Abstract: Along with the global aging of population, the number of people with somatic diseases is increasing, including such interrelated pathologies as obesity, osteoarthritis (OA) and osteoporosis (OP). The objective of the study is to examine the connection between body mass index (BMI), OA and bone mineral density (BMD) of lumbar spine, femoral neck and trabecular bone score (TBS) in postmenopausal women with OA. We have observed 359 postmenopausal women (50-89 years old) and divided them into four groups by age: 50-59 yrs, 60-69 yrs, 70-79 yrs and over 80 years old. In addition, according to the American College of Rheumatology (ACR) Clinical classification criteria for knee and hip OA, we divided them into 2 groups: group I – 117 females with symptomatic OA (including 89 patients with knee OA, 28 patients with hip OA) and group II –242 women with a normal functional activity of large joints. Analysis of data was performed taking into account their BMI, classified by World Health Organization (WHO). Diagnosis of obesity was established when BMI was above 30 kg/m2. In woman with obesity, a symptomatic OA was detected in 44 postmenopausal women (41.1%), a normal functional activity of large joints - in 63 women (58.9%). However, in women with normal BMI – 73 women, who account for 29.0% of cases, a symptomatic OA was detected. According to a chi-squared (χ2) test, a significantly higher level of BMI was detected in postmenopausal women with OA (χ2 = 5.05, p = 0.02). Women with a symptomatic OA had a significantly higher BMD of lumbar spine compared with women who had a normal functional activity of large joints. No significant differences of BMD of femoral necks or TBS were detected in either the group with OA or with a normal functional activity of large joints.
Abstract: The paper declares effects of exercise intervention of the research project “Basic research of balance changes in seniors”, granted by the Czech Science Foundation. The objective of the presented study is to define predictors, which influence bio-psycho-social consequences and effects of balance ability in senior 65 years old and above. We focused on the Fall-Efficacy Scale changes evaluation in seniors. Comprehensive hypothesis of the project declares, that motion uncertainty (dyskinesia) can negatively affect the well-being of a senior in bio-psycho-social context. In total, random selection and testing of 100 seniors (30 males, 70 females) from Prague and Central Bohemian region was provided. The sample was divided by stratified random selection into experimental and control groups, who underwent input and output testing. For diagnostics the methods of Medical Anamnesis, Functional anthropological examinations, Tinetti Balance Assessment Tool, SF-36 Health Survey, Anamnestic comparative self-assessment scale were used. Intervention method called "Life in Balance" based on yoga techniques was applied in four-week cycle. Results of multivariate regression were verified by repeated measures ANOVA: subject factor, phase of intervention (between-subject factor), body fluid (within-subject factor) and phase of intervention × body fluid interaction). ANOVA was performed with a repetition involving the factors of subjects, experimental/control group, phase of intervention (independent variable), and x phase interaction followed by Bonferroni multiple comparison assays with a test strength of at least 0.8 on the probability level p < 0.05. In the paper results of the first-year investigation of the three years running project are analysed. Results of balance tests confirmed no significant difference between females and males in pre-test. Significant improvements in balance and walking ability were observed in experimental group in females comparing to males (F = 128.4, p < 0.001). In the females control group, there was no significant change in post- test, while in the female experimental group positive changes in posture and spine flexibility in post-tests were found. It seems that females even in senior age react better to incentives of intervention in balance and spine flexibility. On the base of results analyses, we can declare the significant improvement in social balance markers after intervention in the experimental group (F = 10.5, p < 0.001). In average, seniors are used to take four drugs daily. Number of drugs can contribute to allergy symptoms and balance problems. It can be concluded that static balance and walking ability of seniors according Tinetti Balance scale correlate significantly with psychic and social monitored markers.
Abstract: This paper presents established 3n enumeration procedure for mixed integer optimization problems for solving multi-objective reliability and redundancy allocation problem subject to design constraints. The formulated problem is to find the optimum level of unit reliability and the number of units for each subsystem. A number of illustrative examples are provided and compared to indicate the application of the superiority of the proposed method.
