Analytical Solutions of the Fractional Mathematical Model for the Concentration of Tumor Cells for Constant Killing Rate

Two generalized mathematical models with memory for the concentration of tumor cells have been analytically studied using the cylindrical coordinate and the integral transform methods. The generalization consists of the formulating of two mathematical models with Caputo-time fractional derivative, models that are suitable to highlight the influence of the history of tumor evolution on the present behavior of the concentration of cancer cells. The time-oscillating concentration of cancer cells has been considered on the boundary of the domain. Analytical solutions of the fractional differential equations of the mathematical models have been determined using the Laplace transform with respect to the time variable and the finite Hankel transform with respect to the radial coordinate. The positive roots of the transcendental equation with Bessel function J0(r)=0, which are needed in our study, have been determined with the subroutine rn=root(J0(r),r,(2n−1)π/4,(2n+3)π/4),n=1,2,… of the Mathcad 15 software. It is found that the memory effects are stronger at small values of the time, t. This aspect is highlighted in the graphical illustrations that analyze the behavior of the concentration of tumor cells. Additionally, the concentration of cancer cells is symmetric with respect to radial angle, and its values tend to be zero for large values of the time, t.

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Weber-Type Integral Transform Connected with Robin-Type Boundary Conditions

Mathematics ◽

10.3390/math8081335 ◽

2020 ◽

Vol 8 (8) ◽

pp. 1335

Author(s):

Thanaa Elnaqeeb ◽

Nehad Ali Shah ◽

Dumitru Vieru

Keyword(s):

Boundary Conditions ◽

Integral Transform ◽

Transcendental Equation ◽

Micro Channels ◽

Type Integral ◽

Positive Roots ◽

Weber Type ◽

Type Boundary ◽

Mathcad Software ◽

Transport Problems

A new Weber-type integral transform and its inverse are defined for the representation of a function f(r,t), (r,t)∈[R,1]×[0,∞) that satisfies the Dirichlet and Robin-type boundary conditions f(R,t)=f1(t), f(1,t)−α∂f(r,t)∂r|r=1=f2(t), respectively. The orthogonality relations of the transform kernel are derived by using the properties of Bessel functions. The new Weber integral transform of some particular functions is determined. The integral transform defined in the present paper is a suitable tool for determining analytical solutions of transport problems with sliding phenomena that often occur in flows through micro channels, pipes or blood vessels. The heat conduction in an annular domain with Robin-type boundary conditions is studied. The subroutine “root(⋅)” of the Mathcad software is used to determine the positive roots of the transcendental equation involved in the definition of the new integral transform.

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Solutions to the fractional diffusion-wave equation in a wedge

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-014-0158-4 ◽

2014 ◽

Vol 17 (1) ◽

Cited By ~ 10

Author(s):

Yuriy Povstenko

Keyword(s):

Wave Equation ◽

Fourier Transforms ◽

Integral Transform ◽

Neumann Boundary ◽

Hankel Transform ◽

Fractional Diffusion ◽

Polar Coordinates ◽

Radial Coordinate ◽

Diffusion Wave ◽

Angular Coordinate

AbstractThe diffusion-wave equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in polar coordinates in a domain 0 ≤ r < ∞, 0 < φ < φ 0 under Dirichlet and Neumann boundary conditions. The Laplace integral transform with respect to time, the finite sin- and cos-Fourier transforms with respect to the angular coordinate, and the Hankel transform with respect to the radial coordinate are used. The numerical results are illustrated graphically.

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Role of exosomes in diagnosis and therapy of prostate cancer

I P Pavlov Russian Medical Biological Herald ◽

10.23888/pavlovj2020283399-405 ◽

2020 ◽

Vol 28 (3) ◽

pp. 399-405

Author(s):

Fabrizio Fontana ◽

Olga A. Babenko

Keyword(s):

Prostate Cancer ◽

Cancer Cells ◽

Tumor Cells ◽

Biological Fluids ◽

Diagnosis And Treatment ◽

Diagnosis And Therapy ◽

The Future ◽

Important Direction ◽

Potential Biomarkers

Aim of this letter is to attract the attention of journal readers to the study of exosomes as an important direction in the development of Oncology, in particular, in the diagnosis and treatment of prostate cancer. Exosomes are produced by tumor cells and regulate proliferation, metastasis, and the development of chemoresistance. Their extraction from biological fluids allows further use of these vesicles as potential biomarkers of prostate cancer. In the future, exosomes can be successfully used in the delivery of drugs and other anti-tumor substances to cancer cells.

