scholarly journals A study on discrete and discrete fractional pharmacokinetics-pharmacodynamics models for tumor growth and anti-cancer effects

2019 ◽  
Vol 7 (1) ◽  
pp. 10-24 ◽  
Author(s):  
Ferhan M. Atıcı ◽  
Mustafa Atıcı ◽  
Ngoc Nguyen ◽  
Tilekbek Zhoroev ◽  
Gilbert Koch
Keyword(s):  
Tumor Growth ◽  
Bayesian Method ◽  
Tumor Volume ◽  
Difference Operator ◽  
Discrete Models ◽  
Fractional Difference ◽  
Nabla Operator ◽  
Anti Cancer ◽  
Fractional Models ◽  
Definition Of

AbstractWe study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale $h\mathbb{N}_0^h$, where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.

scholarly journals On the Definitions of Nabla Fractional Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Ferhan M. Atici
Keyword(s):  
Difference Operator ◽  
Difference Operators ◽  
Fractional Operators ◽  
Initial Value ◽  
Fractional Difference ◽  
Power Rule ◽  
The One ◽  
Definition Of ◽  
The Right ◽  
Commutative Property

We show that two recent definitions of discrete nabla fractional sum operators are related. Obtaining such a relation between two operators allows one to prove basic properties of the one operator by using the known properties of the other. We illustrate this idea with proving power rule and commutative property of discrete fractional sum operators. We also introduce and prove summation by parts formulas for the right and left fractional sum and difference operators, where we employ the Riemann-Liouville definition of the fractional difference. We formalize initial value problems for nonlinear fractional difference equations as an application of our findings. An alternative definition for the nabla right fractional difference operator is also introduced.

scholarly journals Pharmacokinetics and Pharmacodynamics Models of Tumor Growth and Anticancer Effects in Discrete Time

2020 ◽  
Vol 8 (1) ◽  
pp. 114-125
Author(s):  
Ferhan M. Atıcı ◽  
Ngoc Nguyen ◽  
Kamala Dadashova ◽  
Sarah E. Pedersen ◽  
Gilbert Koch
Keyword(s):  
Tumor Growth ◽  
Discrete Time ◽  
Continuous Time ◽  
Discrete System ◽  
Model Parameters ◽  
Discrete Fractional Calculus ◽  
Pharmacokinetics And Pharmacodynamics ◽  
Fractional Difference ◽  
Nabla Operator ◽  
Anticancer Effects

AbstractWe study the h-discrete and h-discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h𝕅0, where h > 0. Since the measurements of the drug concentration in plasma were taken hourly, we consider h = 1/24 and obtain the model in discrete time (i.e. hourly). We then continue with fractionalizing the h-discrete nabla operator in the h-discrete model to obtain the model as a system of nabla h-fractional difference equations. In order to solve the fractional h-discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. After estimating and getting confidence intervals of the model parameters, we compare residual squared sum values of the models in one table. Our study shows that the new introduced models provide fitting as good as the existing models in continuous time.

scholarly journals Preparation of Catechin Nanoemulsion from Oolong Tea Leaf Waste and Its Inhibition of Prostate Cancer Cells DU-145 and Tumors in Mice

Molecules ◽  
2021 ◽  
Vol 26 (11) ◽  
pp. 3260
Author(s):  
Yu-Hsiang Lin ◽  
Chi-Chung Wang ◽  
Ying-Hung Lin ◽  
Bing-Huei Chen
Keyword(s):  
Prostate Cancer ◽  
Cancer Cells ◽  
Tumor Volume ◽  
Tween 80 ◽  
Prostate Cancer Cells ◽  
Caspase 9 ◽  
Oolong Tea ◽  
Induced Tumors ◽  
Anti Cancer ◽  
Tea Leaf

Anti-cancer activity of catechin nanoemulsions prepared from Oolong tea leaf waste was studied on prostate cancer cells DU-145 and DU-145-induced tumors in mice. Catechin nanoemulsions composed of lecithin, Tween-80 and water in an appropriate proportion was prepared with high stability, particle size of 11.3 nm, zeta potential of −67.2 mV and encapsulation efficiency of 83.4%. Catechin nanoemulsions were more effective than extracts in inhibiting DU-145 cell growth, with the IC50 being 13.52 and 214.6 μg/mL, respectively, after 48 h incubation. Furthermore, both catechin nanoemulsions and extracts could raise caspase-8, caspase-9 and caspase-3 activities for DU-145 cell apoptosis, arresting the cell cycle at S and G2/M phases. Compared to control, catechin nanoemulsion at 20 μg/mL and paclitaxel at 10 μg/mL were the most effective in reducing tumor volume by 41.3% and 52.5% and tumor weight by 77.5% and 90.6% in mice, respectively, through a decrease in EGF and VEGF levels in serum.