Abstract: Medical, social, and economic relevance of osteoporosis is caused by reducing quality of life, increasing disability and mortality of the patients as a result of fractures due to the low-energy trauma. This study is aimed to examine the associations of metabolic syndrome components, bone mineral density (BMD) and trabecular bone score (TBS) in menopausal women with non-vertebral fractures. 1161 menopausal women aged 50-79 year-old were examined and divided into three groups: A included 419 women with increased body weight (BMI - 25.0-29.9 kg/m2), B – 442 females with obesity (BMI >29.9 kg/m2)i and C – 300 women with metabolic syndrome (diagnosis according to IDF criteria, 2005). BMD of lumbar spine (L1-L4), femoral neck, total body and forearm was investigated with usage of dual-energy X-ray absorptiometry. The bone quality indexes were measured according to Med-Imaps installation. All analyses were performed using Statistical Package 6.0. BMD of lumbar spine (L1-L4), femoral neck, total body, and ultradistal radius was significant higher in women with obesity and metabolic syndrome compared to the pre-obese ones (p
Abstract: Non-specific chronic low back pain (NSCLBP) is a common condition with no exact diagnosis and mechanism for its occurrence. Recently, different therapeutic exercises have taken into account to manage NSCLBP. So, the aim of this study has mainly been placed on comparing the effects of Pilates and Mackenzie exercises on quality of life (QOL) lumbar spine position sense (LSPS) in patients with NSCLBP. In this randomized clinical trial, 47 patients with NSCLBP were voluntarily divided into three groups of Pilates (n=16) (with mean age 37.1 ± 9.5 years, height 168.9 ± 7.4 cm, body mass 76.1 ± 5.9 k), McKenzie (n=15) (with mean age 42.7 ± 8.1 years, height 165.7 ± 6.8, body mass 74.1 ± 4.8 kg) and control (n=16) (with mean age 39.3 ± 9.8 years, height 168.1 ± 8.1 cm, body mass 74.2 ± 5.8 kg). Primary outcome included QOL and secondary was LSPS. Both variables were assessed by the WHOQOL-BREF questionnaires and electrogoniameter, respectively. The measurements were performed at baseline, following a 6-week intervention, and after a 4-week follow-up. The ANCOVA test at P < 0.05 was administrated to analyze the collected data using SPSS software. There was a statistically significant difference between experimental groups and the control group to improve QOL. But, no difference was seen regarding the effects of two exercises on LSPS (p < 0.05). Both Pilates and Mackenzie exercises demonstrated improvement in QOL after 6-week intervention and a 4-week follow-up while none of them considerably affected LSPS. Further studies are required to establish a supporting evidence for the effectiveness of two exercises on NSCLBP.
Abstract: Magnetic spinel ferrites are materials that possess size, magnetic properties and heating ability adequate for their potential use in biomedical applications. The Mn0.5Ga0.5Fe2O4 magnetic nanoparticles (MNPs) were synthesized by sol-gel method using citric acid as chelating agent of metallic precursors. The synthesized samples were identified by X-Ray Diffraction (XRD) as an inverse spinel structure with no secondary phases. Saturation magnetization (Ms) of crystalline powders was 45.9 emu/g, which was higher than those corresponding to GaFe2O4 (14.2 emu/g) and MnFe2O4 (40.2 emu/g) synthesized under similar conditions, while the coercivity field (Hc) was 27.9 Oe. The average particle size was 18 ± 7 nm. The heating ability of the MNPs was enough to increase the surrounding temperature up to 43.5 °C in 7 min when a quantity of 4.5 mg of MNPs per mL of liquid medium was tested. Cytotoxic effect (hemolysis assay) of MNPs was determined and the results showed hemolytic values below 1% in all tested cases. According to the results obtained, these synthesized nanoparticles can be potentially used as thermoseeds for hyperthermia therapy.
