Improved identifiability of myocardial material parameters by an energy-based cost function

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were \(C_1=3000\pm 1700\,\hbox {Pa}\) and \(\alpha =45\pm 25\) (\(b_f=25\pm 14\), \(b_{ft}=11\pm 6\), \(b_{t}=9\pm 5\)) for the HF cases and \(C_1=1700\,\hbox {Pa}\) and \(\alpha =15\) (\(b_f=8\), \(b_{ft}=4\), \(b_{t}=3\)) for the healthy case.     

Failure properties of vena cava tissue due to deep penetration during filter insertion

In this work, we use an in-vitro mechanical test to explore the resistance of biaxially stretched vena cava tissue against deep perforation and a methodology which integrates experimental and numerical modeling to identify constitutive fracture properties of the vena cava. Six sheep vena cava were harvested just after killing, and cyclic uniaxial tension tests in longitudinal and circumferential directions and biaxial deep penetration tests were performed. After that, we use a nonlinear finite element model to simulate in vitro penetration of the cava tissue in order to fit the fracture properties under penetration of the vena cava by defining a cohesive fracture zone. An iterative process was developed in order to fit the fracture properties of the vena cava using the previously obtained experimental results. The proposed solutions were obtained with fracture energy of 0.22 or 0.33 N/mm. In comparison with the experimental data, the simulation using \(\delta _{0}=0.01\,\hbox {mm}\), \(\delta _{r}=0.35\,\hbox {mm}\), and \(K=220\, \hbox {N}/\hbox {mm}^{3}\) parameters (\(F_{\hbox {max}}=0.92\)) is in good agreement with results from penetration experiments of cava tissue. It is noticeable that the parameter estimation process of the fracture behavior is more accurate than the estimation process of the elastic behavior for the toe region of the curve.     

Mathematical modelling of bone adaptation of the metacarpal subchondral bone in racehorses

In Thoroughbred racehorses, fractures of the distal limb are commonly catastrophic. Most of these fractures occur due to the accumulation of fatigue damage from repetitive loading, as evidenced by microdamage at the predilection sites for fracture. Adaptation of the bone in response to training loads is important for fatigue resistance. In order to better understand the mechanism of subchondral bone adaptation to its loading environment, we utilised a square root function defining the relationship between bone volume fraction \((f_{BM} )\) and specific surface \((S_v )\) of the subchondral bone of the lateral condyles of the third metacarpal bone (MCIII) of the racehorse, and using this equation, developed a mathematical model of subchondral bone that adapts to loading conditions observed in vivo. The model is expressed as an ordinary differential equation incorporating a formation rate that is dependent on strain energy density. The loading conditions applied to a selected subchondral region, i.e. volume of interest, were estimated based on joint contact forces sustained by racehorses in training. For each of the initial conditions of \(f_{BM} \) we found no difference between subsequent homoeostatic \(f_{BM} \) at any given loading condition, but the time to reach equilibrium differed by initial \(f_{BM} \) and loading condition. We found that the observed values for \(f_{BM} \) from the mathematical model output were a good approximation to the existing data for racehorses in training or at rest. This model provides the basis for understanding the effect of changes to training strategies that may reduce the risk of racehorse injury.     

Cell Volume Regulation in the Proximal Tubule of Rat Kidney

We developed a dynamic model of a rat proximal convoluted tubule cell in order to investigate cell volume regulation mechanisms in this nephron segment. We examined whether regulatory volume decrease (RVD), which follows exposure to a hyposmotic peritubular solution, can be achieved solely via stimulation of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. We also determined whether regulatory volume increase (RVI), which follows exposure to a hyperosmotic peritubular solution under certain conditions, may be accomplished by activating basolateral \(\hbox {Na}^+\)/H\(^+\) exchangers. Model predictions were in good agreement with experimental observations in mouse proximal tubule cells assuming that a 10% increase in cell volume induces a fourfold increase in the expression of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. Our results also suggest that in response to a hyposmotic challenge and subsequent cell swelling, \(\hbox {Na}^+\)–\(\hbox {HCO}^-_3\) cotransporters are more efficient than basolateral K\(^+\) and \(\hbox {Cl}^-\) channels at lowering intracellular osmolality and reducing cell volume. Moreover, both RVD and RVI are predicted to stabilize net transcellular \(\hbox {Na}^+\) reabsorption, that is, to limit the net \(\hbox {Na}^+\) flux decrease during a hyposmotic challenge or the net \(\hbox {Na}^+\) flux increase during a hyperosmotic challenge.     

