Mathematical Modelling in Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 19174

Special Issue Editors

Dana-Farber Cancer Institute, Harvard University, Boston, MA 02138, USA
Interests: biotechnology
School of Computer Science and Technology, Xidian University, Xi’an 710071, China
Interests: bioinformatics; machine learning; computational biology; system biology
School of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China
Interests: machine learning; computation mathematics; bioinformatics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

For understanding complex bio-systems, it is required to determine and characterize the biomolecules individually along with identifying the interaction between those biomolecules and respective pathways/Gene-Ontologies. Recent trends include so-called “complex diseases” such as COVID-19, cancer, Parkinson’s disease, Alzheimer’s disease, etc. those need to be detected in earlier stage.

With the recent advancement on various emerging techniques, the main aim of the current biomedical research has shifted toward interpreting the big data generated by single/multi-omics technologies. Various mathematical, statistical and other machine learning-based computational models allow the researchers to investigate how the complex regulatory processes are linked and how their disruptions might lead to the development of those diseases. Those models might cover the number theory, probability and biostatistics, integral and differential systems, optimization, algebra, geometry, game theory, topology, graph theory, machine learning, automata, soft computing, etc.

Various biological problems that associated with the models, fall under following categories: cell organization, genomic organization and gene expression (next generation sequence data), epigenetics (DNA methylation), immune system and disease diagnosis, neurobiology and behavioral science, plant biology and agriculture, industrial biotechnology, radiology (viz., MRI and biomedical imaging), tomography and models of physiological systems, systems biology, etc. Specially, some of the computational challenges might include gene signature discovery, regression model finding, classification model, clustering, network centrality finding, correlation study, feature selection or extraction, network motif discovery, statistical hypothesis test (differential expression analysis), but not limited to that.    

So far, many interesting ongoing research have been conducted on “Mathematical Modelling in Biology”, but still there exit many diversities and numerous challenges. Hence, new mathematical and other computational models are welcome and greatly appreciable that are beneficial for human in many ways being specially in disease diagnosis and therapeutic value.

The purpose of this Topical Collection is to choose and publish review articles, original research articles as well as other perspective article representing novel theory, algorithms and applications of computation modeling applied to various fields of biology especially biomedical areas.

Dr. Saurav Mallik
Dr. Yashika Rustagi
Dr. Guimin Qin
Dr. Aimin Li
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical
  • biostatistical and machine learning models
  • complex biological systems
  • multi-omics data
  • cancer biology

Published Papers (10 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

16 pages, 1564 KiB  
Article
Is Drug Delivery System a Deterministic or Probabilistic Approach? A Theoretical Model Based on the Sequence: Electrodynamics–Diffusion–Bayes
by Huber Nieto-Chaupis
Mathematics 2023, 11(21), 4528; https://doi.org/10.3390/math11214528 - 03 Nov 2023
Viewed by 516
Abstract
Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the [...] Read more.
Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the uptake of nanoparticles by tumors. Once they are injected into the bloodstream, it is unclear as to which process governs the directing of nanoparticles towards the desired target, deterministic or stochastic. In any scenario, an optimal outcome, small toxicity and minimal dispersion of drugs is expected. Commonly, it is expected that an important fraction of them can be internalized into tumor. In this manner, due to the fraction of nanoparticles that have failed to uptake, the success of the drug delivery scheme might be at risk. In this paper, a theory based on the sequence electrodynamics–diffusion–Bayes theorem is presented. The Bayesian probability that emerges at the end of the sequence might be telling us that dynamical processes based on the injection of electrically charged nanoparticles might be dictated by stochastic formalism. Thus, rather than expecting a deterministic process, the chain of events would convert the drug delivery scheme to be dependent on a sequence of conditional probabilities. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Graphical abstract