Abstract: Among the different cancer treatments that are currently used, hyperthermia has a promising potential due to the multiple benefits that are obtained by this technique. In general terms, hyperthermia is a method that takes advantage of the sensitivity of cancer cells to heat, in order to damage or destroy them. Within the different ways of supplying heat to cancer cells and achieve their destruction or damage, the use of magnetic nanoparticles has attracted attention due to the capability of these particles to generate heat under the influence of an external magnetic field. In addition, these nanoparticles have a high surface area and sizes similar or even lower than biological entities, which allow their approaching and interaction with a specific region of interest. The most used magnetic nanoparticles for hyperthermia treatment are those based on iron oxides, mainly magnetite and maghemite, due to their biocompatibility, good magnetic properties and chemical stability. However, in order to fulfill more efficiently the requirements that demand the treatment of magnetic hyperthermia, there have been investigations using ferrites that incorporate different metallic ions, such as Mg, Mn, Co, Ca, Ni, Cu, Li, Gd, etc., in their structure. This paper reports the synthesis of nanosized MgxMn1-xFe2O4 (x = 0.3 and 0.4) ferrites by sol-gel method and their evaluation in terms of heating capability and in vitro hemolysis to determine the potential use of these nanoparticles as thermoseeds for the treatment of cancer by magnetic hyperthermia. It was possible to obtain ferrites with nanometric sizes, a single crystalline phase with an inverse spinel structure and a behavior near to that of superparamagnetic materials. Additionally, at concentrations of 10 mg of magnetic material per mL of water, it was possible to reach a temperature of approximately 45°C, which is within the range of temperatures used for the treatment of hyperthermia. The results of the in vitro hemolysis assay showed that, at the concentrations tested, these nanoparticles are non-hemolytic, as their percentage of hemolysis is close to zero. Therefore, these materials can be used as thermoseeds for the treatment of cancer by magnetic hyperthermia.
Abstract: This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3n enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3n integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.
Abstract: Osteoporosis and obesity are widespread diseases in people over 50 years associated with changes in structure and body composition. Нigher body mass index (BMI) values are associated with greater bone mineral density (BMD). However, trabecular bone score (TBS) indirectly explores bone quality, independently of BMD. The aim of our study was to evaluate the relationship between the BMD and TBS parameters in Ukrainian men suffering from obesity. We examined 396 men aged 40-89 years. Depending on their BMI all the subjects were divided into two groups: Group I – patients with obesity whose BMI was ≥ 30 kg/m2 (n=129) and Group II – patients without obesity and BMI of < 30 kg/m2 (n=267). The BMD of total body, lumbar spine L1-L4, femoral neck and forearm were measured by DXA (Prodigy, GEHC Lunar, Madison, WI, USA). The TBS of L1- L4 was assessed by means of TBS iNsight® software installed on DXA machine (product of Med-Imaps, Pessac, France). In general, obese men had a significantly higher BMD of lumbar spine L1-L4, femoral neck, total body and ultradistal forearm (p < 0.001) in comparison with men without obesity. The TBS of L1-L4 was significantly lower in obese men compared to non-obese ones (p < 0.001). BMD of lumbar spine L1-L4, femoral neck and total body significantly differ in men aged 40-49, 50-59, 60-69, and 80-89 years (p < 0.05). At the same time, in men aged 70-79 years, BMD of lumbar spine L1-L4 (p=0.46), femoral neck (p=0.18), total body (p=0.21), ultra-distal forearm (p=0.13), and TBS (p=0.07) did not significantly differ. A significant positive correlation between the fat mass and the BMD at different sites was observed. However, the correlation between the fat mass and TBS of L1-L4 was also significant, though negative.
Abstract: Osteoporosis is one of the important problems in postmenopausal women due to an increased risk of sudden and unexpected fractures. This study is aimed to determine the connection between bone mineral density (BMD) and trabecular bone score (TBS) in Ukrainian women suffering from metabolic syndrome. Participating in the study, 566 menopausal women aged 50-79 year-old were examined and divided into two groups: Group A included 336 women with no obesity (BMI ≤ 29.9 kg/m2), and Group B – 230 women with metabolic syndrome (diagnosis according to IDF criteria, 2005). Dual-energy X-ray absorptiometry was used for measuring of lumbar spine (L1-L4), femoral neck, total body and forearm BMD and bone quality indexes (last according to Med-Imaps installation). Data were analyzed using Statistical Package 6.0. A significant increase of lumbar spine (L1-L4), femoral neck, total body and ultradistal radius BMD was found in women with metabolic syndrome compared to those without obesity (p < 0.001) both in their totality and in groups of 50-59 years, 60-69 years, and 70-79 years. TBS was significantly higher in non-obese women compared to metabolic syndrome patients of 50-59 years and in the general sample (p < 0.05). Analysis showed significant positive correlation between body mass index (BMI) and BMD at all levels. Significant negative correlation between BMI and TBS (L1-L4) was established. Despite the fact that BMD indexes were significantly higher in women with metabolic syndrome, the frequency of vertebral and non-vertebral fractures did not differ significantly in the groups of patients.