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Recent Advances on Therapeutic Peptides for Breast Cancer Treatment

Current Protein and Peptide Science ◽

10.2174/1389203721999201117123616 ◽

2020 ◽

Vol 21 ◽

Author(s):

Samad Beheshtirouy ◽

Farhad Mirzaei ◽

Shirin Eyvazi ◽

Vahideh Tarhriz

Keyword(s):

Breast Cancer ◽

Cancer Cells ◽

Tumor Cells ◽

Breast Cancer Cells ◽

Specific Binding ◽

High Specificity ◽

The Novel ◽

Anti Cancer ◽

Therapeutic Peptides ◽

Low Toxicity

: Breast cancer is a heterogeneous malignancy which is the second cause of mortality among women in the world. Increasing the resistance to anti-cancer drugs in breast cancer cells persuades researchers to search the novel therapies approaches for the treatment of the malignancy. Among the novel methods, therapeutic peptides which target and disrupt tumor cells have been of great interest. Therapeutic peptides are short amino acids monomer chains with high specificity to bind and modulate a protein interaction of interest. Several advantages of peptides such as specific binding on tumor cells surface, low molecular weight and low toxicity on normal cells make the peptides as an appealing therapeutic agents against solid tumors, particularly breast cancer. Also, National Institutes of Health (NIH) describes therapeutic peptides as suitable candidate for the treatment of drug-resistant breast cancer. In this review, we attempt to review the different therapeutic peptides against breast cancer cells which can be used in treatment and diagnosis of the malignancy. Meanwhile, we presented an overview of peptide vaccines which have been developed for the treatment of breast cancer.

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Peptide-conjugated PEGylated PAMAM as a highly affinitive nanocarrier towards HER2-overexpressing cancer cells

RSC Advances ◽

10.1039/c6ra19552k ◽

2016 ◽

Vol 6 (109) ◽

pp. 107337-107343 ◽

Cited By ~ 10

Author(s):

Iman Rostami ◽

ZiJian Zhao ◽

ZiHua Wang ◽

WeiKai Zhang ◽

Yeteng Zhong ◽

...

Keyword(s):

Drug Delivery ◽

Cancer Cells ◽

Tumor Cells ◽

Targeting Peptide

Efficient drug delivery to the tumor cells was carried out with HER2 targeting peptide-conjugated PEGlyted PAMAM.

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The Blockade of Tumoral IL1β-Mediated Signaling in Normal Colonic Fibroblasts Sensitizes Tumor Cells to Chemotherapy and Prevents Inflammatory CAF Activation

International Journal of Molecular Sciences ◽

10.3390/ijms22094960 ◽

2021 ◽

Vol 22 (9) ◽

pp. 4960

Author(s):

Natalia Guillén Díaz-Maroto ◽

Gemma Garcia-Vicién ◽

Giovanna Polcaro ◽

María Bañuls ◽

Nerea Albert ◽

...

Keyword(s):

Cancer Cells ◽

Tumor Cells ◽

Cell Types ◽

Colorectal Tumor ◽

Cytotoxic Drugs ◽

Differential Sensitivity ◽

Paracrine Signaling ◽

Inflammatory Phenotype ◽

Heterotypic Interactions ◽

Carcinoma Associated Fibroblasts

Heterotypic interactions between newly transformed cells and normal surrounding cells define tumor’s fate in incipient carcinomas. Once homeostasis has been lost, normal resident fibroblasts become carcinoma-associated fibroblasts, conferring protumorogenic properties on these normal cells. Here we describe the IL1β-mediated interplay between cancer cells and normal colonic myofibroblasts (NCFs), which bestows differential sensitivity to cytotoxic drugs on tumor cells. We used NCFs, their conditioned media (CM), and cocultures with tumor cells to characterize the IL1β-mediated crosstalk between both cell types. We silenced IL1β in tumor cells to demonstrate that such cells do not exert an influence on NCFs inflammatory phenotype. Our results shows that IL1β is overexpressed in cocultured tumor cells. IL1β enables paracrine signaling in myofibroblasts, converting them into inflammatory-CAFs (iCAF). IL1β-stimulated-NCF-CM induces migration and differential sensitivity to oxaliplatin in colorectal tumor cells. Such chemoprotective effect has not been evidenced for TGFβ1-driven NCFs. IL1β induces the loss of a myofibroblastic phenotype in NCFs and acquisition of iCAF traits. In conclusion, IL1β-secreted by cancer cells modify surrounding normal fibroblasts to confer protumorogenic features on them, particularly tolerance to cytotoxic drugs. The use of IL1β-blocking agents might help to avoid the iCAF traits acquisition and consequently to counteract the protumorogenic actions these cells.