Towards the prediction of flow-induced shear stress distributions experienced by breast cancer cells in the lymphatics

Tumour metastasis in the lymphatics is a crucial step in the progression of breast cancer. The dynamics by which breast cancer cells (BCCs) travel in the lymphatics remains poorly understood. The goal of this work is to develop a model capable of predicting the shear stresses metastasising BCCs experience using numerical and experimental techniques. This paper models the fluidic transport of large particles (\(\eta =d_{\mathrm{p}}/W=0.1-0.4\) where \(d_{\mathrm{p}}\) is the particle diameter and W is the channel width) subjected to lymphatic flow conditions (\({ Re}=0.04\)), in a \(100\times 100\,\upmu \hbox {m}\) microchannel. The feasibility of using the dynamic fluid body interaction (DFBI) method to predict particle motion was assessed, and particle tracking experiments were performed. The experiments found that particle translational velocity decreased from the undisturbed fluid velocity with increasing particle size (5–14% velocity lag for \(\eta =0.1-0.3\)). DFBI simulations were found to better predict particle behaviour than theoretical predictions; however, mesh restrictions in the near-wall region (\(0.2\,\mathrm{W}>y>0.8\,\mathrm{W}\)) result in computationally expensive models. The simulations were in good agreement with the experiments (\(<12\%\) difference) across the channel (\(0.2\,\mathrm{W}\le y\le 0.8\,\mathrm{W}\)), with differences up to 25% in the near-wall region. Particles experience a range of shear stresses (0.002–0.12 Pa) and spatial shear gradients (\(0.004-0.137\,\hbox {Pa}/\upmu \hbox {m}\)) depending on their size and radial position. The predicted shear gradients are far in excess of values associated with BCC apoptosis (\(0.004-0.023\,\hbox {Pa}/\upmu \hbox {m}\)). Increasing our understanding of the shear stress magnitudes and gradients experienced by BCCs could be leveraged to elucidate whether a particular BCC size or location exists that encourages metastasis within the lymphatics.     

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus \(\textit{E}_\mathrm{s}\) on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of \(\lambda =1.1\), were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and \(\textit{E}_\mathrm{s}\,=\,\)140 KPa and (2) \(\textit{E}_\mathrm{s}\,=\,10\), 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35\(\text {e}^{-2}\), 0.235\(\text {e}^{-2}\) and 0.6\(\text {e}^{-2}\)) than for FA attachment (0.0952\(\text {e}^{-2}\), 0.0472\(\text {e}^{-2}\) and 0.05\(\text {e}^{-2}\)). For increasing \(\textit{E}_\mathrm{s}\), the largest maximum principal strain was 4.4\(\text {e}^{-4}\), 5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\) and 5.3\(\text {e}^{-4}\) in the membrane, 9.5\(\text {e}^{-4}\), 1.1\(\text {e}^{-4}\), 1.2\(\text {e}^{-3}\) and 1.2\(\text {e}^{-3}\) in the cytosol, and 4.5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\), 5.7\(\text {e}^{-4}\) and 5.7\(\text {e}^{-4}\) in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.     

Mechanical behavior of an individual adherent MLO-Y4 osteocyte under shear flow

Mechanical properties of a single cell and its mechanical response under stimulation play an important role in regulating interactions between cell and extracellular matrix and affecting mechanotransduction. Osteocytes exhibit solid-like viscoelastic behavior in response to the interstitial fluid shear resulting from tissue matrix deformation. This study intends to quantitatively describe the mechanical behavior of osteocytes combining in vitro experiment and fluid–structure interaction (FSI) finite element (FE) model. The cell is configured in the FSI FE model using the observed data from quasi-3D images. Instead of simply assigning the cellular viscoelastic parameters by statistical data, the mechanical parameters are determined by an iterative algorithm comparing the experimental and the computational results from the FE model. The viscoelastic parameters of osteocytes are obtained as: the equilibrium elasticity modulus \(k_{1}=0.15\pm 0.038\,\hbox {kPa}\), instantaneous elasticity modulus \((k_{1}+k_{2})=0.77\pm 0.23\,\hbox {kPa}\), viscosity coefficient \(\eta =1.38\pm 0.33\,\hbox {kPa}\,\hbox {s}\). A novel index to quantify the cell adhesion is also put forward. In addition, an interesting competition phenomenon is revealed on the cell surface concerning stress and strain, i.e., the place with high stress has low strain and that with low stress has high strain. The proposed method provides a novel technique to study the mechanical behavior of individual adherent cell in vitro. It is believed that this quantitative technique not only determines cell mechanical behavior but also helps elucidate the mechanism of mechanotransduction in various types of cells.     

