Citation: Konstantin E. Starkov, Giovana Andres Garfias. Dynamics of the tumor-immune-virus interactions: Convergence conditions to tumor-only or tumor-free equilibrium points[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 421-437. doi: 10.3934/mbe.2019020
| [1] | Nafi Ananda Utama, Yulianti, Putrika Citta Pramesi . The effects of alginate-based edible coating enriched with green grass jelly and vanilla essential oils for controlling bacterial growth and shelf life of water apples. AIMS Agriculture and Food, 2020, 5(4): 756-768. doi: 10.3934/agrfood.2020.4.756 |
| [2] | Burcu Bozova, Muharrem Gölükcü, Haluk Tokgöz, Demet Yıldız Turgut, Orçun Çınar, Ertuğrul Turgutoglu, Angelo Maria Giuffrè . The physico-chemical characteristics of peel essential oils of sweet orange with respect to cultivars, harvesting times and isolation methods. AIMS Agriculture and Food, 2025, 10(1): 40-57. doi: 10.3934/agrfood.2025003 |
| [3] | R. Amilia Destryana, Teti Estiasih, Sukardi, Dodyk Pranowo . The potential uses of Galangal (Alpinia sp.) essential oils as the sources of biologically active compounds. AIMS Agriculture and Food, 2024, 9(4): 1064-1109. doi: 10.3934/agrfood.2024057 |
| [4] | Tarik Ainane, Fatouma Mohamed Abdoul-Latif, Asmae Baghouz, Zineb El Montassir, Wissal Attahar, Ayoub Ainane, Angelo Maria Giuffrè . Essential oils rich in pulegone for insecticide purpose against legume bruchus species: Case of Ziziphora hispanica L. and Mentha pulegium L.. AIMS Agriculture and Food, 2023, 8(1): 105-118. doi: 10.3934/agrfood.2023005 |
| [5] | Muharrem Gölükcü, Burcu Bozova, Haluk Tokgöz, Demet Yıldız Turgut, Orçun Çınar, Ertuğrul Turgutoglu, Angelo Maria Giuffrè . Effects of cultivar, harvesting time and isolation techniques on the essential oil compositions of some lemon cultivars. AIMS Agriculture and Food, 2024, 9(3): 904-920. doi: 10.3934/agrfood.2024049 |
| [6] | Nubia Amaya Olivas, Cindy Villalba Bejarano, Guillermo Ayala Soto, Miriam Zermeño Ortega, Fabiola Sandoval Salas, Esteban Sánchez Chávez, Leon Hernández Ochoa . Bioactive compounds and antioxidant activity of essential oils of Origanum dictamnus from Mexico. AIMS Agriculture and Food, 2020, 5(3): 387-394. doi: 10.3934/agrfood.2020.3.387 |
| [7] | Joshua D. Klein, Amanda Firmansyah, Nurhaya Panga, Waffa Abu-Aklin, Miriam Dekalo-Keren, Tanya Gefen, Ronit Kohen, Yonit Raz Shalev, Nativ Dudai, Lea Mazor . Seed treatments with essential oils protect radish seedlings against drought. AIMS Agriculture and Food, 2017, 2(4): 345-353. doi: 10.3934/agrfood.2017.4.345 |
| [8] | Mahdi Rashvand, Abbas Akbarnia . The feasibility of using image processing and artificial neural network for detecting the adulteration of sesame oil. AIMS Agriculture and Food, 2019, 4(2): 237-243. doi: 10.3934/agrfood.2019.2.237 |
| [9] | Sangam Dahal, Basanta Kumar Rai, Anish Dangal, Kishor Rai, Prekshya Timsina, Ramesh Koirala, Sanjay Chaudhary, Pankaj Dahal, Tanka Bhattarai, Angelo Maria Giuffrè . Evaluation of storage stability of refrigerated buffalo meat coated with hydrothermally treated potato starch incorporated with thyme (Thymus vulgaris) and ginger (Zingiber officinale) essential oil. AIMS Agriculture and Food, 2024, 9(4): 1110-1133. doi: 10.3934/agrfood.2024058 |
| [10] | Saber Ibrahim, Amany Badr El-Deen Abd El-Aziz, Hanan Hassan Abdel-Khalek . Effect of γ irradiation on the antibacterial activity of poly lactic acid films encapsulated with essential oils against some common food borne pathogens. AIMS Agriculture and Food, 2020, 5(4): 715-733. doi: 10.3934/agrfood.2020.4.715 |
Sausages are processed meat products; and frankfurters are of emulsion type sausages, which are cured and added with seasonings [1]. Sausages are added with several food additives, such as nitrites and nitrates, in order to control the growth and toxin production of Clostridium botulinum as well as the development of desired flavor and color [2,3]. Nitrite can also be utilized as an antioxidant in cured meat products [3,4,5]. However, these compounds can have adverse health effects and cause N-nitrosamine production [3,6]. Thus, it is crucial to control and limit the level of nitrites and nitrates used in the production of cured meat products.
