Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
BULGARIAN SOCIETY OF BIOMECHANICS
INSTITUTE OF MECHANICS, BAS
„Days of Biomechanics - 2014”
20.11-21.11.2014 г.
BOOK OF ABSTRACTS
Organizing Committee:
Stoyan Stoytchev
Svetoslav Nikolov
Rositsa Raikova
Gergana Nikolova
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Study of the blood flow in the common carotid artery bifurcation
N. Antonova1, X. Dong2, I.Velcheva3, E. Kaliviotis4, P. Tosheva1
1
Department of Biomechanics, Institute of Mechanics, Bulgarian Academy of Sciences, 1113
Sofia Acad. G. Bonchev str., bl. 4, Bulgaria
2
School of Civil Engineering, Tianjin University, China, 300072
3
Department of Neurology, University Hospital of Neurology and Psychiatry
“St. Naum”, Medical University, Sofia, Bulgaria
4
Department of Engineering, University College London, London, UK
Blood flow in the carotid artery bifurcation is studied on the basis of the
Navier-Stokes equations performing numerical simulations by a finite volume method
and considering one wave period. Four different cases of the common carotid
bifurcation were examined: without stenoses, with one, two and three stenoses. Based
on geometry reconstruction a mesh generation is done. The case studies are based on
different anatomies presented by the one, two or three stenoses of common carotid
bifurcation vessel. The physiological geometry can be imported into a CFD solver.
The numerical results of the blood flow in the common carotid bifurcation
give detail picture of the axial velocity and WSS distribution. For the case of carotid
bifurcation without stenoses results for the axial velocity distribution are presented in
six characteristic time points T=0 s, 0.1s 0.2s, 0.3s, 0.4s, 0.5s.
The results show that the blood flow in the carotid bifurcation is unsteady and
the flow disturbances depend on the time and type of the stenoses. The pattern of the
velocity and the WSS are obtained and comparison of the peak wall shear stress
(WSS) is done for the four considered cases. The recirculation zone behind the
bifurcation and stenosis is the area with low shear stress. The peak WSS are
increasing and the maximum is being achieved earlier with increase of the number of
stenoses. The dependence of the peak WSS on time reflects the changes due to the
velocity of the pulse wave. Comparison of the peak wall shear stress for the four
different cases (without stenoses and with 1, 2 and 3 stenoses correspondingly)
reveals the peak WSS maximum value at the characteristic point of T=0.2 s for the
cases with two and three stenoses. In the case of a bifurcation without or with one
stenosis, the maximum WSS is achieved with a delay of 0.02 seconds compared to the
other two cases. The differences in the maximal WSS value (1.8 Pa) for the cases with
1, 2 and 3 stenoses in comparison to the case without stenosis (1.5 Pa) are observed at
the characteristic point of the pulse wave at T= 0.45 s.
The results could play an important role in understanding the formation,
growth, rupture and prognosis of damage of the vessel wall and may be a practical
tool for planning treatment and follow-up of patients after neurosurgical or
endovascular interventions with 3D angiography. The results also present the potential
of using numerical simulation to provide existing clinical prerequisites for diagnosis
and therapeutic treatment.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Gait control of humans with assistive devices
R. Antonova, S. Karastanev, P. Kiriazov
Department of Biomechanics, Institute of Mechanics, Bulgarian Academy of Sciences,
1113 Sofia, Acad. G. Bonchev str., bl. 4, Bulgaria
Gait control is a complex process which has an intrinsic focus on planning,
execution and adaptation of the whole-body movement by the CNS. An underlying
assumption in our work is that the motion of healthy people is optimal with respect to
speed, positioning accuracy, and energy expenditure. Motor control may become
much more complicated for people having stroke, traumas or neurological diseases.
Generally speaking, we need to consider complicated optimisation problems for
complex neuro-musculoskeletal systems.
Patients need to restore their motor control functions and motion performance
to the best possible level. Various assistive devices may be used for restoration of
human movement abilities: crutches, prostheses, passive and active orthoses, robotic
exoskeletons, etc. To meet the above challenges, it is very important how to properly
decompose complex modelling, identification and optimisation tasks into sets of much
easier-to-find satisfactory solutions. It is of primary importance to properly identify
the structure of the walking dynamics for every locomotion phase and the
corresponding control functions. At first, a set of variables (controlled outputs) that
best characterize human dynamic performance in the locomotion task has to be
defined. Second, we have to find those driving forces/torques that mostly contribute to
the dynamic performance in this task.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Mathematical model for estimating of external mechanical work in step test
Z. Arakchiyski
National Sports Academy “V. Levski”, Sofia, Bulgaria
Introduction
Typically, the options for determining the physical condition are based on the use of
bicycle ergometers, treadmills and a number of devices for carrying out the step tests. Interest
is the development of method, which is based on a known step tests for determination of the
indirect VO2 max and allow the calculation of PWC170. Results of another study, where
mechanical work for steps is based on a variant of equation, proposed by the author, are
reported to the 4th Congress of FIEP [1] and World Congress of Performance Analysis of
Sport VІІІ [2]. The aim of this study was to develop an equation to quantify the external
mechanical work in step test, enabling calculation of PWC170 using the classical Margaria
Step Test, considering the rhythmicity of the test performance.