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, \(A_\mathrm{R}\) and \(B_\mathrm{R}\), each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for \(A_\mathrm{R}\) and \(B_\mathrm{R}\), we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., \(f \Delta t\)-long for DrugA and \((1-f) \Delta t\)-long for DrugB with \(0 \le f \le 1\) and \(\Delta t \ge 0\)). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, \(\mathcal {A/B} = A_\mathrm{R}/B_\mathrm{R}\), and the effect of each drug. We determine a critical ratio, which we term \(\mathcal {(A/B)}^{*}\), at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, \(\mathcal {A/B}\) changes monotonically to \(\mathcal {(A/B)}^{*}\) and then, during the second stage, remains at \(\mathcal {(A/B)}^{*}\) thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.     

Glutathione <Emphasis Type="BoldItalic">S</Emphasis>-transferase P1 gene polymorphisms and susceptibility to coronary artery disease in a subgroup of north Indian population

The present study aimed to investigate the association of \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) and \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) polymorphisms of GSTP1 with coronary artery disease (CAD) in a subgroup of north Indian population. In the present case–control study, CAD patients (\(n = 200\)) and age-matched, sex-matched and ethnicity-matched healthy controls (\(n = 200\)) were genotyped for polymorphisms in GSTP1 using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) method. Genotype distribution of \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) and \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) polymorphisms of GSTP1 gene was significantly different between cases and controls (\(P = 0.005\) and 0.024, respectively). Binary logistic regression analysis showed significant association of A/G (odds ratio (OR): 1.6, 95% CI: 1.08–2.49, \(P = 0.020\)) and G/G (OR: 3.1, 95% CI: 1.41–6.71, P \(=\) 0.005) genotypes of GSTP1 \(\hbox {g}.313\hbox {A}{\!>\!}\hbox {G}\), and C/T (OR: 5.8, 95% CI: 1.26–26.34, \(P = 0.024\)) genotype of GSTP1 \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) with CAD. The A/G and G/G genotypes of \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) and C/T genotype of \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) conferred 6.5-fold increased risk for CAD (OR: 6.5, 95% CI: 1.37–31.27, \(P = 0.018\)). Moreover, the recessive model of GSTP1 \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) is the best fit inheritance model to predict the susceptible gene effect (OR: 2.3, 95% CI: 1.11–4.92, \(P = 0.020\)). In conclusion, statistically significant associations of GSTP1 \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) (A/G, G/G) and \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) (C/T) genotypes with CAD were observed.     

A finite-element model of mechanosensation by a Pacinian corpuscle cluster in human skin

The Pacinian corpuscle (PC) is the cutaneous mechanoreceptor responsible for sensation of high-frequency (20–1000 Hz) vibrations. PCs lie deep within the skin, often in multicorpuscle clusters with overlapping receptive fields. We developed a finite-element mechanical model of one or two PCs embedded within human skin, coupled to a multiphysics PC model to simulate action potentials elicited by each PC. A vibration was applied to the skin surface, and the resulting mechanical signal was analyzed using two metrics: the deformation amplitude ratio (\({\rho }_{\mathrm{1S}} \), \({\rho }_{\mathrm{2S}} )\) and the phase shift of the vibration (\({\delta }_{\mathrm{S}1}^{\mathrm{mech}} \), \({\delta }_{\mathrm{S}2}^{\mathrm{mech}} )\) between the stimulus and the PC. Our results showed that the amplitude attenuation and phase shift at a PC increased with distance from the stimulus to the PC. Differences in amplitude (\(\rho _{12} )\) and phase shift (\({\delta }_{12}^{\mathrm{mech}} )\) between the two PCs in simulated clusters directly affected the interspike interval between the action potentials elicited by each PC (\({\delta }_{12}^{\mathrm{spike}} )\). While \({\delta }_{12}^{\mathrm{mech}} \) had a linear relationship with \({\delta }_{12}^{\mathrm{spike}} \), \(\rho _{12} \)’s effect on \({\delta }_{12}^{\mathrm{spike}} \) was greater for lower values of \(\rho _{12} \). In our simulations, the separation between PCs and the distance of each PC from the stimulus location resulted in differences in amplitude and phase shift at each PC that caused \({\delta }_{12}^{\mathrm{spike}} \) to vary with PC location. Our results suggest that PCs within a cluster receive different mechanical stimuli which may enhance source localization of vibrotactile stimuli, drawing parallels to sound localization in binaural hearing.     

