresponding hourly $Q$ values for all the monitored sites on the four arterial roads are presented in Figure 2. The morning, afternoon, evening and night hours are represented by observation numbers 1–57, 58–114, 115–152, and 153–228 respectively. The plot revealed that noise levels are directly dependent on traffic flow irrespective of the duration (morning, afternoon, evening and night) of the day. Therefore, a relationship/model can be attempted to predict the $L_{e q,}$ from the corresponding $Q$ values.

Figure 2.

Equivalent noise levels ( $L_{e q}$ ) and the corresponding traffic flow ( $Q$ ) on hourly basis at monitored sites.

Development mathematical TNM

Hourly $L_{e q}$ and $Q$ values of the training data set are plotted using Microsoft excel, and various inbuilt trend line options are tried. The best fit curve or relationship with highest coefficient of determination ( $R^{2}$ = 0.8761) is obtained with logarithmic relationship as shown in Figure 3 and the developed mathematical TNM (2) is represented by equation (2).

L_{e q} = 35.37 \cdot \log_{10} Q - 45.24

(2)

Figure 3.

Graphical representation of developed mathematical TNM (2) using training data set.

The TNM (2) is then tested on the test data set and measured $L_{e q}$ are plotted against the predicted $L_{e q}$ values as reported in Figure 4. The plot shows majority of the predicted values lies within ±20 %. The statistical analysis of the TNM (2) resulted in excellent statistical output in terms of correlation coefficient ( $r$ = 0.929), average absolute error ( $e$ = −0.081) and root mean square error ( $r m s e$ = 5.571). Thus, the equation (2) is in line with the general logarithmic formula/model (1), and can be used for noise level prediction for mid-sized cities like Kurukshetra.

Figure 4.

Testing of developed mathematical TNM (2) on test data set.

Comparison with other models

The reported mathematical TNMs have also adopted $L_{e q}$ as the variable that depends on the corresponding traffic flow ( $Q$ ) and other road parameters. In the present study, the four already reported TNMs (equations (3)–(6)) have been tested upon the urban traffic on the arterial roads of the study area using the same test data set as used in the development of TNM (2).

Calixto et al. model²⁶:

L_{e q} = 10 \cdot {Log}_{10} [Q \cdot (1 + 10 \cdot \frac{P}{100})]

(3)

Burgess model¹¹:

L_{e q} = 55.5 + 10.2 \cdot {Log}_{10} (Q) + 0.3 \cdot P - 19.3 \cdot Log (L / 2)

(4)

Josse model¹²:

L_{e q} = 38.8 + 15 \cdot {Log}_{10} (Q) - 10 \cdot {Log}_{10} (L)

(5)

Fagotti-Poggi model²⁷:

L_{e q} = 10 \cdot {Log}_{10} (N_{c} + N_{m} + {8 \cdot N}_{h v} + 88 {\cdot N}_{b}) + 33.5

(6)

where

L_{e q}

is in dB(A);

Q

is traffic flow or total number of vehicles per hour;

P

is the percentage of heavy vehicles;

L

is the road width or distance of observation point to center of the road/carriageway (in

m

);

N_{c}

N_{m}

N_{h v}

and

N_{b}

are number of light vehicles, motorcycles, heavy vehicles and buses per hour respectively;

H V

L V

and

M C

are heavy vehicles (bus, truck, etc.), light vehicles (car, van, etc.) and motorcycles (bike, moped, etc.) per hour respectively. In the context of vehicle typology/classification for urban roads, IRC²³ classification (Table 1) is used –

P

is considered equivalent to percentage of

D

class vehicles (

P_{D}

) in Calixto et al. (3) and Burgess (4) TNMs. In case of Fagotti-Poggi TNM (6),

N_{c}

N_{m}

N_{h v}

and

N_{b}

are considered/mapped in different ways to IRC’s vehicle classification to arrive at the best equivalent of vehicle class as per IRC guidelines. The analysis revealed that the accuracy of the model does change with the way in which the

N_{c}

N_{m}

N_{h v}

and

N_{b}

are considered/mapped with IRC’s vehicle classification. The best results are obtained (in terms of statistical parameters) when

N_{c}

N_{m}

N_{h v}

and

N_{b}

are considered/mapped to

B

A

C

and

D

class vehicles respectively followed by B, A, D and C consideration/mapping in Fagotti-Poggi TNM (6). The Fagotti-Poggi TNM (6) was also tested by considering the Others

(O

) class vehicles in various combinations, and found to be best performing by not-considering

O

class vehicles, hence

N_{c}

N_{m}

N_{h v}

and

N_{b}

are considered/mapped to

B

A

C

and

D

class vehicles respectively, and

O

class vehicles are not adopted in this study.