Abstract: In the diagnostics of osteoporosis, the gold standard is considered to be bone mineral density; however, X-ray densitometry is not an accurate indicator of osteoporotic fracture risk under all circumstances. In this regard, the search for new methods that could determine the indicators not only of the mineral density, but of the bone tissue quality, is a logical step for diagnostic optimization. One of these methods is the evaluation of trabecular bone quality. The aim of this study was to examine the quality and mineral density of spine bone tissue, femoral neck, and body composition of women depending on the duration of the postmenopausal period, to determine the correlation of body fat with indicators of bone mineral density and quality. The study examined 179 women in premenopausal and postmenopausal periods. The patients were divided into the following groups: Women in the premenopausal period and women in the postmenopausal period at various stages (early, middle, late postmenopause). A general examination and study of the above parameters were conducted with General Electric X-ray densitometer. The results show that bone quality and mineral density probably deteriorate with advancing of postmenopausal period. Total fat and lean mass ratio is not likely to change with age. In the middle and late postmenopausal periods, the bone tissue mineral density of the spine and femoral neck increases along with total fat mass.
Abstract: In the case of high-speed fighter aircrafts, seat ejection is designed mainly for the safety of the pilot in case of an emergency. Strong windblast due to the high velocity of flight is one main difficulty in clearing the tail of the aircraft. Excessive G-forces generated, immobilizes the pilot from escape. In most of the cases, seats are ejected out of the aircrafts by explosives or by rocket motors attached to the bottom of the seat. Ejection forces are primarily in the vertical direction with the objective of attaining the maximum possible velocity in a specified period of time. The safe ejection parameters are studied to estimate the critical time of ejection for various geometries and velocities of flight. An equivalent analytical 2-dimensional biomechanical model of the human spine has been modelled consisting of vertebrae and intervertebral discs with a lumped mass approach. The 24 vertebrae, which consists of the cervical, thoracic and lumbar regions, in addition to the head mass and the pelvis has been designed as 26 rigid structures and the intervertebral discs are assumed as 25 flexible joint structures. The rigid structures are modelled as mass elements and the flexible joints as spring and damper elements. Here, the motions are restricted only in the mid-sagittal plane to form a 26 degree of freedom system. The equations of motions are derived for translational movement of the spinal column. An ejection force with a linearly increasing acceleration profile is applied as vertical base excitation on to the pelvis. The dynamic vibrational response of each vertebra in time-domain is estimated.
Abstract: Wireless sensor networks can be tiny, low cost, intelligent sensors connected with advanced communication systems. WSNs have pulled in significant consideration as a matter of fact that, industrial as well as medical solicitations employ these in monitoring targets, conservational observation, obstacle exposure, movement regulator etc. In these applications, sensor hubs are thickly sent in the unattended environment with little non-rechargeable batteries. This constraint requires energy-efficient systems to drag out the system lifetime. There are redundancies in data sent over the network. To overcome this, multiple virtual spine scheduling has been presented. Such networks problems are called Maximum Lifetime Backbone Scheduling (MLBS) problems. Though this sleep wake cycle reduces radio usage, improvement can be made in the path in which the group heads stay selected. Cluster head selection with emphasis on geometrical relation of the system will enhance the load sharing among the nodes. Also the data are analyzed to reduce redundant transmission. Multi-hop communication will facilitate lighter loads on the network.