Methods
15 players from the senior team of FC "CSKA" - Sofia with bodyweight 77.5 ± 5.3 kg
and height 183.3 ± 4.0 cm were studied. All test persons are loaded once by the aerobic steptest of Margaria at platform height 0.4 m. The protocol of the conducted a two-stage test is 15
steps per minute during the first 5-minute load and 25 steps per minute for the second 5minute load. Rhythm is determined by a metronome. Heart rate (HR) was measured with a
Sport Tester PE-3000. By visual assessment into protocol is noted in two categories rhythm of
execution of movements during the test, which are also registered with a standard video
camera for subsequent comparisons. Results were compared with these from bicycle
ergometer test, carried out two days before step test. For analytical calculation of the
mechanical work on Margaria step-test, one step is divided into two phases - move up and
down.
Results
The results from bicycle ergometer test and step test for PWC170 form a two group.
In the first group, the differences are in the range -1 – +2 %, wile in the other group is 5 – 8 %
higher in step test. The significantly higher values for the second group are due to the marked
unrhythmic execution of step test. This is most often in the downward movement, when the
player comes down for a shorter time than is provided in the protocol. In this case is
performed less muscle work in alighting from the platform, leading to less fatigue, lower
values of heart rate and ultimately to a higher calculated working capacity. The introduced
coefficient reduces the differences between the two tests in these cases within 3%.
Discussion/Conclusion
External work is the work performed by external forces – mainly from the ground – to
move the center of mass through a displacement. The proposed model is based on several
assumptions. One is that external work satisfactorily estimates the total mechanical work
performed on the body. Another assumption is that the time of downward movement first
single support is equally for all test steps and the center of mass motion is uniformly
accelerated. This allows easily estimating the downward movement external work and gives
us satisfactorily results for the purposes of this study. Finally, the relevance of estimates of
mechanical work performed on the body to actual work performed by the muscles is based on
presume that there is little mechanical energy storage and little muscular co-contraction
during step. These latter suppositions are legitimate sources of error, but they also apply to all
other non-invasive estimates of mechanical work. Given the existing methods for determining
the mechanical work on step loads, this work is original and more accurate method that takes
into account not only the influence of negative work, but also acceleration of the center of
mass in one step.
References
[1] Pavlova, E., Uzunova, G., Arakchiyski, Z. (2007). Margaria Step Test for Estimating
WC170. 4th FIEP European Congress Physical Education and Sports, 160 – 166. ISBN: 97880-89324-00-2.
[2] Pavlova, E., Uzunova, G., Arakchiyski, Z. (2008). Comparison between PWC170
estimated by equation and Krastev’s table in step test. World Congress of Performance
Analysis of Sport VІІІ, 123 – 127, ISBN: 19012880011.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
A study of indomethacin release from polymersome nanoparticles solution under
the presence of ethanol
R. Blagoeva1, A. Nedev1 , V. Michailova2
Institute of Mechanics – Bulgarian Academy of Sciences, Acad. G. Bonchev Str.,
bl. 4, 1113 Sofia
2
Faculty of Pharmacy – Medical University, 2 Dunav Str., 1000 Sofia
1
A study of indomethacin release in vitro from polymersome nanoparticles
solution is presented.In vitro release was conducted in distilled water
containing different ethanol content, as well as different rate of ethanol
injection, using the dialysis tube method.
The recently proposed by the author’s mathematical model for drug
release was validated under the obtained experimental results. It was used for
establishing the effect of ethanol concentration and rate of injection in the
nanoparticles solution upon drug release. Numerical simulation of
indomethacin release was performed within a period of 2 days in the case of
membrane presence, as well as when neglecting it.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Traffic jams on chains with a shortcut of arbitrary length
(in the framework of TASEP - a model of biological transport)
N. Zh. Bunzarova 1,2, N. C. Pesheva2 , J. G. Brankov 1,2
1
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,
141980 Dubna, Russia
2
Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
We report here results of our study on the appearance of traffic jams on chains
with a shortcut between two simple chain segments in the framework of the Totally
Asymmetric Simple Exclusion Process (TASEP) in the maximal current phase. We
study this problem both numerically (by numerical simulations) and analytically
within the mean-field approximation (by the effective rates approximation (ERA)
method, developed in our previous study of TASEP on simple networks). The
conditions for the occurrence of traffic jams are determined for arbitrary length of the
shortcut. The problem presents interest on its own since the conditions for coexistence
of low- and high-density phases are essentially different from those for a simple chain
between two reservoirs. In the considered case of equal probability for a particle to
take the main segment or the shortcut, the model displays an unexpected feature: the
current through the longer shunted segment is larger than the current through the
shortcut. Our findings are of interest to vehicular traffic jams on single-lane roads but
they also may have relevance to biological transport processes - phenomena like
crowding of molecular motors moving along twisted proto filaments.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Efficient control learning in sport and rehabilitation
D. Despotova, P. Kiriazov, G. Nikolova
Department of Biomechanics, Institute of Mechanics, Bulgarian Academy of Sciences,
1113 Sofia, Acad. G. Bonchev str., bl. 4, Bulgaria
Motivation
Normally, goal-directed voluntary movements are performed optimally as
regards motion speed, positioning accuracy, and energy expenditure. The control
functions (neural signals to muscles) are to be learnt and optimised with respect to
these performance indices.
Method
In our study, a natural approach for efficient motor learning is proposed.
Optimal control functions have a 3-step shape and a set of key parameters is found for
describing them. Those are intrinsic parameters human has to learn in dynamic pointto-point motion tasks. We make corrections in the control parameters until reach the
target, applying an optimal, convergent and natural learning algorithm.