A Mathematical Model for the Macrophage Response to Respiratory Viral Infection in Normal and Asthmatic Conditions

Respiratory viral infections are common in the general population and one of the most important causes of asthma aggravation and exacerbation. Despite many studies, it is not well understood how viral infections cause more severe symptoms and exacerbations in asthmatics. We develop a mathematical model of two types of macrophages that play complementary roles in fighting viral infection: classically \((\hbox {CA}\)-\(\hbox {M}\Phi )\) and alternatively activated macrophages \((\hbox {AA}\)-\(\hbox {M}\Phi )\). \(\hbox {CA}\)-\(\hbox {M}\Phi \) destroy infected cells and tissues to remove viruses, while \(\hbox {AA}\)-\(\hbox {M}\Phi \) repair damaged tissues. We show that a higher viral load or longer duration of infection provokes a stronger immune response from the macrophage system. By adjusting the parameters, we model the differences in response to respiratory viral infection in normal and asthmatic subjects and show how this skews the system toward a response that generates more severe symptoms in asthmatic patients.     

Backbone resonance assignments for the SET domain of the human methyltransferase NSD2

Aberrant NSD2 methyltransferase activity is implicated as the oncogenic driver in multiple myeloma, suggesting opportunities for novel therapeutic intervention. The methyltransferase activity of NSD2 resides in its catalytic SET domain, which is conserved among most lysine methyltransferases. Here we report the backbone \(\hbox {H}^{\mathrm{N}}\), N, C\(^{\prime }\), \(\hbox {C}^\alpha\) and side-chain \(\hbox {C}^\beta\) assignments of a 25 kDa NSD2 SET domain construct, spanning residues 991–1203. A chemical shift analysis of C\(^{\prime }\), \(\hbox {C}^\alpha\) and \(\hbox {C}^\beta\) resonances predicts a secondary structural pattern that is in agreement with homology models.     

A Mathematical Model Supports a Key Role for Ae4 (Slc4a9) in Salivary Gland Secretion

We develop a mathematical model of a salivary gland acinar cell with the objective of investigating the role of two \(\mathrm{Cl}^-/\mathrm{HCO}_3^-\) exchangers from the solute carrier family 4 (Slc4), Ae2 (Slc4a2) and Ae4 (Slc4a9), in fluid secretion. Water transport in this type of cell is predominantly driven by \(\mathrm{Cl}^-\) movement. Here, a basolateral \(\mathrm{Na}^+/ \mathrm{K}^+\) adenosine triphosphatase pump (NaK-ATPase) and a \(\mathrm{Na}^+\)–\(\mathrm{K}^+\)–\(2 \mathrm{Cl}^-\) cotransporter (Nkcc1) are primarily responsible for concentrating the intracellular space with \(\mathrm{Cl}^-\) well above its equilibrium potential. Gustatory and olfactory stimuli induce the release of \(\mathrm{Ca}^{2+}\) ions from the internal stores of acinar cells, which triggers saliva secretion. \(\mathrm{Ca}^{2+}\)-dependent \(\mathrm{Cl}^-\) and \(\mathrm{K}^+\) channels promote ion secretion into the luminal space, thus creating an osmotic gradient that promotes water movement in the secretory direction. The current model for saliva secretion proposes that \(\mathrm{Cl}^-/ \mathrm{HCO}_3^-\) anion exchangers (Ae), coupled with a basolateral \(\mathrm{Na}^+/\hbox {proton}\) (\(\hbox {H}^+\)) (Nhe1) antiporter, regulate intracellular pH and act as a secondary \(\mathrm{Cl}^-\) uptake mechanism (Nauntofte in Am J Physiol Gastrointest Liver Physiol 263(6):G823–G837, 1992; Melvin et al. in Annu Rev Physiol 67:445–469, 2005.  https://doi.org/10.1146/annurev.physiol.67.041703.084745). Recent studies demonstrated that Ae4 deficient mice exhibit an approximate \(30\%\) decrease in gland salivation (Peña-Münzenmayer et al. in J Biol Chem 290(17):10677–10688, 2015). Surprisingly, the same study revealed that absence of Ae2 does not impair salivation, as previously suggested. These results seem to indicate that the Ae4 may be responsible for the majority of the secondary \(\mathrm{Cl}^-\) uptake and thus a key mechanism for saliva secretion. Here, by using ‘in-silico’ Ae2 and Ae4 knockout simulations, we produced mathematical support for such controversial findings. Our results suggest that the exchanger’s cotransport of monovalent cations is likely to be important in establishing the osmotic gradient necessary for optimal transepithelial fluid movement.     