Antitumor effects of Auraptene in 4T1 tumor‐bearing Balb/c mice

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammad Reza. Shiran ◽  
Davar Amani ◽  
Abolghasem Ajami ◽  
Mahshad Jalalpourroodsari ◽  
Maghsoud Khalizadeh ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Body Weight ◽  
Tumor Volume ◽  
Serum Levels ◽  
Ki 67 ◽  
Tumor Bearing ◽  
Paraffin Oil ◽  
Anti Cancer ◽  
Before And After ◽  
Ifn Γ

Abstract Objectives Breast cancer is a common malignant tumor in women with limited treatment options and multiple side effects. Today, the anti-cancer properties of natural compounds have attracted widespread attention from researchers worldwide. Methods In this study, we treated 4T1 tumor-bearing Balb/c mice with intraperitoneal injection of Auraptene, paraffin oil, and saline as two control groups. Body weight and tumor volume were measured before and after treatment. Hematoxylin and eosin (H & E) staining and immunohistochemistry of Ki-67 were used as markers of proliferation. In addition, ELISA assays were performed to assess serum IFN-γ and IL-4 levels. Results There was no significant change in body weight in all animal groups before and after treatment. 10 days after the last treatment, Auraptene showed its anti-cancer effect, which was confirmed by the smaller tumor volume and H & E staining. In addition, Ki-67 expression levels were significantly reduced in tumor samples from the Auraptene-treated group compared to the paraffin oil and saline-treated groups. In addition, in tumor-bearing and normal mice receiving Auraptene treatment, IL-4 serum production levels were reduced, while serum levels of IFN-γ were significantly up-regulated in tumor-bearing mice after Auraptene treatment. Conclusions In the case of inhibition of tumor volume and Ki-67 proliferation markers, Auraptene can effectively inhibit tumor growth in breast cancer animal models. In addition, it might increases Th1 and CD8 + T cell responses after reducing IL-4 serum levels and IFN-γ upregulation, respectively. However, further research is needed to clarify its mechanism of action.

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

2020 ◽  
Vol 26 (2) ◽  
pp. 173-183
Author(s):  
Kuldip Raj ◽  
Kavita Saini ◽  
Anu Choudhary
Keyword(s):  
Difference Operator ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Normed Spaces ◽  
Fractional Difference ◽  
New Approach ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Bounded Sequences

AbstractRecently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

scholarly journals Effects of Steady Low-Intensity Exercise on High-Fat Diet Stimulated Breast Cancer Progression Via the Alteration of Macrophage Polarization

2020 ◽  
Vol 19 ◽  
pp. 153473542094967
Author(s):  
Min Kyoon Kim ◽  
Yesl Kim ◽  
SeungHwa Park ◽  
Eunju Kim ◽  
Yerin Kim ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Tumor Growth ◽  
High Fat Diet ◽  
Tumor Volume ◽  
Macrophage Polarization ◽  
M2 Macrophage ◽  
High Fat ◽  
Low Intensity ◽  
M2 Macrophage Polarization ◽  
Low Intensity Exercise

Physical inactivity and high-fat diet, especially high saturated fat containing diet are established risk factors for breast cancer that are amenable to intervention. High-fat diet has been shown to induce tumor growth and metastasis by alteration of inflammation but steady exercise has anti-tumorigenic effects. However, the mechanisms underlying the effects of physical activity on high-fat diet stimulated breast cancer initiation and progression are currently unclear. In this study, we examined how the intensity of physical activity influences high fat diet-stimulated breast cancer latency and progression outcomes, and the possible mechanisms behind these effects. Five-week-old female Balb/c mice were fed either a control diet or a high-fat diet for 8 weeks, and then 4T1 mouse mammary tumor cells were inoculated into the mammary fat pads. Exercise training occurred before tumor cell injection, and tumor latency and tumor volume were measured. Mice with a high-fat diet and low-intensity exercise (HFLE) had a longer tumor latency period, slower tumor growth, and smaller tumor volume in the final tumor assessment compared with the control, high-fat diet control (HFDC), and high-fat diet with moderate-intensity exercise (HFME) groups. Steady low- and moderate-intensity exercise had no effect on cell proliferation but induced apoptosis by activating caspase-3 through the alteration of Bcl-2, Bcl-xL, and Bax expression. Furthermore, steady exercise reduced M2 macrophage polarization in breast tumor tissue, which has been linked to tumor growth. The myokine, myostatin, reduced M2 macrophage polarization through the inhibition of the JAK-STAT signaling pathway. These results suggest that steady low-intensity exercise could delay breast cancer initiation and growth and reduce tumor volume through the induction of tumor cell apoptosis and the suppression of M2 macrophage polarization.

scholarly journals Herbal Medicine Goshajinkigan Prevents Paclitaxel-Induced Mechanical Allodynia without Impairing Antitumor Activity of Paclitaxel

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Muh. Akbar Bahar ◽  
Tsugunobu Andoh ◽  
Keisuke Ogura ◽  
Yoshihiro Hayakawa ◽  
Ikuo Saiki ◽  
...  
Keyword(s):  
Peripheral Neuropathy ◽  
Herbal Medicine ◽  
Tumor Growth ◽  
Mechanical Allodynia ◽  
Chemotherapeutic Agents ◽  
Antitumor Action ◽  
Effective Strategies ◽  
Anti Cancer ◽  
Mammary Fat Pad ◽  
4T1 Cells