Results
Our control learning approach was applied to dynamic models of human
body/limbs with two, three, and six degrees of freedom. In the computer simulations,
we verified that the control learning converges and the number of trials is very small.
In addition, we did some real (able-bodied) experiments with rapid aiming
movements of the arm and they confirm the feasibility of the proposed approach.
Discussion
The neural structures that compute the required control forces are the so-called
internal models presenting a fundamental part of the voluntary motor control. We
believe that the proposed approach can be used to rebuild such models (cortical
reorganization) by proper training procedures.
Conclusion
Thus we have the necessary scientific basis to develop efficient rehabilitation
for various movement disorders and various motion tasks in activities of daily living.
The proposed concepts and algorithms could be very useful in designing also
adequate control strategies for efficient motion analysis and sport performance
optimization.
Key words
goal-directed movements, control optimization;
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Prognosis, monitoring and prevention of the risk of postoperative infectious
I. Edissonov, S.Ranchev
Institute of Mechanic and Biomechanics. Bulgarian Academy of Science
Acad. G. Bonchev str., bl. 4, 1113 Sofia, Bulgaria
In light of the current understanding of the ethnological determinants and the
pathophysiological mechanisms, responsible for developing of postoperative
infectious complications, the authors present an own predictive model and report their
two years experience findings. The main objective of our prospective study was to
establish a well – motivated parameters for early identification of an risk patient
populations with a predictable response to the surgery intervention and to investigate
the benefits of appropriate prevention steps. Our initial attempts to use indicators,
predicting the host response to major surgical intervention and our first results has
proved the here discussed complex approach beneficial in the reduction of the
postoperative infectious mortality and morbidity frequencies and in the early
diagnosis of the postoperative infectious complications.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Computational modeling of blood flow dynamics in brain aneurysms
I. Georgiev1, N. Nikolov2, E. Nikolova2
1
Institute of Mathematics and Informatics, Bulgarian Academy of
Sciences, Sofia, Bulgaria
2
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Brain aneurysms are localized dilations of the walls of brain blood vessels, due
to the structural weakening of the walls. Mostly they lead to sudden death, through
rupture causing massive hemorrhage. Currently, the investigations of such
pathogenesis have used various methodologies, from in vitro to in vivo models, but
most studies are related to computational modeling and numerical simulations (or
CFD (computational fluid dynamics) of blood flow, since it is now well established
that blood hemodynamics plays a major role in the development, progression and
rupture of aneurysms.
In this work we present numerical simulations of blood flow dynamics in ideal
and real aneurysms using a commercial software ANSYS and a specific medical
software MEDVIS 3D. For the simulations we consider the blood as Newtonian as
well as non-Newtonian fluid, and the artery/aneurysm wall –as “rigid” as well as with
linear elastic properties.
Our interest is focused on the distributions of tangential stresses on the wall
and vortex appearance in the aneurysm dome as possible predictors for the rupture of
the brain aneurysms.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Rheological and electrical characteristics of RBC suspensions after treatment
with different types of polymeric nanoparticles solutions of poly(acrilic)acid
I. Ivanov1,2, N. Antonova1
1
Department of Biomechanics, Institute of Mechanics, Bulgarian Academy of Sciences,
1113 Sofia, Acad. G. Bonchev str., bl. 4, Bulgaria
2
National Sports Academy “V. Levski”, Sofia, Bulgaria
The study of different types of nanomaterials increases progressively in
relation to their huge application in various fields of biology, medicine and
technology. The aim of the work is to study the influence of the shape, concentration
and molecular weight of different types of nanoparticles on blood rheological
behavior and electrical properties of RBC suspensions. Three different types of
nanoparticles suspended in 0.9% NaCl solutions were added to RBC suspensions: (i) a
new core–shell type star polymer whose interior forms hyperbranched polystyrene
bearing arms of poly(acrylic acid) with molecular weight Mn=56 920 kDa (AK); (ii)
linear polyacrylic chains with average molecular weights Mn=225000, 20000 and
6000 (PAA); (iii) polymeric micelles with a mixed shell. The apparent RBC
suspension viscosity η and electrical conductivity σ were measured in parallel by the
rotational viscometer LS30 Contraves. RBC suspensions conductivity is quantified at
a steady flow conditions by means of electrorheological techniques. It includes a resin
replica of the Couette type measuring system MS 1/1 of the rheometer with a pair of
platinum electrodes embedded into the wall of the measuring cup. These two
parameters were considered as characteristics of the changes in the RBC suspensions’
structure and cell interactions. The obtained results showed that the addition of the
studied nanoparticles influence the apparent viscosity and electrical conductivity of
RBC suspensions. The rheological and electrical properties of the RBC suspensions
show direct relation with the shape, molecular weight, concentrations and the type of
nanoparticles.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Mechanical behaviour of explanted hernia meshes
M. Kirilova-Doneva1,2, D. Pashkouleva2, V. Kavardzhikov2, S.Sopotenski3,
G. Petrova1, N. Gerasimov4
1
Medical University - Sofia, Faculty of Pharmacy, Sofia, Bulgaria
Department of Biomechanics, Institute of Mechanics, Bulgarian Academy of Sciences,
1113 Sofia, Acad. G. Bonchev str., bl. 4, Bulgaria
3
UMH „N.I.Pirogov“ , Sofia
4
Dobrich Farma –Dobrich, Bulgaria
2
One of the problems which influence the outcome of operations is age-related
variability of mechanical properties of hernia meshes. The effects of age on the
mechanical properties of hernia meshes depend on their structure, pore size, type of
used material, filament diameter, coatings of the surface or number of layers.