The statistical analysis of the above four TNMs on the test data is presented in Table 2. It is observed that all the four TNMs predicted the

L_{e q}

with high correlation (

r

= 0.800 to 0.929) but with higher errors (

e

and

r m s e

). The statistical analysis revealed that

L_{e q}

values predicted by Calixto et al. model (3) are substantially on lower side (

e

= +31.125); whereas, on higher side by all other models (

e

varying from −8.590 to −16.189). For further analysis and comparison – the observed and predicted

L_{e q}

values obtained by different TNMs are plotted to interpret the scattering (Figure 5(a)), and predicted

L_{e q}

verses

Q

values are plotted to compare the trend of the models (Figure 5(b)). It can be observed from Figure 5(a) that there is scattering of above +20% for only at lower observed noise levels ranging between 32 and 57 dB(A) but within ±20% at higher observed noise levels in case of Burges (4), Josse (5) and Fagotti-Poggi (6) TNMs. However, scattering is above −20% in case of Calixto et al. (3) model and is increasing with increase in observed

L_{e q}

values. The explanation and possible reasons can be inferenced from the models’ trend as shown in Figure 5(b). The trends of all the models is similar to that of the developed TNM (2). The TNM (2) provided plausible results in all traffic flow (

Q

) ranges; whereas, the other TNMs either over-estimated or under-estimated the noise levels for the present case study data in lower traffic flow (

Q

) regions. This may be attributed to the peculiarities of the study area, such as vehicle types and categorization, non-uniform and heterogeneous traffic flow patterns, traffic congestion, queue length, traffic regulations, human behaviour, honking, weather features, etc. that governs the constants or coefficients of the model, that is

C_{1}

and

C_{2}

in equation (1), that needs to be evaluated from the analysis of experimental data of the study area.

Table 2.

Results of statistical analysis with various TNMs on test data set.

Traffic noise model (TNM)	Statistical parameters
Traffic noise model (TNM)	Correlation coefficient (r)	Mean absolute error (e)	Root mean square error (rmse)
Calixto et al.(3)	0.892	31.125	32.917
Burgess (4)	0.875	−16.189	19.841
Josse (5)	0.929	−9.228	13.588
Faggotti-Poggi (6)	0.800	−8.590	14.390
Present study: TNM (2)	0.929	−0.081	5.571

Figure 5.

Scatter and trend plots of mathematical TNMs on test data set.

Machine-learning based TNMs

Machine-learning techniques are usually used where the dependent (output) attribute depends on multiple independent attributes (input), and also requires less time and effort in developing models. Three machine-learning techniques are used in the present study. The M5 model tree is used as it provides model equations (equations (7)–(10)) that represent the mathematical relationship between the parameters; whereas; RF and SVM are attempted as these approaches have not been employed for developing TNMs to the best of the author’s knowledge. For all three techniques, the output attribute is

L_{e q}

and the five input attributes are numbers of class

A

B

C

D

and

O

vehicles per hour, that is

Q_{A}

Q_{B}

Q_{C}

Q_{D}

and

Q_{O}

respectively as per IRC guidelines.²³ In the case of SVM, RBF kernel has been used. The optimal values of user-defined parameters for machine-learning techniques are presented in Table 3, and the statistical results are tabulated in Table 4. As computation cost of machine-learning models are an important issue while using them for any modelling study, this study suggests that all three machine-learning used have a very small computational time (M5: 0.16 sec, RF: 0.05 sec and SVM: 0.04 sec).

Table 3.

User-defined parameters for soft computing techniques.

Approach	User-defined parameters
Random forest (RF)	Number of input feature used to generate tree = 2; number of trees = 100
Support vector machines (SVM)	RBF kernel; C = 2.0; gamma = 3.5

Table 4.

Results of statistical analysis of machine-learning based TNMs on test data set.

Traffic noise model (TNM)	Statistical parameters
Traffic noise model (TNM)	Correlation coefficient (r)	Mean absolute error (e)	Root mean square error (rmse)
M5 model tree (7 to 10)	0.962	3.091	4.331
RF	0.970	2.463	3.706
SVM	0.958	2.919	4.277
Present study: TNM (2)	0.929	−0.081	5.571

All the three machine-learning TNMs have performed well on the test data set with comparable statistical results in comparison with mathematical TNM (2). The scatter plot (Figure 6) shows majority of predicted values within ±20% for all the three machine-learning models. Thus, exhibiting the potential application of all the three machine-learning techniques in the development of TNMs.

Figure 6.

Scatter plot of machine-learning based TNMs on test data set.

The M5 model tree provides a set of four linear models – LM1, LM2, LM3 and LM4 as under:

LM1: When $Q_{A} \leq 531 & Q_{B} \leq 138$

L_{e q} = 0.039 \cdot Q_{A} + 0.0107 \cdot Q_{B} + 0.0646 \cdot Q_{C} + 0.0377 \cdot Q_{D} + 0.0307 \cdot Q_{O} + 29.2601

(7)

LM2: When $Q_{A} \leq 531, Q_{B} > 138 & Q_{D} \leq 96$

L_{e q} = 0.017 \cdot Q_{A} - 0.0164 \cdot Q_{B} + 0.0216 \cdot Q_{C} + 0.0278 \cdot Q_{D} + 0.0307 \cdot Q_{O} + 51.1445

(8)

LM3: When $Q_{A} \leq 531$ , $Q_{B} > 138$ & $Q_{D} > 96$

L_{e q} = 0.017 \cdot Q_{A} + 0.0138 \cdot Q_{B} + 0.0216 \cdot Q_{C} + 0.0304 \cdot Q_{D} + 0.0307 \cdot Q_{O} + 45.9026

