A study of fractional order dual-phase-lag bioheat transfer model.

In this study, we have established a space-time fractional DPL bioheat transfer model in the presence of temperature-dependent metabolic and space-time dependent electromagnetic heat sources. Applying the Legendre wavelet collocation method, the fractional order partial differential equation is reduced into the system of algebraic equations, which has been solved using the Newton iteration method. The error bound as well as stability analysis and numerical scheme validation are provided. The time to achieve for the position of hyperthermia is discussed in three cases: the DPL model, the time-fractional DPL model, and the space-time-fractional DPL model. The effect of variability of time and space fractional derivative orders (α and ß), transmitted power (P) and lagging times on the temperature profile in biological tissue at a different time are discussed in detail. We conclude that a suitable value of α, ß, τT, τq, and P provides a desirable temperature at a particular time in thermal therapies. Such knowledge will be very useful in the clinical therapeutic application.

Identification of heterotic groups in South-Asian-bred hybrid parents of pearl millet.

KEY MESSAGE: Pearl millet breeding programs can use this heterotic group information on seed and restorer parents to generate new series of pearl millet hybrids having higher yields than the existing hybrids. Five hundred and eighty hybrid parents, 320 R- and 260 B-lines, derived from 6 pearl millet breeding programs in India, genotyped following RAD-GBS (about 0.9 million SNPs) clustered into 12 R- and 7 B-line groups. With few exceptions, hybrid parents of all the breeding programs were found distributed across all the marker-based groups suggesting good diversity in these programs. Three hundred and twenty hybrids generated using 37 (22 R and 15 B) representative parents, evaluated for grain yield at four locations in India, showed significant differences in yield, heterosis, and combining ability. Across all the hybrids, mean mid- and better-parent heterosis for grain yield was 84.0% and 60.5%, respectively. Groups G12 B × G12 R and G10 B × G12 R had highest heterosis of about 10% over best check hybrid Pioneer 86M86. The parents involved in heterotic hybrids were mainly from the groups G4R, G10B, G12B, G12R, and G13B. Based on the heterotic performance and combining ability of groups, 2 B-line (HGB-1 and HGB-2) and 2 R-line (HGR-1 and HGR-2) heterotic groups were identified. Hybrids from HGB-1 × HGR-1 and HGB-2 × HGR-1 showed grain yield heterosis of 10.6 and 9.3%, respectively, over best hybrid check. Results indicated that parental groups can be formed first by molecular markers, which may not predict the best hybrid combination, but it can reveal a practical value of assigning existing and new hybrid pearl millet parental lines into heterotic groups to develop high-yielding hybrids from the different heterotic groups.

A study of heat transfer during cryosurgery of lung cancer.

In this study, a mathematical model describing two-dimensional bio-heat transfer during cryosurgery of lung cancer is developed. The lung tissue is cooled by a cryoprobe by imposing its surface at a constant temperature or a constant heat flux or a constant heat transfer coefficient. The freezing starts and the domain is distributed into three stages namely: unfrozen, mushy and frozen regions. In stage I where the only unfrozen region is formed, our problem is an initial-boundary value problem of the hyperbolic partial differential equation. In stage II where mushy and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations and in stage III where frozen, mushy, and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations. The solution consists of the three-step procedure: (i) transformation of problem in non-dimensional form, (ii) by using finite differences, the problem converted into ordinary matrix differential equation and moving boundary problem of ordinary matrix differential equations, (iii) applying Legendre wavelet Galerkin method the problem is transferred into the generalized system of Sylvester equations which are solved by applying Bartels-Stewart algorithm of generalized inverse. The complete analysis is presented in the non-dimensional form. The consequence of the imposition of boundary conditions on moving layer thickness and temperature distribution are studied in detail. The consequence of Stefan number, Kirchoff number and Biot number on moving layer thickness are also studied in specific.

A study of cryosurgery of lung cancer using Modified Legendre wavelet Galerkin method.