Understanding of time-dependent variations of mechanical properties of hernia
meshes is important for predicting their mechanical behaviour after long-term
implantation in organism. The aim of this study is to quantify the long-term changes
in mechanical properties of explanted polypropylene hernia meshes and compare
them with properties of three commercially available hernia meshes as well as human
abdominal fascia.
Tensile test was applied to mesh specimens from Surgimech(SM),
Tecnomesh(TM) and Surgipro(SP) before and after their expiration date. The
specimens were cut along the rows of loops(T direction) and parallel to the column of
loops (L direction). From the stress - stretch ratio curves the secant modulus at 5%
strain were determined. The mechanical properties of fascia were studied using 84
samples taken from 13 donors aged 45 - 87 years and divided into three groups - up to
64 years (group A), 65-80 years (group B) and 81-90 years (group C). The samples
were cut along the fibers and perpendicular to them. Tensile tests were performed.
The average value of secant modulus for three meshes was compared with secant
modulus of explanted meshes and human abdominal fascia.
Time-dependent variations in elasticity of polypropylene meshes were
pronounced. The results reveal asymmetry of elasticity in chosen directions which
changes with time. The elastic properties of hernia meshes in L direction approaches
the elastic properties of the fascia in direction parallel to fibers for 45-64 years old
patients. In T direction the value of secant modulus for all meshes exceeds
considerably the physiological elasticity of investigated fascia.
This study adds new data for the material properties of hernia meshes which
can be used not only for prevention of material related complications but also in
mathematical models of herniated abdominal wall.
Key words
hernia meshes, mechanical compatibility, age-related changes
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Osteogenesis imperfecta – mutagenesis and biomechanical material tissue
properties
M. Kuklik1,2, M. Tothova3, V. HeleŠic3, I. Marik4
1
Genetic department, Prague, CZ
Department of Molecular Endocrinology, Institute of Endocrinology, Prague, CZ
3
GENVIA, Genetic laboratory, Prague, CZ
4
Ambulant Centre for Defects of Locomotor Apparatus, Prague, CZ
2
Introduction
Osteogenesis imperfecta (OI) is the group very heterogenous diseases, but in most
cases determined mutation in the alfa 1 or alfa 2 chain for bone (pro)collagen, type I. Genetic
determined disease OI is widespread and common in all populations of the world. We don´t
know the predilection for some ethnical groups. The frequency of disease is unclear (1:50 000
?) and many cases fade the diagnostics. The mild cases are diagnosed as osteoporosis at an
advanced age. It is impairment of osteoblasts and at many patients from the osteoblastic
lines derivated cells. The disease is previously advanced from the bone collagen I. The
diagnostics on the molecular level is important and facilitates the treatment. Bone is present
as non mature tissue, typical is liability to fractures and microfractures with tendency to
skeleton deformities. Sillence (1979) recognised according to different phenotypes of OI type
I,II,III and IV, which are determined by collagen mutations. The other very rare (together 11
types OI) are the results of gene mutations for non – collagen proteins. The mutations in the
alfa 1 chain are most often, the second one are alfa 2 mutations. The heredity is mostly
autosomal dominant (AD), some cases are autosomal recessive (AR) type, namely at non –
collagenous peculiary types of OI. This is order pathobiomechanical consequencies leading to
instability triple helix collagen and insuficient ossification and calcification. The mutations
caused lower melting temperature ™ DNA – lower termoresistance double helix DNA.
Contemporary is noted the lower melting temperature of collagen macromolecules
heterotrimers. The collagen macromolecule stability is totally affected.
Methodology
Our aim is detection the point mutations alfa 1 and alfa 2 procollagen chains. From
the methodic point of view DNA isolation and their analysis from peripheral blood samples of
36 probands were analysed with using PCR methods and following direct PCR products
sequencing. The investigation was focused on the causative mutations detections in coding
gene regions for COLI alfa 1 and alfa 2 chains that are responsive for OI type I, II, III and IV.
The methods are provided according to Gajk-Galicka et. al. 2002 and Politts, R. 2006.
Results
In the cohort 36 OI patients the causative mutations were detected at 32 paients and
negative were 4 patients. The most common are mutations in glycine triplets – 12 cases and
each one mutation is located to the alfa 1 chain. At 24 from 32 positive mutations are
displaced at alfa 1 chain only 8 cases at alfa 2 chain. Another mutations changes were
detected in codons for proline, asparagin, arginin, glutamin and tyrosin. Accidentally we
found suspected splicing error. All of detected mutations were in heterozygous compositions.