19 pages, 26793 KiB  
Article
Predicting the Future Appearances of Lost Children for Information Forensics with Adaptive Discriminator-Based FLM GAN
by Brijit Bhattacharjee, Bikash Debnath, Jadav Chandra Das, Subhashis Kar, Nandan Banerjee, Saurav Mallik and Debashis De
Mathematics 2023, 11(6), 1345; https://doi.org/10.3390/math11061345 - 10 Mar 2023
Cited by 2 | Viewed by 1888
Abstract
This article proposes an adaptive discriminator-based GAN (generative adversarial network) model architecture with different scaling and augmentation policies to investigate and identify the cases of lost children even after several years (as human facial morphology changes after specific years). Uniform probability distribution with [...] Read more.
This article proposes an adaptive discriminator-based GAN (generative adversarial network) model architecture with different scaling and augmentation policies to investigate and identify the cases of lost children even after several years (as human facial morphology changes after specific years). Uniform probability distribution with combined random and auto augmentation techniques to generate the future appearance of lost children’s faces are analyzed. X-flip and rotation are applied periodically during the pixel blitting to improve pixel-level accuracy. With an anisotropic scaling, the images were generated by the generator. Bilinear interpolation was carried out during up-sampling by setting the padding reflection during geometric transformation. The four nearest data points used to estimate such interpolation at a new point during Bilinear interpolation. The color transformation applied with the Luma flip on the rotation matrices spread log-normally for saturation. The luma-flip components use brightness and color information of each pixel as chrominance. The various scaling and modifications, combined with the StyleGan ADA architecture, were implemented using NVIDIA V100 GPU. The FLM method yields a BRISQUE score of between 10 and 30. The article uses MSE, RMSE, PSNR, and SSMIM parameters to compare with the state-of-the-art models. Using the Universal Quality Index (UQI), FLM model-generated output maintains a high quality. The proposed model obtains ERGAS (12 k–23 k), SCC (0.001–0.005), RASE (1 k–4 k), SAM (0.2–0.5), and VIFP (0.02–0.09) overall scores. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

22 pages, 1600 KiB  
Article
A Game-Theoretic Approach for Rendering Immersive Experiences in the Metaverse
by Anjan Bandyopadhyay, Ansh Sarkar, Sujata Swain, Debajyoty Banik, Aboul Ella Hassanien, Saurav Mallik, Aimin Li and Hong Qin
Mathematics 2023, 11(6), 1286; https://doi.org/10.3390/math11061286 - 07 Mar 2023
Cited by 5 | Viewed by 1819
Abstract
The metaverse is an upcoming computing paradigm aiming towards blending reality seamlessly with the artificially generated 3D worlds of deep cyberspace. This giant interactive mesh of three-dimensional reconstructed realms has recently received tremendous attention from both an academic and commercial point of view [...] Read more.
The metaverse is an upcoming computing paradigm aiming towards blending reality seamlessly with the artificially generated 3D worlds of deep cyberspace. This giant interactive mesh of three-dimensional reconstructed realms has recently received tremendous attention from both an academic and commercial point of view owing to the curiosity instilled by its vast possible use cases. Every virtual world in the metaverse is controlled and maintained by a virtual service provider (VSP). Interconnected clusters of LiDAR sensors act as a feeder network to these VSPs which then process the data and reconstruct the best quality immersive environment possible. These data can then be leveraged to provide users with highly targeted virtual services by building upon the concept of digital twins (DTs) representing digital analogs of real-world items owned by parties that create and establish the communication channels connecting the DTs to their real-world counterparts. Logically, DTs represent data on servers where postprocessing can be shared easily across VSPs, giving rise to new marketplaces and economic frontiers. This paper presents a dynamic and distributed framework to enable high-quality reconstructions based on incoming data streams from sensors as well as to allow for the optimal allocation of VSPs to users. The optimal synchronization intensity control problem between the available VSPs and the feeder network is modeled using a simultaneous differential game, while the allocation of VSPs to users is modeled using a preference-based game-theoretic approach, where the users give strict preferences over the available VSPs. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