In this paper, we have developed a new mathematical model describing bio-heat transfer during cryosurgery of lung cancer. The lung tissue cooled by a flat probe whose temperature decreases linearly with time. The freezing process occurs in three stages and the whole region is divided into solid, mushy and liquid region. The heat released in the mushy region is considered as discontinuous heat generation. The model is an initial-boundary value problem of the hyperbolic partial differential equation in stage 1 and moving boundary value problem of parabolic partial differential equations in stage 2 and 3. The method of the solution consists of four-step procedure as transformation of problem in dimensionless form, the problem of hyperbolic partial differential equation converted into ordinary matrix differential equation and the moving boundary problem of parabolic partial differential equations converted into moving boundary problem of ordinary matrix differential equations by using finite differences in space, transferring the problem into the generalized system of Sylvester equations by using Legendre wavelet Galerkin method and the solution of the generalized system of Sylvester equation are solved by using Bartels-Stewart algorithm of generalized inverse. The whole analysis is presented in dimensionless form. The effect of cryoprobe rate on temperature distribution and the effect of Stefan number on moving layer thickness is discussed in detail.

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form.

Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy.

In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy.

A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach.

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment.

Numerical simulation of dual-phase-lag bioheat transfer model during thermal therapy.

This paper theoretically investigates the thermal behavior in a living biological tissue under various coordinate systems and different non-Fourier boundary conditions with the dual-phase-lag bioheat transfer model during thermal therapy. The properties of Legendre wavelets together with the finite difference scheme are used to find an approximate analytical solution of the present problem. It has been observed that surrounding healthy tissues are less affected in second and third kind of boundary condition when applied along with spherical symmetric coordinate system. Also greater temperature rise and fast achievement of peak hyperthermia temperature is achieved when second and third kind of boundary conditions are used in combination with Cartesian coordinate system. It is observed that due to the presence of blood perfusion and temperature dependent metabolic heat generation term, the dual-phase-lag bioheat transfer model reduces to Pennes bioheat transfer model only when τq=τT=0s, not for arbitrary τq=τT. Further, in case of dual-phase-lag bioheat transfer model wave-like or diffusion-like behavior will dominate depends whether the ratio τq/τT > 1 or τq/τT < 1. Effect of temperature dependent metabolic heat generation rate, thermal conductivity and blood perfusion rate on dimensionless temperature are discussed in details. The whole analysis is presented in dimensionless form.

Non-linear dual-phase-lag model for analyzing heat transfer phenomena in living tissues during thermal ablation.

In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method.

A study on DPL model of heat transfer in bi-layer tissues during MFH treatment.

In this paper, dual-phase-lag bioheat transfer model subjected to Fourier and non-Fourier boundary conditions for bi-layer tissues has been solved using finite element Legendre wavelet Galerkin method (FELWGM) during magnetic fluid hyperthermia. FELWGM localizes small scale variation of solution and fast switching of functional bases. It has been observed that moderate hyperthermia temperature range (41-46°C) can be better achieved in spherical symmetric coordinate system and treatment method will be independent of the Fourier and non-Fourier boundary conditions used. The effect of phase-lag times has been observed only in tumor region. FCC FePt magnetic nano-particle produces more effective treatment with respect to other magnetic nano-particles. The effect of variability of magnetic heat source parameters (magnetic induction, frequency, diameter of magnetic nano-particles, volume fractional of magnetic nano-particles and ligand layer thickness) has been investigated. The physical property of these parameters has been described in detail during magnetic fluid hyperthermia (MFH) treatment and also discussed the clinical application of MFH in Oncology.

A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment.