Discussion and conclusions
There were described (Marini et al. 2007) about 832 causative mutations up to date
2007 which cause OI type II, III and IV. More obvious are variants in the alfa 1 chain. The
variants in the alfa 2 chain are not so numerary as in the previously mentioned alfa 1 chain
There are the intrafamiliar variable expresivity and penetrance in the families with multiple
incidence. There are the different suffering patients in the same family with the same type of
mutation. The aminoacid glycin is the most obvious in the collagen sequency and correlate
with frequency of targeted mutations which were founded.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Dynamics of Acidithiobacillus ferrooxidans JCM3863 biofilm formation on two
different inert carriers
V. Mamatarkova, M. Tsenov
Sofia University “St. Kl. Ohridski”, Faculty of Biology, Department of Biotechnology, Sofia,
Bulgaria
The most spread laboratory bioreactor is the shake flasks for submerged cultures of
microorganisms. They allow simultaneous performance of many experiments and accumulation of
knowledge in a relatively short time. On this basis in Laboratory of Bioprocess Systems, Faculty of
Biology, Sofia University was developed a version of shake flasks for cultivation of bacteria
Аcidithiobacillus ferrooxidans in biofilm. It gives opportunities for investigations on formation and
function of this biofilm under different conditions e.g. different concentrations of energy source
ferrous ions, metal ions and other substances as well as the interactions between microorganisms and
carriers.
The aim of present work is the investigation of dynamics of formation of Аcidithiobacillus
ferrooxidans JCM 3863 biofilm on two different inert supports regarding their chemical nature,
surface structure and geometrical form. The first carrier - parallelepiped-shaped is from polystyrene
with open pores on the surface when the second one - polyethylene cylinders with relatively
smoother surfaces, mechanical modified by sandpaper.
The biofilm on two carriers has been formatted using an identical procedure developed in
Laboratory for biofilm of Аcidithiobacillus ferrooxidans which includes five cycles of fed-batch
cultivation at 28±0.5°C, 190 rpm in nutrient medium with different initial concentrations of
ferrous ions. During 7 days cultivation under these conditions the thickness of biofilm formed on the
two carriers has been found to be rather different – on polystyrene parallelepipeds it has been in
range 80-94 µm when on polyethylene cylinders - 45-50 µm respectively. The different growth rate
of biofilm has been probably due to different surfaces of carriers. The porous polystyrene obviously
facilitated the initial adhesion of microbial cells and protected them during formation of biofilm in
difference to relatively smoother polyethylene surface.
Due to slower biofilm growth on polyethylene cylinders, the procedure for it formation
has been modified – each cycle of fed-batch cultivation has been repeated and it has been formed
new biofilm. In such a way the thickness of biofilms has been relatively of same dimensions. These
procedures allowed find that the thickness of biofilm formed on polyethylene surface has been with
different thickness in dependence of depth of immersion in the liquid phase. The thickest biofilm in
this case has been formed in the deepest liquid layers. Data processing showed linear relationship
between biofilm thickness and depth of immersion in liquid phase. Such differences in biofilm
thickness have been observed when the biofilm has been cultivated in various conditions - low
concentration of ferrous ions – 2 g/l, in presence of different concentrations of nickel ions and
mixtures of nickel, cobalt and copper ions. The differences in biofilm thickness at the top and the
bottom of liquid phase have been reached to 40% approximately. The use of same procedure for
biofilm thickness determination on polystyrene parallelepipeds showed that there had not difference
in biofilm thickness.
These results show that in shake flasks hydrodynamics conditions are different in depth of
liquid phase. Near the liquid phase surface the shear stress is bigger and the biofilm is thinner due to
mechanical coercions. Despite of soft hydromechanics conditions near the bottom of the flaks
probably ensure enough dissolved oxygen and nutrients, otherwise the biofilm will be thinner.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
On the mathematical modelling of batch fermentation processes using reaction
schemes and verification methods
S. Markov
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia,
Bulgaria
An experiment in a batch laboratory bioreactor for the EPS production by
Aeribacillus pallidus 418 bacteria is performed and experimental data for the biomassproduct dynamics are obtained [1]. The dynamics of microbial growth and product
synthesis is described by means of bio-chemical reaction schemes, aiming an
understanding of the underlying biochemical/metabolic mechanisms [2,3]. The
proposed reaction schemes lead to differential models that are fitted to the observed
interval experimental data. By means of suitable parameter identification of the
mathematical models the numerically computed results are compared to experimental
data. Thereby we follow an interval verification approach and make use of advance
computational tools offered by the Computer algebra system Mathematica. The
proposed models reflect specific features of the mechanism of the fermentation
process, which may suggest further experimental and theoretical work. Using the
proposed methodology one can study the basic mechanisms underlying the dynamics
of cell growth, substrate uptake and product synthesis.
The fundamentals of the proposed approach include as an essential part the V.
Henri reaction scheme describing the single enzyme-substrate action involving
enzymes with one active site. The transition of the enzyme from bound to free form
and vice versa is an important two-compartmental mechanism which we apply to cell
growth as indicated in [3]. Thereby the dividing cells play the role of the bound
enzymes, whereas the non-dividing ones resemble the action of the free enzymes. In
addition we hybridize this mechanism with the well-known Verhulst-Pearl mechanism
of reproduction used in population dynamics.
All above described mechanisms are implemented into dynamical systems
under the application of the mass action law. The respective differential models are
studied numerically and are richly illustrated by means of graphics and figures.
Key words
enzyme kinetics, batch fermentation processes, reaction schemes, dynamic models,
numerical simulations, verification methods
References
[1] Radchenkova, N., M. Kambourova, S. Vassilev, R. Alt, S. Markov, On the
Mathematical Modelling of EPS Production by a Thermophilic Bacterium, Biomath 4
(2014), 1407121,
[2] Alt, R. S. Markov, Theoretical and computational studies of some bioreactor
models,Computers and Mathematics with Applications, 64 (2012), 350--360.
[3] Markov, S. M. Cell Growth Models Using Reaction Schemes: Batch Cultivation,
Biomath 2/2 (2013), 1312301.