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Bi-Functional Radiotheranostics of 188Re-Liposome-Fcy-hEGF for Radio- and Chemo-Therapy of EGFR-Overexpressing Cancer Cells

International Journal of Molecular Sciences ◽

10.3390/ijms22041902 ◽

2021 ◽

Vol 22 (4) ◽

pp. 1902 ◽

Cited By ~ 1

Author(s):

Yi-Shu Huang ◽

Wei-Chuan Hsu ◽

Chien-Hong Lin ◽

Sheng-Nan Lo ◽

Chu-Nian Cheng ◽

...

Keyword(s):

Fusion Protein ◽

Cancer Cells ◽

Tumor Cells ◽

Cytotoxic Effect ◽

Cytosine Deaminase ◽

Growth Factor Receptor ◽

Size Exclusion ◽

Specific Therapy ◽

Egfr Expression ◽

Epidermal Growth

Epidermal growth factor receptor (EGFR) specific therapeutics is of great importance in cancer treatment. Fcy-hEGF fusion protein, composed of yeast cytosine deaminase (Fcy) and human EGF (hEGF), is capable of binding to EGFR and enzymatically convert 5-fluorocytosine (5-FC) to 1000-fold toxic 5-fluorocuracil (5-FU), thereby inhibiting the growth of EGFR-expressing tumor cells. To develop EGFR-specific therapy, 188Re-liposome-Fcy-hEGF was constructed by insertion of Fcy-hEGF fusion protein onto the surface of liposomes encapsulating of 188Re. Western blotting, MALDI-TOF, column size exclusion and flow cytometry were used to confirm the conjugation and bio-activity of 188Re-liposome-Fcy-hEGF. Cell lines with EGFR expression were subjected to treat with 188Re-liposome-Fcy-hEGF/5-FC in the presence of 5-FC. The 188Re-liposome-Fcy-hEGF/5-FC revealed a better cytotoxic effect for cancer cells than the treatment of liposome-Fcy-hEGF/5-FC or 188Re-liposome-Fcy-hEGF alone. The therapeutics has radio- and chemo-toxicity simultaneously and specifically target to EGFR-expression tumor cells, thereby achieving synergistic anticancer activity.

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The Mechanical Fingerprint of Circulating Tumor Cells (CTCs) in Breast Cancer Patients

Cancers ◽

10.3390/cancers13051119 ◽

2021 ◽

Vol 13 (5) ◽

pp. 1119

Author(s):

Ivonne Nel ◽

Erik W. Morawetz ◽

Dimitrij Tschodu ◽

Josef A. Käs ◽

Bahriye Aktas

Keyword(s):

Breast Cancer ◽

Cancer Cells ◽

Cancer Patients ◽

Tumor Cells ◽

Circulating Tumor Cells ◽

Hematopoietic Cells ◽

Surrogate Marker ◽

Clinical Samples ◽

Breast Cancer Patients ◽

Shape Restoration

Circulating tumor cells (CTCs) are a potential predictive surrogate marker for disease monitoring. Due to the sparse knowledge about their phenotype and its changes during cancer progression and treatment response, CTC isolation remains challenging. Here we focused on the mechanical characterization of circulating non-hematopoietic cells from breast cancer patients to evaluate its utility for CTC detection. For proof of premise, we used healthy peripheral blood mononuclear cells (PBMCs), human MDA-MB 231 breast cancer cells and human HL-60 leukemia cells to create a CTC model system. For translational experiments CD45 negative cells—possible CTCs—were isolated from blood samples of patients with mamma carcinoma. Cells were mechanically characterized in the optical stretcher (OS). Active and passive cell mechanical data were related with physiological descriptors by a random forest (RF) classifier to identify cell type specific properties. Cancer cells were well distinguishable from PBMC in cell line tests. Analysis of clinical samples revealed that in PBMC the elliptic deformation was significantly increased compared to non-hematopoietic cells. Interestingly, non-hematopoietic cells showed significantly higher shape restoration. Based on Kelvin–Voigt modeling, the RF algorithm revealed that elliptic deformation and shape restoration were crucial parameters and that the OS discriminated non-hematopoietic cells from PBMC with an accuracy of 0.69, a sensitivity of 0.74, and specificity of 0.63. The CD45 negative cell population in the blood of breast cancer patients is mechanically distinguishable from healthy PBMC. Together with cell morphology, the mechanical fingerprint might be an appropriate tool for marker-free CTC detection.