The undesired effects of the additives used in the processed meat products as antioxidants, antimicrobials, and color enhancers can be prevented by replacing them with natural plant extracts. For instance, Viuda-Martos, Ruiz-Navajas, Fernández-López and Pérez-Álvarez [7] reported that bologna sausages exhibited lower lipid oxidation and residual nitrite and higher sensory acceptance when they were added with citrus fiber washing water and rosemary essential oil. Moreover, addition of cassia and holy basil essential oils in fresh chicken sausages was also recommended by Sharma, et al. [8]. In addition, Alirezalu, Hesari, Eskandari, Valizadeh and Sirousazar [9] observed that ethanolic extracts of several plants, such as stinging nettle, olive leaves, and green tea, were effective on increasing the shelf life of frankfurter sausages.
It has been stated that tarragon has good antioxidant and antimicrobial properties [10,11,12]. For instance, Sharafati-Chaleshtori, et al. [13] reported that tarragon essential oil addition decreased microbial growth and increased overall acceptability of beef burgers. It was also stated that tarragon essential oil was effective on shelf life extension of beef slices [11].
There have been no studies in literature evaluating the addition of tarragon essential oil to sausages. The aim of the study was to investigate the effects of tarragon essential oil on the sensory properties and color of the frankfurter type sausages.
Fresh tarragon (Artemisia dracunculus) leaves were obtained from a local producer. All other ingredients were purchased from local market.
A 100 g of fresh tarragon leaves were added with 1500 mL distilled water and hydrodistillated for 3 h using a Clevenger-type apparatus. The amount of essential oil obtained was measured using the volumetric scale of the apparatus. The essential oil yield from the fresh tarragon leaves was calculated as 0.3% (v/w). The essential oil (EO) was stored in amber vials at −18 ℃.
The control samples were prepared using the following ingredients per kg: 620 g beef meat, 175 g ice-water, 94 g starch, 75 g sunflower oil, 12 g salt, 12 g white pepper, 6 g granulated garlic, and 6 g ground cumin. Samples with tarragon essential oil (0.1% EO, v/w) were prepared by adding a 100 μL of the essential oil to a 100 g of the prepared sausage batter. The samples without the essential oil were used as the control (0% EO, v/w).
The prepared sausage batter was stuffed into 21 mm-diameter synthetic casings manually. The internal temperature of the samples was maintained below 4 ℃ during preparation. The sausages heated in a steam oven to 74 ℃ internal temperature. The heat-treated sausages were then cooled to 4 ℃ in a blast chiller (RBC201, Electrolux, Sweden). In addition, one random sample of the heat treated frankfurters and the sausage batters (samples before the heat treatment) from each level of essential oil addition and replication were separated in order to be used for color measurement.
A hedonic test and a triangle test were used in the assessment of the sensory properties of the samples. Sausages were cut into approximately 6 g pieces (20 mm × 21 mm) and cooked in a microwave oven (Menumaster RCS511TS, ACP Inc., USA) for 60 s before serving the panelists.
The hedonic test was conducted with 12 panelists. Odor, color intensity, flavor, spiciness, hardness, and overall acceptability properties of the samples were assessed using a 7-point hedonic scale (1: very weak or very unacceptable, 7: very strong or very acceptable).
The triangle test was conducted with 30 panelists. The panelists were given with 3 samples (2 of them were the same and 1 was different), and asked to find the odd sample and whether they prefer any of the samples.
