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Medical students tend to be reluctant to study calculus because they believe it will be unrelated to their jobs. However, the branch of mathematics offers much to other fields of science, including medicine. For instance, cardiology uses calculus for accurately identifying the condition, disease prevention, public reporting, and conducting studies, where one has to apply some of its methods. This paper will highlight those usages and demonstrate the importance of calculus for the specialty.
Electrocardiogram (ECG) is an essential means of identifying whether a person has a heart condition. The curves represent continuous functions, which belong to the field of calculus (Sengupta et al., 2018). However, the graphs can be unreliable, as certain non-differentiable points exist, potentially disguising a disease (for instance, Left Ventricular Hypertrophy) as the absence of pathology (Sengupta et al., 2018). As the incident can have devastating consequences for the patient, a more accurate method using fractional calculus has been developed (Sengupta et al., 2018). It is characterized by fractional derivative, which allows for differentiating between the norm and pathology when applied to ECG, and differs from the classical one (Sengupta et al., 2018). Thus, calculus is used to diagnose heart conditions and improve the process, and ideally, the specialist should be able to do more than interpreting the graphs.
In addition to ECG, calculus also helps identify and classify leukocytes before issuing a diagnosis. It is done through the use of fractional calculus, which helps remove noise during blood cell image processing, leading to more accurate results (Guangnan et al., 2018). However, the Snake of Gradient Vector Flow should be applied later to comb color information; otherwise, calculus alone cannot help classify leukocytes (Guangnan et al., 2018). Regardless, being an essential part of the process solidifies the role of calculus in identifying cardiovascular disease (CVD). Furthermore, even such advanced methods as artificial intelligence rely on the models studied in the field of calculus (Guangnan et al., 2018). In conclusion, calculus is indispensable in diagnosing CVD and subsequently prescribing the most effective treatment.
Another field of calculus application in cardiology is disease prevention. It is evident following the results of the CANTOS trial, which confirmed that inflammation leads to CVD, meaning that anti-inflammatory pharmacotherapy can be used to treat that group of conditions (Verma et al., 2017). To determine the secondary treatment of atherosclerosis, which will theoretically have a positive impact on the cardiovascular system, one should apply calculus because recurrent events and residual risk are multifactorial (Verma et al., 2017). Additional factors requiring consideration also exist, but with the right calculations, a new approach to manipulate immunity will be discovered to decrease the risk of CVD in certain demographic groups (Verma et al., 2017). Thus, calculus is beneficial for improving patient outcomes and potentially advancing the whole field of cardiology.
A major type of calculus application is public reporting, which is arguably as important as making discoveries to share. Its role is in identifying which metrics are the most appropriate to measure a hospital’s quality and report (Kirtane et al., 2016). Using such variables as a patient scenario and mortality and considering the latter’s importance, one can calculate the performance level, which is later reflected publicly (Kirtane et al., 2016). However, the method is flawed, despite calculus’s application still being necessary, and creates a false narrative (Kirtane et al., 2016). Thus, new approaches are being developed to make the information on healthcare quality accurate and reflective of the real state of affairs, which is impossible to achieve without mathematical analysis.
Another sphere where calculus is crucial is research in cardiology. What separates it from the previously discussed application is that calculus methods are used to perform operations with the obtained data, while other cases offer a practical implementation. For instance, one study used latent Dirichlet allocation, which involves select elements of calculus, for topic modeling in electronic health records of cardiology patients (Pérez et al., 2018). A close connection exists between calculus and statistics, especially as far as variables that can be depicted on a function are concerned. For instance, a study in assessing global cardiac risk used multivariable calculus, curves, and statistical analysis to process the data and obtain the results (Voors et al., 2017). The same is partially true for all the referenced sources in the paper, further confirming that the importance of calculus even when working with theoretical information.
In conclusion, the following applications of calculus in cardiology have been highlighted: CVD diagnosis, treatment of the said conditions, public reporting, and research methodology. Some of them are interlinked, as a study can focus on how to use calculus to enhance ECG in a practical manner while applying calculus methods to arrange the obtained data. Although some of the discussed points are valid for any science and or medical subfields, what makes calculus special for cardiology is its use in ECG and blood cell image processing (diagnostics) and disease prevention. Therefore, a specialist should have calculus knowledge to be competent and administer care properly while potentially making discoveries and improving the existing approaches.
References
Guangnan, Z., Weixing, W., Fangnian, L., Fengping, W., Wei, L., & Ting, G. (2018). White blood cell extraction on fractional calculus and Gradient Vector Flow Snake for leukocyte classification on Support Vector Machines.Journal of Medical Imaging and Health Informatics, 8(6), 1249-1257. Web.
Kirtane, A. J., Nallamothu, B. K., & Moses, J. W. (2016). The complicated calculus of publicly reporting mortality after percutaneous coronary intervention.JAMA Cardiology, 1(6), 637-638. Web.
Pérez, J., Pérez, A., Casillas, A., & Gojenola, K. (2018). Cardiology record multi-label classification using latent Dirichlet allocation.Computer Methods and Programs in Biomedicine, 164, 111–119. Web.
Sengupta, S., Ghosh, U., Sarkar, S., & Das, S. (2018). Application of fractional calculus to distinguish left ventricular hypertrophy with normal ECG. In S. Tripathi & A. K. Pal (Eds.), 2018 4th International Conference on Recent Advances in Information Technology (RAIT) (pp. 30-36). Web.
Verma, S., Leiter, L. A., & Bhatt, D. L. (2017). CANTOS ushers in a new calculus of inflammasome targeting for vascular protection—And maybe more.Cell Metabolism, 26(5), 703–705. Web.
Voors, A. A., Ouwerkerk, W., Zannad, F., van Veldhuisen, D. J., Samani, N. J., Ponikowski, P., Ng, L. L., Metra, M., ter Maaten, J. M., Lang, C. C., Hillege, H. L., van der Harst, P., Filippatos, G., Dickstein, K., Cleland, J. G., Anker, S. D., & Zwinderman, A. H. (2017). Development and validation of multivariable models to predict mortality and hospitalization in patients with heart failure.European Journal of Heart Failure, 19(5), 627–634. Web.
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