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Complex dynamics of a colorectal cancer model
S. Nikolov1,2,3,4, J. Vera4, O. Wolkenhauer1,
1
Department of Systems Biology and Bioinformatics, University of Rostock,
Rostock, Germany
2
Department of Biomechanics , Institute of Mechanics and Biomechanics,
Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia,
Bulgaria
3
University of Transport, Geo Milev Str., 158, 1574 Sofia, Bulgaria
4
Laboratory of Systems Tumor Immunology, Department of Dermatology,
University Hospital Erlangen, Erlangen, Germany
Mathematical models of the stem cell and semi-differentiated cell populations
in colonic crypts can contribute to a better understanding of basic mechanisms
underlying tissue organization. We here study the complex dynamic behaviour of a
time delay model that describes stem cells and semi-differentiated cells in the niche
of colonic crypts. We analyze the conditions for the various regimes that would lead
to oscillations. The work presented here the first description of a chaotic system
describing stem cell and semi-differentiated cell population dynamics in colonic
crypts.
Keywords
colonic crypts, time delay model, nonlinear analysis
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Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Estimation of oxidation rates and oxidation degrees at adaptation of bacterial
strain Acidithiobacillus ferrooxidans JCM 3863 to 21 g/L ferrous ions
E. Petrova1, P. Zlateva2
1
Department of Biomechanics Institute of Mechanics, Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., Block 4, 1113 Sofia, Bulgaria
2
Istitute of System Engineering and Robotics, Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., Block 2, 1113 Sofia, Bulgaria
Acidithioacillus ferrooxidans is an autotrophic, acidophilic, mesophile
occurring in single or occasionally in pairs or chains, depending on growth conditions.
They oxidize ferrous ions and used in waste water, tail gas treatment. The use of
bacteria in environmentally friendly technologies of wastewater treatment, it may fall
in areas with high concentrations of iron and lead, and this is toxic for the strain. In
order to avoid inhibition of the bacterial action, it is necessary to adapt
Acidithiobacillus ferrooxidans to high initial concentrations of iron ions. The aim of
present work is to estimate the processes of substrate oxidation compare the assessed
oxidation rates and oxidation degrees of the strain at determined hours of batch
cultivation. The bacterial cells were adapted to substrate concentration near 21g/L.
There is influence of the high substrate concentrations on oxidation rates and
oxidation degrees. The obtained experimental results show stability in the strains
behavior at the begining stages of cells adaptation to high concentrations of ferrous
ions.
Keywords
oxidation rate, oxidation degree, ferrous ions, biooxidation, Acidithiobacillus
ferroocsidans
16
Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Which can be the errors when a muscle is modeled as a complex of motor units?
R. Raikova1, J. Celichowski2
1
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia,
Bulgaria
2
Department of Neurobiology, University School of Physical Education, Poznań, Poland
The muscle force is a sum of forces of all active muscle MUs. First, the
exactness of a muscle model composed by motor units (MUs) depends on the accurate
estimation of the number and the type of modeled MUs (slow-S, fast-resistant-to
fatigue - FR, fast-fatigable - FF). Second, an appropriate modeling of the force
developing from each MU has to be proposed. This requires enough accurate
modeling of the MUs individual contractions (the twitches) and their summation into
infused tetanus due to consecutive regular or inrregular impulsation (with constant
inter-pulse intervals or with random inter-pulse interval with given mean frequency).
It was previously shown, using a few MUs, that modeling of unfused tetanic
force curves by summation of equal twitches (which is the most used approach) is not
accurate, especially for slow MUs. The aim is to evaluate this inaccuracy on a
statistical number of experimentally investigated 45 MUs of the rat medial
gastrocnemius muscle (15 from S type, 15 from FR type and 15 from FF type).
Unfused tetanic contractions were evoked by trains of 41 stimuli at random
(which case resembled discharge patterns observed during natural muscle activity)
and at constant inter-pulse intervals and different mean frequencies. The tetanic
curves were calculated summing equal twitches according to the respective
experimental patterns. A previously described 6-parameter analytical function for
twitch modeling was used. Comparisons between the experimental and the modeled
curves were made by using two coefficients: the fit coefficient (FIC) and the area
coefficient (AC). The errors between modeled and experimental tetanic contractions
were substantially different for the three MU types. The error was the most significant
for slow MUs, which develop much higher forces in real contractions than could have
been predicted on the basis of summation of equal twitches and the smallest for FF
MUs, as their recorded tetanic forces were similar to those predicted by modeling.
A regression approach is necessary for the prediction of the parameters of each
next contraction in an unfused tetanus. It is questionable whether it has to be the same
for: each type of MUs; for regular and irregular impulsation patterns; for different
muscles.
Acknowledgments
This study was partly supported by the Bilateral Agreement between the
Bulgarian Academy of Sciences and the Polish Academy of Sciences
17
Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Experimental investigation of human elbow flexions in the sagittal plane with
different speeds
R. Raikova1, D. Lochynsk2, D. Kaczmarek2, H. Aladjov1
1
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia,
Bulgaria
2
Department of Motor Rehabilitation, University School of Physical Education, Poznań,
Poland
One degree of freedom (DOF) macro-biomechanical models can not predict
antagonistic co-contraction using conventional optimization approaches. For models
with more DOF, if biarticular muscles are properly modeled, muscles from two
antagonistic groups can be simultaneously active under some conditions. This is more
evident for fast motions where the influence of the inertial forces increases.