The CIELAB L* (lightness, 0–100), a* (negative: greenness, positive: redness) and b* (negative: blueness, positive: yellowness) values were measured using a color meter (CR-400, Konica Minolta Sensing, Inc., Japan). The device was calibrated using a white plate before the measurement. Three different measurements were taken, and the averages were recorded. Chroma (C*) values were also calculated according to Eq 1.
| C∗=√a∗2+b∗2 | (1) |
All treatments were replicated twice in the study. Statistical analysis of data was performed using Minitab 17 statistical software. The hedonic test data were assessed using a completely randomized block design. The data obtained by the triangle test was assessed according to Roessler, Pangborn, Sidel and Stone [14].
Tarragon essential oil was added to the sausages at a concentration of 0.1% (v/w), and similar amounts of tarragon essential oil was reported to exhibit antimicrobial activity in meat products previously [11,13]. It was also reported that tarragon essential oil may contain 75% estragole (methyl chavicol) [15,16,17]. However, the consumption of estragole should be limited, as it was reported to have carcinogenic and genotoxic properties [15,16]. Thus, higher concentrations of tarragon were not assessed in this study.
The effects of tarragon essential oil on the sensory properties of the frankfurters are demonstrated in Table 1. The sensory odor, color intensity, and hardness of the tarragon essential oil added frankfurters were not significantly different than those of the control (P > 0.05). The spiciness of the frankfurters added with the tarragon essential oil was stronger than the control (P < 0.05). The flavor of the control was more acceptable compared to the samples with the essential oil (P < 0.05). Thus, it could be said that the difference in the flavor of the samples is due to the difference in spiciness rather than odor. In addition, the overall acceptability of the control was also higher compared to samples with the essential oil (P < 0.05). Similarly, da Silveira, et al. [18] reported that Tuscan sausages without essential oil had higher acceptability compared to 0.05% and 0.1% bay leaf essential oil added samples. The sensory scores of cooked pork sausages containing aqueous extract of mint were lower compared to control samples without the extract in a study by Latoch and Stasiak [19]. According to Kos, et al. [20] addition of 0.005% and 0.01% bay leaf essential oil decreased the consumers' willingness to buy and acceptability of dry game sausages.
| Sensory Attribute | Treatment | |
| 0% EO(Control) | 0.1% EO | |
| Odor | 4.4 ± 0.5A | 4.7 ± 0.2A |
| Color intensity | 4.1 ± 0.5A | 4.7 ± 0.1 A |
| Flavor | 3.6 ± 0.0A | 3.0 ± 0.1B |
| Spiciness | 3.7 ± 0.2B | 5.0 ± 0.2A |
| Hardness | 3.7 ± 0.1A | 4.2 ± 0.7A |
| Overall acceptability | 4.1 ± 0.3A | 2.9 ± 0.1B |
| Data that were labelled with different superscript letters (A, B) in a row are significantly different (P < 0.05). | ||
DownLoad:
CSV
The flavor and overall acceptability of the frankfurters can be increased by decreasing the amount of the essential oil. Garcia-Diez, et al. [21] reported that the consumer acceptance of dry cured sausages (churiço) was significantly decreased with 0.05% addition of essential oils from several herbs and spices, such as bay, garlic, nutmeg, oregano, rosemary, and thyme to the formulation; however, it was higher when the concentration of the essential oils were reduced to 0.005%. Moreover, Sharafati-Chaleshtori, et al. [13] reported that addition of tarragon essential oil at 0.125% concentration increased overall acceptability of beef burgers compared to the samples with 0%, 0.25% and 0.062% essential oil.
The difference between the control and the samples with the essential oil was significant according to the triangle test (P < 0.05). A 27% of the panelists participated in the triangle test preferred the essential oil containing sausages, whereas a 63% of the panelists preferred the control.
The essential oil addition did not significantly affect the L*, a*, b*, or C* values of the frankfurters (heat treated) (Figure 1) or the sausage batter samples that were not heat treated (Figure 2). Similarly, it has been stated that the addition of oregano essential oil did not affect the L*, a*, b* values of fermented sausages [22]. Sojic, et al. [23] reported that nutmeg essential oil addition did not change the color of cooked sausages similar to our results. However, frankfurters added with rosemary essential oil had different L* and b* values compared to the samples without the essential oil [24]. On the other hand, the a*, b*, and C* values were decreased after the heat treatment (P < 0.05).