17 pages, 2670 KiB  
Article
Hybrid Whale and Gray Wolf Deep Learning Optimization Algorithm for Prediction of Alzheimer’s Disease
by Chitradevi Dhakhinamoorthy, Sathish Kumar Mani, Sandeep Kumar Mathivanan, Senthilkumar Mohan, Prabhu Jayagopal, Saurav Mallik and Hong Qin
Mathematics 2023, 11(5), 1136; https://doi.org/10.3390/math11051136 - 24 Feb 2023
Cited by 5 | Viewed by 2362
Abstract
In recent years, finding the optimal solution for image segmentation has become more important in many applications. The whale optimization algorithm (WOA) is a metaheuristic optimization technique that has the advantage of achieving the global optimal solution while also being simple to implement [...] Read more.
In recent years, finding the optimal solution for image segmentation has become more important in many applications. The whale optimization algorithm (WOA) is a metaheuristic optimization technique that has the advantage of achieving the global optimal solution while also being simple to implement and solving many real-time problems. If the complexity of the problem increases, the WOA may stick to local optima rather than global optima. This could be an issue in obtaining a better optimal solution. For this reason, this paper recommends a hybrid algorithm that is based on a mixture of the WOA and gray wolf optimization (GWO) for segmenting the brain sub regions, such as the gray matter (GM), white matter (WM), ventricle, corpus callosum (CC), and hippocampus (HC). This hybrid mixture consists of two steps, i.e., the WOA and GWO. The proposed method helps in diagnosing Alzheimer’s disease (AD) by segmenting the brain sub regions (SRs) by using a hybrid of the WOA and GWO (H-WOA-GWO, which is represented as HWGO). The segmented region was validated with different measures, and it shows better accuracy results of 92%. Following segmentation, the deep learning classifier was utilized to categorize normal and AD images. The combination of WOA and GWO yields an accuracy of 90%. As a result, it was discovered that the suggested method is a highly successful technique for identifying the ideal solution, and it is paired with a deep learning algorithm for classification. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

20 pages, 6097 KiB  
Article
Segmentation and Analysis Emphasizing Neonatal MRI Brain Images Using Machine Learning Techniques
by Saritha Saladi, Yepuganti Karuna, Srinivas Koppu, Gudheti Ramachandra Reddy, Senthilkumar Mohan, Saurav Mallik and Hong Qin
Mathematics 2023, 11(2), 285; https://doi.org/10.3390/math11020285 - 05 Jan 2023
Cited by 13 | Viewed by 2082
Abstract
MRI scanning has shown significant growth in the detection of brain tumors in the recent decade among various methods such as MRA, X-ray, CT, PET, SPECT, etc. Brain tumor identification requires high exactness because a minor error can be life-threatening. Brain tumor disclosure [...] Read more.
MRI scanning has shown significant growth in the detection of brain tumors in the recent decade among various methods such as MRA, X-ray, CT, PET, SPECT, etc. Brain tumor identification requires high exactness because a minor error can be life-threatening. Brain tumor disclosure remains a challenging job in medical image processing. This paper targets to explicate a method that is more precise and accurate in brain tumor detection and focuses on tumors in neonatal brains. The infant brain varies from the adult brain in some aspects, and proper preprocessing technique proves to be fruitful to avoid miscues in results. This paper is divided into two parts: In the first half, preprocessing was accomplished using HE, CLAHE, and BPDFHE enhancement techniques. An analysis is the sequel to the above methods to check for the best method based on performance metrics, i.e., MSE, PSNR, RMSE, and AMBE. The second half deals with the segmentation process. We propose a novel ARKFCM to use for segmentation. Finally, the trends in the performance metrics (dice similarity and Jaccard similarity) as well as the segmentation results are discussed in comparison with the conventional FCM method. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

19 pages, 1544 KiB  
Article
HistoSSL: Self-Supervised Representation Learning for Classifying Histopathology Images
by Xu Jin, Teng Huang, Ke Wen, Mengxian Chi and Hong An
Mathematics 2023, 11(1), 110; https://doi.org/10.3390/math11010110 - 26 Dec 2022
Cited by 2 | Viewed by 2547
Abstract
The success of image classification depends on copious annotated images for training. Annotating histopathology images is costly and laborious. Although several successful self-supervised representation learning approaches have been introduced, they are still insufficient to consider the unique characteristics of histopathology images. In this [...] Read more.
The success of image classification depends on copious annotated images for training. Annotating histopathology images is costly and laborious. Although several successful self-supervised representation learning approaches have been introduced, they are still insufficient to consider the unique characteristics of histopathology images. In this work, we propose the novel histopathology-oriented self-supervised representation learning framework (HistoSSL) to efficiently extract representations from unlabeled histopathology images at three levels: global, cell, and stain. The model transfers remarkably to downstream tasks: colorectal tissue phenotyping on the NCTCRC dataset and breast cancer metastasis recognition on the CAMELYON16 dataset. HistoSSL achieved higher accuracies than state-of-the-art self-supervised learning approaches, which proved the robustness of the learned representations. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