The aim of the study was to investigate the electromyographic (EMG) activity
of 4 muscles of human upper limb (i.e. long heads of biceps brachii and triceps brachii
and anterior and posterior deltoideus) and flexion/extension angular displacements in
elbow and shoulder joints during full elbow flexion movements in the sagittal plane
performed at gradually increasing movements velocities - from very slow to very fast.
The experiments were conducted on eleven healthy volunteers (4 women and
7 men) aged 24.2 ± 5.5 years. The angular displacements in the sagittal plane of the
elbow and shoulder joints were recorded with two flexible goniometers (SG110 and
SG115, Penny and Giles, Cwmfelinfach, Gwent, UK). Surface EMGs were recorded
by Ag/AgCl electrodes (Data Link, Biometrics UK, attached according to SENIAM
recommendations. The participants were seated on a chair (Isokinetic Dynamometer,
Biodex, USA). The initial position was always resting vertical position of the right
upper limb (0˚ abduction and flexion in the shoulder joint, full extended elbow and
forearm held in a neutral position with respect to the supination and pronation). To
normalize EMG data, initially maximum isokinetic contractions were performed
during elbow flexion and extension motions at 4 different angular velocities
(approximately 45, 90, 180 and 360 deg/s). Thereafter, subjects were asked to perform
elbow flexions with the same angular velocities with and without external load (0.5
kg) attached to the wrist. To control the movement velocity a visual feedback for the
angular displacement in the elbow joint was provided on the monitor screen, and
subjects had to match the potentiometer output generated by a custom made software.
The obtained experimental data were processed by a custom made computer program
written in MATLAB. Two normalizations of the EMGs were performed and
compared.
The main conclusion is that increasing the speed of the motion causes an
increase in the EMG amplitudes of flexor muscles, and antagonistic activity of the
monoarticular deltoideus posterior muscle is observed only for the fastest motions.
The stability of the shoulder joint when high inertial forces occur (during fast
acceleration and deceleration) is rather assured by the monoarticular deltoideus
muscles than by biarticular biceps and triceps muscles.
Acknowledgments
This study was partly supported by the Bilateral Agreement between the
Bulgarian Academy of Sciences and the Polish Academy of Sciences
18
Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Biomechanics of glaucoma: factors influencing the intraocular pressure (IOP)
S. Stoytchev1, R. Collins2
1
Institute of Mechanics, BAS, Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
Biomedical Engineering Program, Mechanical Engineering Department, University of
Nevada, Las Vegas
2
Glaucoma is the most common causes of blindness, affecting approximately
70million people in the world, of whom more than 7 million are blind. About 70
thousand of Bulgarian citizens suffer from glaucoma. In the vast majority of such
cases the intraocular pressure (IOP) is higher than normal and therefore, the
hypothesis that evaluation of IOP causes optic nerve damage and hence visual
impairment is generally accepted.
We present simple biomechanical model which describes volume and pressure
changes within the eye as functions of measurable ocular properties. We suppose that
the rate of the volume change of the whole eyeball is sum of the rate of the volume
change of the eye arterial bed and the rate of the volume change of the aqueous
humor. The mechanical characteristics of cornea and sclera are expressed throughout
the so called ocular rigidity function in Friedenwald approximation. Blood flow
circulation within the eye is represented as equivalent vessel, that is, a single
cylindrical vessel represents the whole vascular bed. The aqueous humor dynamics is
predisposed by the difference of production and outflow. Finally, ordinary differential
equation for the intraocular pressure was obtained. In this equation, the rigidity of the
corneo-scleral envelop and the blood vessels, the production, critical pressure and
outflow of aqueous humor stay as constants. The variation of their values over the
suitable physiological range elucidates the interdependence of the IOP on those
parameters.
The results of the parametric study can be summarized as follows: 1) The
arterial blood pressure in the ocular bed practically does not affect the IOP; 2) The
increased rigidity of the corneo-scleral envelop increases slightly IOP (by 0.5 mmHg);
3) The parameters describing the aqueous humor production in their combinations
increase or diminish IOP significantly; 4) The resistance to aqueous outflow plays
determining role in increasing the IOP.
19
Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Structure and design of an active orthosis of human body
M. Tsveov, I. Veneva, D. Chakarov, D. Trifonov
Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev
Str., Bl. 4, 1113 Sofia, Bulgaria
In this paper the biomechanical design of an active-assistive orthosis system as
a lower and upper-limb force-feedback exoskeleton is presented. The orthosis have a
wearable structure and anthropomorphic workspace that can cover the full range of
human motion. The device is designed for application where both motion tracking and
force feedback are required, such as robotized rehabilitation or interaction with virtual
environment.
A scheme of the mechanical structure is presented as kinematical equivalent to
the structure of the human body. The mechanical exoskeleton structure includes left
and right upper limb, left and right lower limb and structure corresponding to human
torso and waist, supporting upper and lower limbs. The device, which can be seen to
function as a powered exoskeleton, is build up as a branched serial kinematics
structure consisting of rotational joints kinematics equivalent to the joints in the
human body structure.
Actuation of the system is based on braided pneumatic muscle. An
antagonistic drive system with pulley and Bowden cable transmissions is used for
each joint. Two factors determine the length and the diameter of the actuator. The first
is the range of joint motion and the second is the torque required at that joint. The
mass geometric parameters of the system human body-exoskeleton are defined. The
lengths of the segments are determined according to the height of the individual. The
range of joint motions and maximal natural torques in the major human joint are
assessed.