Abstract: Transforaminal lumbar interbody fusion (TLIF) surgeries have nowadays became popular for treatment of degenerated spinal disorders. The interbody fusion technique like TLIF maintains load bearing capacity of the spine and a suitable disc height. Currently many techniques have been introduced to cure Spondylolisthesis. This surgery provides greater rehabilitation of degenerative spines. While performing this TLIF surgery existing methods use guideway, which is a troublesome surgery technique as the use of two separate instruments is required to perform this surgery. This paper presents a concept which eliminates the use of guideway. This concept also eliminates problems that occur like reverting the cage. The concept discussed in this paper also gives high accuracy while performing surgery.
Abstract: A systematic study was conducted to explore the photocatalytic reduction of carbon dioxide (CO2) into methanol on TiO2 loaded copper ferrite (CuFe2O4) photocatalyst under visible light irradiation. The phases and crystallite size of the photocatalysts were characterized by X-ray diffraction (XRD) and it indicates CuFe2O4 as tetragonal phase incorporation with anatase TiO2 in CuFe2O4/TiO2 hetero-structure. The XRD results confirmed the formation of spinel type tetragonal CuFe2O4 phases along with predominantly anatase phase of TiO2 in the CuFe2O4/TiO2 hetero-structure. UV-Vis absorption spectrum suggested the formation of the hetero-junction with relatively lower band gap than that of TiO2. Photoluminescence (PL) technique was used to study the electron–hole (e−/h+) recombination process. PL spectra analysis confirmed the slow-down of the recombination of electron–hole (e−/h+) pairs in the CuFe2O4/TiO2 hetero-structure. The photocatalytic performance of CuFe2O4/TiO2 was evaluated based on the methanol yield with varying amount of TiO2 over CuFe2O4 (0.5:1, 1:1, and 2:1) and changing light intensity. The mechanism of the photocatalysis was proposed based on the fact that the predominant species of CO2 in aqueous phase were dissolved CO2 and HCO3- at pH ~5.9. It was evident that the CuFe2O4 could harvest the electrons under visible light irradiation, which could further be injected to the conduction band of TiO2 to increase the life time of the electron and facilitating the reactions of CO2 to methanol. The developed catalyst showed good recycle ability up to four cycles where the loss of activity was ~25%. Methanol was observed as the main product over CuFe2O4, but loading with TiO2 remarkably increased the methanol yield. Methanol yield over CuFe2O4/TiO2 was found to be about three times higher (651 μmol/gcat L) than that of CuFe2O4 photocatalyst. This occurs because the energy of the band excited electrons lies above the redox potentials of the reaction products CO2/CH3OH.
Abstract: Chromite ores are primarily used for extraction of chromium, which is an expensive metal. For low grade chromite ores (containing less than 40% Cr2O3), the chromium extraction is not usually economically viable. India possesses huge quantities of low grade chromite reserves. This deposit can be utilized after proper physical beneficiation. Magnetic separation techniques may be useful after reduction for the beneficiation of low grade chromite ore. The sample collected from the sukinda mines is characterized by XRD which shows predominant phases like maghemite, chromite, silica, magnesia and alumina. The raw ore is crushed and ground to below 75 micrometer size. The microstructure of the ore shows that the chromite grains surrounded by a silicate matrix and porosity observed the exposed side of the chromite ore. However, this ore may be utilized in refractory applications. Chromite ores contain Cr2O3, FeO, Al2O3 and other oxides like Fe-Cr, Mg-Cr have a high tendency to form spinel compounds, which usually show high refractoriness. Initially, the low grade chromite ore (containing 34.8% Cr2O3) was reduced at 1200 0C for 80 minutes with 30% coke fines by weight, before being subjected to magnetic separation. The reduction by coke leads to conversion of higher state of iron oxides converted to lower state of iron oxides. The pre-reduced samples are then characterized by XRD. The magnetically inert mass was then reacted with 20% MgO by weight at 1450 0C for 2 hours. The resultant product was then tested for various refractoriness parameters like apparent porosity, slag resistance etc. The results were satisfactory, indicating that the resultant spinel compounds are suitable for refractory applications for elevated temperature processes.