The success of hyperthermia in the treatment of cancer depends on the precise prediction and control of temperature. It was absolutely a necessity for hyperthermia treatment planning to understand the temperature distribution within living biological tissues. In this paper, dual-phase-lag model of bio-heat transfer has been studied using Gaussian distribution source term under most generalized boundary condition during hyperthermia treatment. An approximate analytical solution of the present problem has been done by Finite element wavelet Galerkin method which uses Legendre wavelet as a basis function. Multi-resolution analysis of Legendre wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. The whole analysis is presented in dimensionless form. The dual-phase-lag model of bio-heat transfer has compared with Pennes and Thermal wave model of bio-heat transfer and it has been found that large differences in the temperature at the hyperthermia position and time to achieve the hyperthermia temperature exist, when we increase the value of τT. Particular cases when surface subjected to boundary condition of 1st, 2nd and 3rd kind are discussed in detail. The use of dual-phase-lag model of bio-heat transfer and finite element wavelet Galerkin method as a solution method helps in precise prediction of temperature. Gaussian distribution source term helps in control of temperature during hyperthermia treatment. So, it makes this study more useful for clinical applications.

Pathogenic Variation in the Pearl Millet Blast Pathogen Magnaporthe grisea and Identification of Resistance to Diverse Pathotypes.

Blast, also known as leaf spot, caused by Pyricularia grisea (teleomorph: Magnaporthe grisea), has emerged as a serious disease affecting both forage and grain production in pearl millet in India. Pathogenic variation was studied in a greenhouse using 25 M. grisea isolates collected from four major pearl-millet-growing states in India (Rajasthan, Haryana, Maharashtra, and Uttar Pradesh) on 10 pearl millet genotypes (ICMB 02444, ICMB 02777, ICMB 06444, ICMB 93333, ICMB 96666, ICMB 97222, ICMB 99444, 863B, ICMR 06222, and ICMB 95444). Differential reactions to the test isolates were recorded on ICMB 02444, ICMB 93333, ICMB 97222, 863B, and ICMR 06222. The 25 isolates were grouped into five different pathotypes based on their reaction types (virulent = score ≥ 4 and avirulent = score ≤ 3 on a 1-to-9 scale). For the identification of resistance sources, a pearl millet mini-core comprising 238 accessions was evaluated under greenhouse conditions against five M. grisea isolates (Pg118, Pg119, Pg56, Pg53, and Pg45) representing the five pathotypes. Of 238 accessions, 32 were found to be resistant to at least one pathotype. Resistance to multiple pathotypes (two or more) was recorded in several accessions, while three accessions (IP 7846, IP 11036, and IP 21187) exhibited resistance to four of the five pathotypes. Four early-flowering (≤50 days) blast-resistant mini-core accessions (IP 7846, IP 4291, IP 15256, and IP 22449) and four accessions (IP 5964, IP 11010, IP 13636, and IP 20577) having high scores (≥7) for grain and green fodder yield potential and overall plant aspect were found to be promising for utilization in pearl millet improvement programs. Identification of five pathotypes of M. grisea and sources of resistance to these pathotypes will provide a foundation for breeding for blast resistance in pearl millet in India.

Preparation and characterization of polymer nanocomposite containing PMMA, styrene and nanoalumina.

Polymer syrup of polymethyl methacrylate and polystyrene reinforced with 2% non settling nanoalumina particles was prepared by dual initiating system containing benzoylperoxide (BPO), azo-bisisobutyro nitrile (AIBN) and dimethylaniline (DMA). Nanoalumina particles were prepared using autoignition of aluminum nitrate and urea. Nanoalumina particles show the tendency of agglomeration in the polymer matrix because of the presence of hydroxyl groups on its surface. To get better dispersion in polymer matrix, the alumina surface was treated with methacrylol isocyanate, synthesized by the reaction of methacrylol chloride and sodium azide in the presence of dry benzene at 0 degrees C. The polymer syrup prepared this way was applied between two PMMA sheets of 10 cms x 10 cms x 2 mm dimensions each and the composite thus prepared was tested with Bullet Firing Machine as well as Vertical Drop Weight Impact Testing Machine. The impact strength measurements of two plates composite using both these procedures showed that the impact resistance was found to double in case of nanoalumina. The composite of ten layers and of eleven layers was further tested by 0.32 IOF revolver and Sub Machine Gun Carbine 9 mm 1A1 respectively from 10 m distance which produced an ordinary indent with no penetration.

Genetic Resistance of Pearl Millet Male-Sterile Lines to Diverse Indian Pathotypes of Sclerospora graminicola.