CAD simulation of the exoskeleton is presented, according to the structure
scheme carried out. Exoskeleton design includes left and right upper limb, left and
right lower limb and central exoskeleton structure corresponding to human torso and
waist. The mass geometric parameters of the exoskeleton links are defined using the
CAD program.
20
Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Управление напряжениями и деформациями в задачах биомеханики
В.А. Лохов, Ю.И. Няшин
Пермский национальный исследовательский политехнический университет, Пермь,
Россия
Известно, что в органах и тканях живого организма постоянно
происходят процессы, приводящие к развитию напряжений, например, это
относится к процессам филогенеза, онтогенеза, резорбции, перестройки,
различным оперативным вмешательствам. Важную роль играют также
температурные напряжения, вызванные нагревом или охлаждением органов и
тканей или их искусственных заменителей. Во многих работах обсуждается
роль ростовых деформаций, возникающих в живых системах, начиная с самого
начала их развития (например, для человека напряжения возникают уже в
период внутриутробного развития).
Для анализа и управления напряжениями в живых системах удобно
ввести подход, предложенный Рейсснером, 1931, основанный на понятии
«собственная деформация».
Под термином «собственная деформация» (eigenstrain) понимается
неупругая деформация любой природы: температурная деформация,
пьезоэлектрическая деформация, деформация фазовых переходов, деформация
роста и перестройки живых тканей и др. Предполагается, что собственная
деформация может быть вычислена независимо и в уравнениях краевой задачи
считается известной (например, можно независимо найти температурные
деформации, пьезоэлектрические деформации, деформации фазовых переходов,
и т.д.).
Использование данного понятия позволяет разработать единый подход к
решению двух классов задач, имеющих большое значение при проектировании
и разработке интеллектуальных систем: создание в теле заданного поля
напряжений, сохраняя поле деформаций, и создание заданной формы системы,
не меняя напряженного состояния системы.
Решение этих задач основано на теореме, согласно которой любое
распределение собственной деформации, существующее в теле, может быть
единственным образом разложено на две части: первая часть – stress-free
eigenstrain – не вызывает напряжений в системе, вторая часть – deformation-free
eigenstrain – не вызывает деформаций в системе. Разработанный подход
является развитием работ Пермской школы, проводимых под руководством
А.А. Поздеева в области управления остаточными напряжениями в процессах
обработки металлов давлением.
Показано, что указанные виды собственной деформации образуют
подпространства в энергетическом функциональном пространстве собственных
деформаций. Для построения данных подпространств разработаны алгоритмы
построения систем базисных функций.
В докладе будут представлены алгоритмы решения обозначенных
классов задач, учитывающие особенности создания в теле собственных
деформаций (температурных, пьезоэлектрических, деформаций фазовых
переходов и т.д.). В качестве примеров будут рассмотрены задачи об
управлении напряжениями и деформациями в биомеханике.
21
Days of Biomechanics 2014, Sofia, 20.11-21.11.2014г.
Развитие биомеханической модели «Виртуальный физиологический
человек»
Лохов В.А., Няшин Ю.И.
Пермский национальный исследовательский политехнический университет
Концепция «Виртуальный физиологический человек» начала развиваться
сначала в США, а затем в странах Западной Европы с конца ХХ столетия
(VirtualPhysiologicalHuman, VPH). Согласно этой концепции организм человека
рассматривается как сложная многоблочная биомеханическая система. В состав
этой системы входят все подсистемы организма человека (сердечно-сосудистая
система, система дыхания, нервная система, зубочелюстная система, билиарная
система, опорно-двигательный аппарат и др.). Каждая из указанных подсистем
состоит из ряда других подсистем различного уровня сложности (от
макроуровня до наноуровня).Цель развития концепции «Виртуальный
физиологический человек» состоит в детальном исследовании всех подсистем
организма человека и установлении количественных и качественных связей
между ними. Развитие данной концепции позволит значительно ускорить и
улучшить диагностику, А также найти оптимальный метод лечения каждого
индивидуального пациента, включая проведение виртуальной операции.
В предлагаемом исследовании особое внимание уделяется анализу структуры
и физиологических особенностей зубочелюстной системы человека в динамике
ее развития, начиная от рождения, и далее в течение всей жизни
человека.Анализируется влияние биомеханического давления на процессы
филогенеза и онтогенеза в зубочелюстной системе, в частности, показано
развитие различных элементов системы в норме и при различных
патологиях.Особенно важным элементом исследования в рамках поставленной
проблемы является анализ связи патологических изменений в зубочелюстной
системе и в других системах организма. Показывается связь неправильной
окклюзии (неправильного прикуса) с нарушениями шейного отдела
позвоночника и нарушениями в системе кровообращения.
Очень важным и интересным объектом исследования с точки зрения
биомеханики и связей с другими системами организма является парный
височно-нижнечелюстной сустав. Диски суставов являются аваскулярными
(лишенными кровеносных сосудов) и питание их производится не за счет
кровеносных капилляров, а за счет втекающей и вытекающей внутритканевой
жидкости.
В заключение, наиболее подробно анализируются связанные патологии в
зубочелюстной системе, нарушения усилий в мышцах лицевой области,
патологические деформации и смещения в дисках суставов, деформации и
нарушения проводимости внутренней сонной артерии, нарушения
внутримозгового кровообращения, включая инсульт сосудов головного мозга.
22