Trend analysis of variations in carbon stock using stock big data

Changes in land use affect the terrestrial carbon stock through changes in the land cover. Research on land use and analysis of variations in carbon stock have practical applications in the optimization of land use and the mitigation of climate change effects. This study was conducted in Baixiang and Julu counties in the Taihang Piedmont by employing the trend analysis method to characterize the variation in county land use and carbon stock. The findings show that in both counties, agricultural and unused land areas decreased while built-up land area increased, and the reduction in cropland was the main reason behind the agricultural land reduction. An inflection point appeared on the cropland curves of Julu, because the cropland area decreased by 1576.97 hm\(^{2}\) from 2004 to 2006. Cropland area in Baixiang decreased from 1996 to 1998 by a total of 129.89 hm\(^{2}\) and then remained relatively stable after 1998. The total carbon storage and variation in land use in the two counties displayed similar trends. Total carbon reserves in Julu increased by 2.76 \(\times \) 10\(^{4}\) tC (carbon equivalent), while those in Baixiang decreased by 0.63 \(\times \) 10\(^{4}\) tC. Carbon stock of built-up land in Julu and Baixiang increased by 2.44 \(\times \) 10\(^{4}\) and 1.22 \(\times \) 10\(^{4}\) tC, respectively.     

Analysis of two susceptibility SNPs in HLA region and evidence of interaction between rs6457617 in <Emphasis Type="BoldItalic">HLA-DQB1</Emphasis> and <Emphasis Type="BoldItalic">HLA-DRB1</Emphasis>*04 locus on Tunisian rheumatoid arthritis

Previous genomewide association studies (GWAS) and meta-analyses have enumerated several genes/loci in major histocompatibility complex region, which are consistently associated with rheumatoid arthritis (RA) in different ethnic populations. Given the genetic heterogeneity of the disease, it is necessary to replicate these susceptibility loci in other populations. In this case, we investigate the analysis of two SNPs, rs13192471 and rs6457617, from the human leukocyte antigen (HLA) region with the risk of RA in Tunisian population. These SNPs were previously identified to have a strong RA association signal in several GWAS studies. A case–control sample composed of 142 RA patients and 123 healthy controls was analysed. Genotyping of rs13192471 and rs6457617 was carried out using real-time PCR methods by TaqMan allelic discrimination assay. A trend of significant association was found in rs6457617 TT genotype with susceptibility to RA (\(P = 0.04\), \(p_{c} = 0.08\), \(\hbox {OR} = 1.73\)). Moreover, using multivariable analysis, the combination of rs6457617*TT–HLA-DRB1*\(04^{+}\) increased risk of RA (\(\hbox {OR} = 2.38\)), which suggest a gene–gene interaction event between rs6457617 located within the HLA-DQB1 and HLA-DRB1. Additionally, haplotypic analysis highlighted a significant association of rs6457617*T–HLA-DRB1*\(04^{+}\) haplotype with susceptibility to RA (\(P = 0.018\), \(p_{c} = 0.036\), \(\hbox {OR} = 1.72\)). An evidence of association was shown subsequently in \(\hbox {antiCCP}^{+}\) subgroup with rs6457617 both in T allele and TT genotype (\(P = 0.01\), \(p_{c} = 0.03\), \(\hbox {OR} = 1.66\) and \(P = 0.008\), \(p_{c} = 0.024\), \(\hbox {OR} = 1.28\), respectively). However, no association was shown for rs13192471 polymorphism with susceptibility and severity to RA. This study suggests the involvement of rs6457617 locus as risk variant for susceptibility/severity to RA in Tunisian population. Secondly, it highlights the gene–gene interaction between HLA-DQB1 and HLA-DRB1.     

A new indicator-based many-objective ant colony optimizer for continuous search spaces

In this paper, we propose a novel multi-objective ant colony optimizer (called iMOACO\(_{\mathbb {R}}\)) for continuous search spaces, which is based on ACO\(_{\mathbb {R}}\) and the R2 performance indicator. iMOACO\(_{\mathbb {R}}\) is the first multi-objective ant colony optimizer (MOACO) specifically designed to tackle continuous many-objective optimization problems (i.e., multi-objective optimization problems having four or more objectives). Our proposed iMOACO\(_{\mathbb {R}}\) is compared to three state-of-the-art multi-objective evolutionary algorithms (NSGA-III, MOEA/D and SMS-EMOA) and a MOACO algorithm called MOACO\(_{\mathbb {R}}\) using standard test problems and performance indicators taken from the specialized literature. Our experimental results indicate that iMOACO\(_{\mathbb {R}}\) is very competitive with respect to NSGA-III and MOEA/D and it is able to outperform SMS-EMOA and MOACO\(_{\mathbb {R}}\) in most of the test problems adopted.