15 pages, 4359 KiB  
Article
Early Detection of Parkinson’s Disease Using Fusion of Discrete Wavelet Transformation and Histograms of Oriented Gradients
by Himanish Shekhar Das, Akalpita Das, Anupal Neog, Saurav Mallik, Kangkana Bora and Zhongming Zhao
Mathematics 2022, 10(22), 4218; https://doi.org/10.3390/math10224218 - 11 Nov 2022
Cited by 5 | Viewed by 1334
Abstract
Parkinson’s disease primarily affects people in their later years, and there is no cure for this disease; however, the proper medication of patients can lead to a healthy life. Appropriate care and treatment of Parkinson’s disease can be improved if the disease is [...] Read more.
Parkinson’s disease primarily affects people in their later years, and there is no cure for this disease; however, the proper medication of patients can lead to a healthy life. Appropriate care and treatment of Parkinson’s disease can be improved if the disease is detected in its early phase. Thus, there is an urgent need to develop novel methods for early illness detection. With this aim for the early detection of Parkinson’s disease, in this study, we utilized hand-drawn images by Parkinson’s disease patients to effectively reduce the clinical experimental costs for poor people. Initially, discrete wavelet coefficients were extracted for each pattern of images; thereafter, on top of that, histograms of oriented gradient features were also extracted to refine the level of features. Thereafter, the fusion approach-based features were fed to various machine learning algorithms. The proposed work was validated on two different datasets, each of which consisted of various patterns, including spiral, wave, cube, and triangle images. The main contribution of this work is the fusion of two feature extraction techniques, which are histograms of oriented gradient features and discrete wavelet transform coefficients. The extracted features were then provided as input into different machine learning algorithms. In our experiment(s) on two datasets, the results achieved an accuracy of 79.7% and 97.8%, respectively, for all four discrete wavelet transform coefficients. This work demonstrates the utilities of fusion-based features for all four discrete wavelet transformation coefficients to detect Parkinson’s disease, using image processing and machine learning techniques. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

11 pages, 886 KiB  
Article
Machine Learning Based Approach for Automated Cervical Dysplasia Detection Using Multi-Resolution Transform Domain Features
by Kangkana Bora, Lipi B. Mahanta, Kasmika Borah, Genevieve Chyrmang, Barun Barua, Saurav Mallik, Himanish Shekhar Das and Zhongming Zhao
Mathematics 2022, 10(21), 4126; https://doi.org/10.3390/math10214126 - 04 Nov 2022
Cited by 4 | Viewed by 1177
Abstract
Pattern detection and classification of cervical cell dysplasia can assist with diagnosis and treatment. This study aims to develop a computational model for real-world applications for cervical dysplasia that has the highest degree of accuracy and the lowest computation time. Initially, an ML [...] Read more.
Pattern detection and classification of cervical cell dysplasia can assist with diagnosis and treatment. This study aims to develop a computational model for real-world applications for cervical dysplasia that has the highest degree of accuracy and the lowest computation time. Initially, an ML framework is created, which has been trained and evaluated to classify dysplasia. Three different color models, three multi-resolution transform-based techniques for feature extraction (each with different filters), two feature representation schemes, and two well-known classification approaches are developed in conjunction to determine the optimal combination of “transform (filter) ⇒ color model ⇒ feature representation ⇒ classifier”. Extensive evaluations of two datasets, one is indigenous (own generated database) and the other is publicly available, demonstrated that the Non-subsampled Contourlet Transform (NSCT) feature-based classification performs well, it reveals that the combination “NSCT (pyrexc,pkva), YCbCr, MLP” gives most satisfactory framework with a classification accuracy of 98.02% (average) using the F1 feature set. Compared to two other approaches, our proposed model yields the most satisfying results, with an accuracy in the range of 98.00–99.50%. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