The 0.1% (v/w) addition of tarragon essential oil decreased the flavor and overall acceptability of the frankfurter type sausages. The spiciness of the frankfurters with the essential oil was higher compared to the control. However, the effects of the treatment on the other sensory properties and the color were not significant. In conclusion, it can be said that the undesired effect of the tarragon essential oil on the flavor and the overall acceptability could be eliminated by modifying the amount of the essential oil added. The amount of the tarragon essential oil that could be used in frankfurter type sausage formulation should be optimized by further studies also evaluating the antioxidant and antimicrobial properties.
We would like to thank Prof. Dr. Gurbuz Gunes of Istanbul Technical University for letting us use the laboratory facilities and reading the manuscript. Yildiz Gıda Yapi A.S. (Istanbul, Turkey) is also acknowledged for providing the sausage casings.
The authors declare no conflict of interests in this research.
| [1] | Ž. Bajzer, T. Carr, K. Josić, S.J Russell and D. Dingli, Modeling of cancer virotherapy with recombinant measles viruses, J. Theor. Biol. 252 (2008), 109–122. |
| [2] | M. Biesecker, J.H. Kimn, H. Lu, D. Dingli and Ž. Bajzer, Optimization of virotherapy for cancer, Bulletin Math. Biol., 72 (2010), 469–489. |
| [3] | B.W. Bridle, K.B. Stephenson, J.E. Boudreau, S. Koshy, N. Kazdhan, E. Pullenayegum, J. Brunellière, J.L. Bramson, B.D. Lichty and Y. Wan, Potentiating cancer immunotherapy using an oncolytic virus, Mol. Ther., 18 (2010), 1430–1439. |
| [4] | R.M. Diaz, F. Galivo, T. Kottke, P.Wongthida, J. Qiao, J. Thompson, M. Valdes, G. Barber and R.G Vile, Oncolytic immunovirotherapy for melanoma using vesicular stomatitis virus, Cancer Res., 67 (2007), 2840–2848. |
| [5] | R. Eftimie, J. Dushoff, B.M. Bridle, J.L. Bramson and D.J.D. Earn, Multi-stability and multiinstability phenomena in a mathematical model of tumor-immune-virus interactions, Bulletin Math. Biol., 73 (2011), 2932–2961. |
| [6] | R. Eftimie, C.K. Macnamara, J. Dushoff, J.L. Bramson and D.J.D. Earn, Bifurcations and chaotic dynamics in a tumour-immune-virus system, Math. Modell. Nat. Pheno., 11 (2016), 65–85. |
| [7] | M.W. Hirsch, Systems of differential equations that are competitive or cooperative II: Convergence almost everywhere, SIAM J. Math. Analysis, 16 (1985), 423–439. |
| [8] | B.Y. Hwang and D.V. Schaffer, Engineering a serum-resistant and thermostable vesicular stomatitis virus G glycoprotein for pseudotyping retroviral and lentiviral vectors, Gene Ther., 20 (2013), 807– 815. |
| [9] | A.P. Krishchenko, Estimation of domains with cycles, Computer Math. Appl., 34 (1997), 325–332. |
| [10] | A.P. Krishchenko, Localization of invariant compact sets of dynamical systems, Differ. Equations, 41 (2005), 1669–1676. |
| [11] | A.P. Krishchenko and K.E. Starkov, Localization of compact invariant sets of the Lorenz system, Phys. Lett. A, 353 (2006), 383–388. |
| [12] | A.P. Krishchenko and K.E. Starkov, On the global dynamics of a chronic myelogenous leukemia model, Commun. Nonlin. Sci. Numer. Simul., 33 (2016), 174–183. |
| [13] | A.P. Krishchenko and K.E. Starkov, The four-dimensional Kirschner-Panetta type cancer model: how to obtain tumor eradication? Math. Biosci. Eng., 15 (2018), 1243–1254. |