Abstract: Mineral mapping on the Moon surface provides the clue to understand the origin, evolution, stratigraphy and geological history of the Moon. Recently, reflectance imaging spectroscopy plays a significant role in identifying minerals on the planetary surface in the Visible to NIR region of the electromagnetic spectrum. The Moon Mineralogy Mapper (M3) onboard Chandrayaan-1 provides unprecedented spectral data of lunar surface to study about the Moon surface. Here we used the M3 sensor data (hyperspectral imaging spectroscopy) for analysing mineralogy of Orientale basin region on the Moon surface. Reflectance spectrums were sampled from different locations of the basin and continuum was removed using ENvironment for Visualizing Images (ENVI) software. Reflectance spectra of unknown mineral composition were compared with known Reflectance Experiment Laboratory (RELAB) spectra for discriminating mineralogy. Minerals like olivine, Low-Ca Pyroxene (LCP), High-Ca Pyroxene (HCP) and plagioclase were identified. In addition to these minerals, an unusual type of spectral signature was identified, which indicates the probable Fe-Mg-spinel lithology in the basin region.
Abstract: NiFe2O4 (nickel ferrite), ZnFe2O4 (zinc ferrite) and
Ni0.5Zn0.5Fe2O4 (nickel-zinc ferrite) were prepared by
mechanochemical route in a planetary ball mill starting from mixture
of the appropriate quantities of the Ni(OH)2/Fe(OH)3,
Zn(OH)2/Fe(OH)3 and Ni(OH)2/Zn(OH)2/Fe(OH)3 hydroxide
powders. In order to monitor the progress of chemical reaction and
confirm phase formation, powder samples obtained after 25 h, 18 h
and 10 h of milling were characterized by X-ray diffraction (XRD),
transmission electron microscopy (TEM), IR, Raman and Mössbauer
spectroscopy. It is shown that the soft mechanochemical method, i.e.
mechanochemical activation of hydroxides, produces high quality
single phase ferrite samples in much more efficient way. From the IR
spectroscopy of single phase samples it is obvious that energy of
modes depends on the ratio of cations. It is obvious that all samples
have more than 5 Raman active modes predicted by group theory in
the normal spinel structure. Deconvolution of measured spectra
allows one to conclude that all complex bands in the spectra are made
of individual peaks with the intensities that vary from spectrum to
spectrum. The deconvolution of Raman spectra allows to separate
contributions of different cations to a particular type of vibration and
to estimate the degree of inversion.
Abstract: Recently attention has been focused on incomplete
spinal cord injuries (SCI) to the central spine caused by pressure on
parts of the white matter conduction pathway, such as the pyramidal
tract. In this paper, we focus on a training robot designed to assist with
primary walking-pattern training. The target patient for this training
robot is relearning the basic functions of the usual walking pattern; it is
meant especially for those with incomplete-type SCI to the central
spine, who are capable of standing by themselves but not of
performing walking motions. From the perspective of human
engineering, we monitored the operator’s actions to the robot and
investigated the movement of joints of the lower extremities, the
circumference of the lower extremities, and exercise intensity with the
machine. The concept of the device was to provide mild training
without any sudden changes in heart rate or blood pressure, which will
be particularly useful for the elderly and disabled. The mechanism of
the robot is modified to be simple and lightweight with the expectation
that it will be used at home.
Abstract: Cole-Cole parameters of 40 post-menopausal women
are compared with their DEXA bone mineral density measurements.
Impedance characteristics of four extremities are compared; left and
right extremities are statistically same, but lower extremities are
statistically different than upper ones due to their different fat
content. The correlation of Cole-Cole impedance parameters to bone
mineral density (BMD) is observed to be higher for dominant arm.
With the post-menopausal population, ANOVA tests of the dominant
arm characteristic frequency, as a predictor for DEXA classified
osteopenic and osteoporic population around lumbar spine, is
statistically very significant. When used for total lumbar spine
osteoporosis diagnosis, the area under the Receiver Operating Curve
of the characteristic frequency is 0.830, suggesting that the Cole-Cole
plot characteristic frequency could be a useful diagnostic parameter
when integrated into standard screening methods for osteoporosis.
Moreover, the characteristic frequency can be directly measured by
monitoring frequency driven angular behavior of the dominant arm
without performing any complex calculation.