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Melatonin as an Adjuvant to Antiangiogenic Cancer Treatments

Cancers ◽

10.3390/cancers13133263 ◽

2021 ◽

Vol 13 (13) ◽

pp. 3263

Author(s):

Alicia González ◽

Carolina Alonso-González ◽

Alicia González-González ◽

Javier Menéndez-Menéndez ◽

Samuel Cos ◽

...

Keyword(s):

Synergistic Effect ◽

Protective Effect ◽

Cancer Cells ◽

Tumor Cells ◽

Chemotherapeutic Agents ◽

Inhibitory Effects ◽

Anticancer Effect ◽

Cancer Treatments ◽

Melatonin Administration ◽

Effects Of Radiation

Melatonin is a hormone with different functions, antitumor actions being one of the most studied. Among its antitumor mechanisms is its ability to inhibit angiogenesis. Melatonin shows antiangiogenic effects in several types of tumors. Combination of melatonin and chemotherapeutic agents have a synergistic effect inhibiting angiogenesis. One of the undesirable effects of chemotherapy is the induction of pro-angiogenic factors, whilst the addition of melatonin is able to overcome these undesirable effects. This protective effect of the pineal hormone against angiogenesis might be one of the mechanisms underlying its anticancer effect, explaining, at least in part, why melatonin administration increases the sensitivity of tumors to the inhibitory effects exerted by ordinary chemotherapeutic agents. Melatonin has the ability to turn cancer totally resistant to chemotherapeutic agents into a more sensitive chemotherapy state. Definitely, melatonin regulates the expression and/or activity of many factors involved in angiogenesis which levels are affected (either positively or negatively) by chemotherapeutic agents. In addition, the pineal hormone has been proposed as a radiosensitizer, increasing the oncostatic effects of radiation on tumor cells. This review serves as a synopsis of the interaction between melatonin and angiogenesis, and we will outline some antiangiogenic mechanisms through which melatonin sensitizes cancer cells to treatments, such as radiotherapy or chemotherapy.

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Enhanced Vasculogenic Capacity Induced by 5-Fluorouracil Chemoresistance in a Gastric Cancer Cell Line

International Journal of Molecular Sciences ◽

10.3390/ijms22147698 ◽

2021 ◽

Vol 22 (14) ◽

pp. 7698

Author(s):

Sara Peri ◽

Alessio Biagioni ◽

Giampaolo Versienti ◽

Elena Andreucci ◽

Fabio Staderini ◽

...

Keyword(s):

Gastric Cancer ◽

Cancer Cells ◽

Cell Line ◽

Cancer Cell ◽

Intracellular Signaling ◽

Gastric Cancer Cell ◽

Gastric Cancer Cell Line ◽

Cancer Cell Line ◽

Tumor Evolution ◽

Selective Growth Advantage

Chemotherapy is still widely used as a coadjutant in gastric cancer when surgery is not possible or in presence of metastasis. During tumor evolution, gatekeeper mutations provide a selective growth advantage to a subpopulation of cancer cells that become resistant to chemotherapy. When this phenomenon happens, patients experience tumor recurrence and treatment failure. Even if many chemoresistance mechanisms are known, such as expression of ATP-binding cassette (ABC) transporters, aldehyde dehydrogenase (ALDH1) activity and activation of peculiar intracellular signaling pathways, a common and universal marker for chemoresistant cancer cells has not been identified yet. In this study we subjected the gastric cancer cell line AGS to chronic exposure of 5-fluorouracil, cisplatin or paclitaxel, thus selecting cell subpopulations showing resistance to the different drugs. Such cells showed biological changes; among them, we observed that the acquired chemoresistance to 5-fluorouracil induced an endothelial-like phenotype and increased the capacity to form vessel-like structures. We identified the upregulation of thymidine phosphorylase (TYMP), which is one of the most commonly reported mutated genes leading to 5-fluorouracil resistance, as the cause of such enhanced vasculogenic ability.

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