Chemotherapy-induced peripheral neuropathy is a major dose-limiting side effect of commonly used chemotherapeutic agents. However, there are no effective strategies to treat the neuropathy. We examined whether Goshajinkigan, a herbal medicine, would prevent paclitaxel-induced allodynia without affecting the anticancer action in mice. Murine breast cancer 4T1 cells were inoculated into the mammary fat pad. Paclitaxel (10 and 20 mg/kg, intraperitoneal, alternate day from day 7 postinoculation) inhibited the tumor growth, and Goshajinkigan (1 g/kg, oral, daily from day 2 postinoculation) did not affect the antitumor action of paclitaxel. Mechanical allodynia developed in the inoculated region due to tumor growth and in the hind paw due to paclitaxel-induced neuropathy. Paclitaxel-induced allodynia was markedly prevented by Goshajinkigan, although tumor-associated allodynia was not inhibited by Goshajinkigan. These results suggest that Goshajinkigan prevents paclitaxel-induced peripheral neuropathy without interfering with the anti-cancer action of paclitaxel.

scholarly journals Low-Grade Gliomas: Six-month Tumor Growth Predicts Patient Outcome Better than Admission Tumor Volume, Relative Cerebral Blood Volume, and Apparent Diffusion Coefficient

Radiology ◽  
2009 ◽  
Vol 253 (2) ◽  
pp. 505-512 ◽  
Author(s):  
Gisele Brasil Caseiras ◽  
Olga Ciccarelli ◽  
Daniel R. Altmann ◽  
Christopher E. Benton ◽  
Daniel J. Tozer ◽  
...  
Keyword(s):  
Patient Outcome ◽  
Diffusion Coefficient ◽  
Apparent Diffusion Coefficient ◽  
Tumor Growth ◽  
Blood Volume ◽  
Cerebral Blood Volume ◽  
Tumor Volume ◽  
Low Grade ◽  
Apparent Diffusion ◽  
Better Than

572 Fibroblast activating protein (FAP)-targeting IL-12 (anti-FAP/IL-12) TMEkine™ potentiates anti-cancer effects in preclinical cancer models

2020 ◽  
Vol 8 (Suppl 3) ◽  
pp. A606-A606
Author(s):  
Donggeon Kim ◽  
Dahea Lee ◽  
Soomin Ryu ◽  
Yeongseon Byeon ◽  
Kyoung-Ho Pyo ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Solid Tumor ◽  
Immune Modulation ◽  
Therapeutic Option ◽  
Complete Response ◽  
Tumor Burden ◽  
Tumor Growth Inhibition ◽  
Durable Response ◽  
Anti Cancer ◽  
Nih 3T3

BackgroundAlthough cancer immunotherapy showed promising results in hematological malignancies, it has come up with relatively low tumor response for many solid tumors partly due to immune-suppressive tumor microenvironment (TME). Because of the immune-suppressive nature of TME, TME has been an active area of research and therapeutic target for restoring immune system and subsequent tumor growth inhibition. Among the many components in TME, cancer-associated fibroblasts (CAFs) are one of the key cell components of TME where one of the promising solid-tumor TME marker, fibroblast-activating protein (FAP) is highly expressed. Here we have developed an antibody-cytokine fusion protein from our TMEkine™ platform containing anti-FAP and IL-12. Our TMEkine™ (anti-FAP-IL-12) molecule induced strong anti-cancer effects in preclinical solid tumor models by immune-modulation.MethodsIL-12 cytokine was mutated in TMEkine™ (anti-FAP-IL-12) to reduce systemic toxicity and its binding affinity was tested to FAP and IL-12 receptor. The anti-tumor activity of anti-FAP-IL-12 was investigated on CT26 (murine colorectal cancer) syngeneic mouse models with/without NIH-3T3 (murine fibroblast). Additionally, mice showing complete response after anti-FAP-IL-12 administration were re-injected CT26 with/without 4T1 cells for re-challenge study to monitor long-term durable response generated from the initial immune activation.ResultsWe showed that TMEkine™ (anti-FAP-IL-12) interacts with FAP and IL-12 receptor. IL-12 activity was attenuated by our IL-12 mutants. We also showed that TMEkine™ (anti-FAP-IL-12) induced IFN-γ from primary human T cells and NK cells. TMEkine™ (anti-FAP-IL-12) administration resulted in significant reduction of the tumor burden in both CT26+NIH-3T3/FAP+ and CT26/FAP+ models. In the re-challenge experiments, CT26 tumor growth was inhibited significantly compared to 4T1 tumor suggesting memory immune response was generated in TMEkine™ (anti-FAP-IL-12) treated mice.ConclusionsThese findings provide evidences that the treatment of anti-FAP/IL-12 TMEkine™ induced anti-cancer effects without serious adverse effects. Anti-FAP/IL-12 has a strong potential to provide a therapeutic option for cancer-specific immunomodulator and cancer cell eradication.

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