| [14] | S. Varghese and S.D. Rabkin, Oncolytic herpes simplex virus vectors for cancer virotherapy, Cancer Gene Ther., 9 (2002), 967–978. |
| [15] | M.Y. Li and S.J. Muldowney, On R.A. Smith's autonomous convergence theorem, Rocky Mountain J. Math., 25 (1995), 365–379. |
| [16] | R.A. Smith, Some applications of Hausdorff dimension inequalities for ordinary differential equations, Proceed. Royal Soc. Edinburgh Sec. A: Math., 104 (1986), 235–259. |
| [17] | K.E. Starkov, On dynamic tumor eradication conditions under combined chemical/anti-angiogenic therapies, Phys. Lett. A, 382 (2018), 387–393. |
| [18] | K.E. Starkov and S. Bunimovich-Mendrazitsky, Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy, Math. Biosci. Eng., 13 (2016), 1059–1075. |
| [19] | K.E. Starkov and L. Jimenez Beristain, Dynamic analysis of the melanoma model: from cancer persistence to its eradication, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 27 (2017), 1750151-1– 1750151-11. |
| [20] | K.E. Starkov and A.P. Krishchenko, Ultimate dynamics of the Kirschner-Panetta model: Tumor eradication and related problems, Phys. Lett. A, 381 (2017), 3409–3016. |
| [21] | H.R. Thieme, Asymptotically autonomous differential equations in the plane, Rocky Mountain J. Math., 34 (1994), 351–380. |
| 1. | Mira Serikkyzy, Gulzira Jumabekova, Ainur Zheldybayeva, Ainur Matibayeva, Roza Omirbay, Desislav Balev, Improving the organoleptic and structural-chemical properties of semi-smoked sausages, 2022, 29, 1319562X, 1510, 10.1016/j.sjbs.2021.11.021 | |
| 2. | Mira Serikkyzy, Gulzira Jumabekova, Ainur Zheldybayeva, Ainur Matibayeva, Roza Omirbay, Desislav Balev, Developing a Risk Assessment Methodology for the Production of Semi-Smoked Sausages, 2022, 1542-8052, 1, 10.1080/15428052.2022.2034695 | |
| 3. | Romina Alina Marc (Vlaic), Vlad Mureșan, Andruţa E. Mureșan, Crina Carmen Mureșan, Anda E. Tanislav, Andreea Pușcaș, Georgiana Smaranda Marţiș (Petruţ), Rodica Ana Ungur, Spicy and Aromatic Plants for Meat and Meat Analogues Applications, 2022, 11, 2223-7747, 960, 10.3390/plants11070960 | |
| 4. | Bogdănel Silvestru Munteanu, Cornelia Vasile, Encapsulation of Natural Bioactive Compounds by Electrospinning—Applications in Food Storage and Safety, 2021, 13, 2073-4360, 3771, 10.3390/polym13213771 |
Figures(3)
Konstantin E. Starkov, Giovana Andres Garfias. Dynamics of the tumor-immune-virus interactions: Convergence conditions to tumor-only or tumor-free equilibrium points[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 421-437. doi: 10.3934/mbe.2019020
| Sensory Attribute | Treatment | |
| 0% EO(Control) | 0.1% EO | |
| Odor | 4.4 ± 0.5A | 4.7 ± 0.2A |
| Color intensity | 4.1 ± 0.5A | 4.7 ± 0.1 A |
| Flavor | 3.6 ± 0.0A | 3.0 ± 0.1B |
| Spiciness | 3.7 ± 0.2B | 5.0 ± 0.2A |
| Hardness | 3.7 ± 0.1A | 4.2 ± 0.7A |
| Overall acceptability | 4.1 ± 0.3A | 2.9 ± 0.1B |
| Data that were labelled with different superscript letters (A, B) in a row are significantly different (P < 0.05). | ||
DownLoad:
CSV
| Sensory Attribute | Treatment | |
| 0% EO(Control) | 0.1% EO | |
| Odor | 4.4 ± 0.5A | 4.7 ± 0.2A |
| Color intensity | 4.1 ± 0.5A | 4.7 ± 0.1 A |
| Flavor | 3.6 ± 0.0A | 3.0 ± 0.1B |
| Spiciness | 3.7 ± 0.2B | 5.0 ± 0.2A |
| Hardness | 3.7 ± 0.1A | 4.2 ± 0.7A |
| Overall acceptability | 4.1 ± 0.3A | 2.9 ± 0.1B |
| Data that were labelled with different superscript letters (A, B) in a row are significantly different (P < 0.05). | ||