Single-cross F1 hybrid cultivars based on cytoplasmic-nuclear male-sterility (CMS) system have contributed significantly to increasing productivity of pearl millet (Pennisetum glaucum). Genetic resistance to downy mildew (Sclerospora graminicola) in parental lines is critical for successful commercial cultivation of a hybrid cultivar. In this study, 46 genetically diverse male-sterile lines (A-lines), including 42 test A-lines, four control A-lines, a commercial hybrid, and a highly susceptible line, were evaluated in disease nurseries at four diverse locations in India and compared with pathotype isolates from the same locations under greenhouse environments. Variability in downy mildew incidence (0 to 100%) due to genetic differences among lines, among pathotypes, and that due to line × pathotype interaction were all highly significant (P < 0.001). In the field experiment, eight of the 42 test A-lines, including 841A (control), that recorded ≤10% disease incidence, were identified as resistant compared with 84 to 100% incidence on the control susceptible line 7042S. Resistance in eight of these test A-lines (863A, ICMA 88004, -94333, -98222, -98111, -92777, and -96666) and 841A was confirmed against the four pathotypes in greenhouse experiments. Cluster analysis of downy mildew incidence data from field and greenhouse experiments, using the Euclidian distance, classified the 48 lines into four distinct groups with the above eight A-lines in the resistant group. These resistant A-lines would be useful in the development of F1 hybrids with stable resistance to diverse pathotypes of downy mildew in India.

A new source of cytoplasmic male sterility in pearl millet: RFLP analysis of mitochondrial DNA.

A new source of cytoplasmic male sterility (cms) in pearl millet (Pennisetum glaucum (L.) R.Br.) derived from a half-sib progeny of the Early Gene Pool (EGP 261) and used in a male-sterile line, ICMA 90111, was compared with other known cms sources for RFLP of mitochondrial (mt) DNA. Southern blot hybridization of mtDNA from ICMA 90111 digested with several restriction enzymes and probed with homologous mtDNA clones from pearl millet and heterologous gene clones from maize and wheat revealed the RFLP patterns of ICMA 90111 distinct from others studied so far. The dendrogram of male-sterile lines constructed from the Southern blot hybridization patterns indicated that ICMA 90111 represents a separate group. Our results suggest that this source of cms is unique in several respects.

Diallel analysis of heading date in rice (Oryza sativa L.).

The genetics of heading date was investigated in an 8×8 diallel set of crosses involving diverse rice cultivars. Wr, Vr graph analysis revealed the presence of a complementary type of non-allelic interaction which apparently affected the position and slope of the regression line such as if there were overdominance. Omission of two interacting parents resulted in a 6×6 subset of diallel crosses from which, as observed in the Wr, Vr graph, the non-allelic interaction had disappeared and the regression line exhibited partial dominance. Estimates of the genetic components of variation were in close conformity with the results obtained from the Wr, Vr graph: the average degree of dominance, as measured by (H1/D)(1/2), was in overdominance range in the interacting 8×8 set of diallel crosses whereas it was reduced to partial dominance in the non-interacting 6×6 set of crosses. Further analysis by a standardized deviations graph indicated that earliness was controlled, on the average, by an excess of dominant alleles.

Population biology of Avena : IV. Polymorphism in small populations of Avena fatua.

The population structure of wild oats (Avena fatua) sampled in two prune orchards was described using Wright's model of a population having many largely isolated, small subdivisions. A high degree of genetic differentiation was observed among the individual colonies for lemma color, leaf sheath hairiness and isoenzymatic loci. Estimates of genotypic frequencies and population sizes over a two-year period suggested that random drift played an important role in the population changes toward a highly mosaic pattern of differentiation and local monomorphism in a substantial proportion of colonies. It was recognized, however, that without additional extensive field studies, the hypothesis of irregularly dispersed factors of multiniche selection could not be ruled out. Similar studies are briefly reviewed in order to outline the research needed on the issue of selection versus random drift as the primary force in local differentiation.