(9)

LM4: When $Q_{A} > 531$

L_{e q} = 0.0034 \cdot Q_{A} + 0.0038 \cdot Q_{B} + 0.0082 \cdot Q_{C} + 0.007 \cdot Q_{D} + 0.0291 \cdot Q_{O} + 62.9064

(10)

A closer look at the four multilinear relationships generated by M5 model tree (equations (7)–(10)) reveals that $Q_{A}$ followed by $Q_{B}$ have the highest relative importance among the five input attributes. The RF model provided the relative attribute importance in descending order as $Q_{A}$ , $Q_{B}$ , $Q_{C}$ , $Q_{D}$ and $Q_{O}$ . This is in accordance with the percentage of vehicles in the traffic flow ( $P_{A}$ = 56.68%, $P_{B}$ = 24.33%, $P_{C}$ = 10.66%, $P_{D}$ = 7.09% and $P_{O}$ = 1.24%) in the test data set for the studied urban arterial roads of study area. However, it is not in agreement with Calixto et al. (3), Fagotti-Poggi (4), Josse (5) and Burgess (3) mathematical TNMs in which maximum weightage is provided to $Q_{D}$ attribute possibly due to low percentage of motorized 2-wheelers (class A vehicles) in their respective study areas.

Versatility of mathematical TNM in predicting standard noise descriptors

The national and international standards in respect of noise are expressed in terms of the standard noise descriptors. The Indian noise standards are with respect to

L_{D}

and

L_{N}

which are defined as

L_{e q}

values for Day-time (06 am to 10 pm) and Night-time (10 pm to 06 am) respectively.^28–30 The

L_{e q}

values Day-Night during 24-h day (

L_{D N}

) can be computed by considering a 10 dB(A) night-time penalty to account for the increased sensitivity to noise during night-time. In this section, the applicability of the developed mathematical TNM (2) is attempted for predicting

L_{D}

L_{N}

and

L_{D N}

. For this,

L_{D}

L_{N}

and

L_{D N}

values are computed from the measured hourly

L_{e q}

values for all the monitored locations. The traffic flow per hour (

Q

) is also computed for Day-time, Night-time and Day-Night (24-h) for all the locations in the study area. The TNM (2) predicted

L_{D}

L_{N}

and

L_{D N}

with good statistical results (Table 5) and most of the points lies within 10% (Figure 7). For compensating night-time penalty impact in

L_{D N}

, calibration/tuning of the mathematical TNM (2) is attempted for enhanced performance without altering the functional transformation (

\log_{10} Q

) in the model. A constant (

P_{n}

= 1.05) is found to compensate the night-time penalty and improves the performance of TNM (2), as displayed at S.No. 4 in Table 5 and Figure 7. Thus, the calibrated TNM (2) can be represented by TNM (11) having mathematical expression as:

L_{e q, t} = (35.37 \times P_{n}) \cdot \log_{10} Q_{t} - 45.24

(11)

where ‘

t

’ represents the time-duration for which

L_{e q}

is to be estimated from the corresponding traffic flow per hour (

Q)

. It is noted that

P_{n}

is to be considered as 1.05 for estimating

L_{D N}

levels only; whereas, it will be having a value of one for estimating

L_{e q}

values for other time-durations. Thus, the developed mathematical TNM (11) permits a simple representation of a mathematical formula for the estimation of

L_{e q}

for any time-duration from the corresponding traffic flow per hour.

Table 5.

Result of statistical analysis of developed mathematical TNM in predicting $L_{D}$ , $L_{N}$ and $L_{D N}$ .

S. No.	Standard noise descriptor	TNM	Model constant $P_{n}$	Statistical parameters
S. No.	Standard noise descriptor	TNM	Model constant $P_{n}$	$r$	$e$	$r m s e$
1	$L_{D}$	(2)	1.00	0.970	1.356	3.711
2	$L_{N}$	(2)	1.00	0.898	4.948	6.735
3	$L_{D N}$	(2)	1.00	0.953	5.356	6.132
4	$L_{D N}$	(11)	1.05	0.953	−0.418	3.327

Figure 7.

Computed verses predicted noise descriptors.

Conclusion

Noise pollution is a significant external impact of the urban road transport system. In the majority of TNMs, equivalent noise levels are presumed to be contingent on the logarithm of traffic flows. However, evaluating the model’s constants or coefficients for the specific context is imperative to substantiate this hypothesis.

The developed mathematical TNM (11) can be effectively used to predict the equivalent noise levels for any time-durations, including the standard noise descriptors ( $L_{D}$ , $L_{N}$ and $L_{D N}$ ) for urban arterial roads of medium-sized Indian city. Thus, exhibiting the robustness of the TNM. The present study also demonstrated the potential application of machine-learning based TNMs. However, the conventional mathematical TNMs based on the logarithm of traffic flows not only provide a simple mathematical expression but are observed to be more precise than machine-learning based TNMs.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Surinder Deswal

Prateek Bhardwaj

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