20 pages, 780 KiB  
Article
Unsupervised Learning for Feature Representation Using Spatial Distribution of Amino Acids in Aldehyde Dehydrogenase (ALDH2) Protein Sequences
by Monika Khandelwal, Sabha Sheikh, Ranjeet Kumar Rout, Saiyed Umer, Saurav Mallik and Zhongming Zhao
Mathematics 2022, 10(13), 2228; https://doi.org/10.3390/math10132228 - 25 Jun 2022
Cited by 5 | Viewed by 1373
Abstract
Aldehyde dehydrogenase 2 (ALDH2) enzyme is required for alcohol detoxification. ALDH2 belongs to the aldehyde dehydrogenase family, the most important oxidative pathway of alcohol digestion. Two main liver isoforms of aldehyde dehydrogenase are cytosolic and mitochondrial. Approximately 50% of East Asians have ALDH2 [...] Read more.
Aldehyde dehydrogenase 2 (ALDH2) enzyme is required for alcohol detoxification. ALDH2 belongs to the aldehyde dehydrogenase family, the most important oxidative pathway of alcohol digestion. Two main liver isoforms of aldehyde dehydrogenase are cytosolic and mitochondrial. Approximately 50% of East Asians have ALDH2 deficiency (inactive mitochondrial isozyme), with lysine (K) for glutamate (E) substitution at position 487 (E487K). ALDH2 deficiency is also known as Alcohol Flushing Syndrome or Asian Glow. For people with an ALDH2 deficiency, their face turns red after drinking alcohol, and they are more susceptible to various diseases than ALDH2-normal people. This study performed a machine learning analysis of ALDH2 sequences of thirteen other species by comparing them with the human ALDH2 sequence. Based on the various quantitative metrics (physicochemical properties, secondary structure, Hurst exponent, Shannon entropy, and fractal dimension), these fourteen species were clustered into four clusters using the unsupervised machine learning (K-means clustering) algorithm. We also analyze these species using hierarchical clustering (agglomerative clustering) and draw the phylogenetic trees. The results show that Homo sapiens is more closely related to the Bos taurus and Sus scrofa species. Our experimental results suggest that the testing for discovering medicines may be done on these species before being tested in humans to alleviate the impacts of ALDH2 deficiency. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

11 pages, 3954 KiB  
Article
WAVECNV: A New Approach for Detecting Copy Number Variation by Wavelet Clustering
by Yang Guo, Shuzhen Wang, A. K. Alvi Haque and Xiguo Yuan
Mathematics 2022, 10(12), 2151; https://doi.org/10.3390/math10122151 - 20 Jun 2022
Cited by 1 | Viewed by 1501
Abstract
Copy number variation (CNV) detection based on second-generation sequencing technology is the basis of much gene research, but the read depth is affected by mapping errors, repeated reads, and GC bias. The existing methods have low sensitivity to variation regions with a short [...] Read more.
Copy number variation (CNV) detection based on second-generation sequencing technology is the basis of much gene research, but the read depth is affected by mapping errors, repeated reads, and GC bias. The existing methods have low sensitivity to variation regions with a short length and small variation range. Therefore, it is necessary to improve the sensitivity of algorithms to short-variation fragments. This study proposes a new CNV-detection method named WAVECNV to solve this issue. The algorithm uses wavelet clustering to process the read depth and determine the normal cluster and abnormal cluster according to the size of the cluster. Then, according to the distance between genome bins and normal clusters, the outlier of each genome bin is evaluated. Finally, a statistical model is established, and the p-value test is used for calling CNVs. Through this method, the information of the short variation region is retained. WAVECNV was tested and compared with peer methods in terms of simulated data and real cancer-sequencing data. The results show that the sensitivity of WAVECNV is better than the existing methods. It also has high precision in data with low purity and coverage. In real data experiments, WAVECNV can detect more cancer genes than existing methods. Therefore, this method can be regarded as a conventional method in the field of genomic mutation analysis of cancer samples. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
Show Figures

Figure 1

Back to TopTop