Novel training machine for stimulation of blood circulation in feet

Abstract

The aim of the current work was to identify vibra-tional machine glass epoxy plate eigenfrequencies, numer-ically identify working regimes on different input parame-ters and investigate the blood flow in foot after vibrational excitation using high-sensitivity infrared thermal imaging camera. Novel training machine has been designed for this purpose. Two vibrating motors rotating on different revo-lution per minute value were used to induce beating phe-nomenon and create sufficient force. Comsol Multiphysics model was designed for eigenfrequency analysis of ma-chines' vibrating glass epoxy plate. Natural frequency of 3.28 Hz has been observed on loaded beam. Experiments with training machine were executed with the purpose of identification of beating phenomenon induction regimes on vibrating frequencies close to calculated eigenfrequencies values. Motors supplied by 16.9 V and 13.9 V respectively created beating frequency of 3.311 Hz and generated force to legs of 180.2 N. After that foot temperature was regis-tered. Temperature raise of 0.7 C on Hallux toe, 1 C on Long toe, 0.9 C on right foot point and 1.5 C on left foot point were noted.

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ISSN 1392
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1207. MECHANIKA. 2015 Volume 21(3): 201
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Novel training machine for stimulation of blood circulation in feet
M. Venslauskas*, V. Ostasevicius**, V. Jurenas***
*Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania, E-mail: mantas.venslauskas@ktu.edu
**Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania, E-mail: vytautas.ostasevicius@ktu.lt
***Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania, E-mail: vytautas.jurenas@ktu.lt
http://dx.doi.org/10.5755/j01.mech.21.3.11758
1. Introduction
People with diabetes can develop many different
feet problems. Even ordinary problems can get worse and
lead to serious complications. Poor blood flow or flow
changes in the shape of the feet or toes may also cause
problems. People might not notice a foot injury until the
skin breaks down and becomes infected. Walking on an
ulcer can make it get larger and force the infection deeper
into the foot. The fundamental of diabetic foot problem -
insufficient blood supply. Poor blood flow can make the
foot less able to fight infection and to heal. Diabetes causes
blood vessels of the foot and leg to narrow and harden.
From the three main types of blood vessels - arteries, veins
and capillaries - the most important are capillaries.
Vibrational training is advantageous to improve
muscle strength, power, coordination and even cardiovas-
cular system. Our earlier studies have showed that vibra-
tion training affects blood pressure and respiration rate [1].
It is well known that the primary hypertension is character-
ized by elevated cardiac output, whereas in later stages the
increased blood pressure is due to increased peripheral
resistance. Blood vessels are able to control blood flow
rate by changing its diameter because of elastic properties.
When pressure is constant fluid volume flow rate is re-
duced. This permanent reaction can be characterized as
structural auto regulation [2].
It is known that lower density of capillaries in
limbs tissues occur in patients with essential hypertension.
The capillarity exercise methodology was investigated by
registering temperature changes in hand’s fingers before
and after the exercise. It was noted 0.8 C degree raise of
temperature (not published data). Most are being aware of
hypertension only after suffering heart attack or stroke.
The majority of patients with hypertension do not know
what steps to take to lower blood pressure. In the foreign
research databases could be found lots of testimonies that
high blood pressure is directly related to the rarefaction of
capillary density in body tissues [3-5]. Above mentioned
problems are caused by the various circulatory disorders.
Results of studies on vibration training influence
on cardiovascular system has showed that capillaries are
probably opened in order to keep a necessary level of car-
diac output needed for the body [6].
The effect of whole-body vibration on leg blood
flow was investigated. Young adult males completed a set
of random vibration and nonvibration exercise bouts whilst
squatting vibrating plate. Blood pressure of the common
femoral artery and blood cell velocity were measured in a
standing or rest condition prior to the bouts and during and
after each bout. The results show leg blood flow increased
during the squat or nonvibration bouts and systematically
increased with frequency in the vibration bouts [7].
The purpose of other study was to investigate the
effects of whole-body vibration on blood flow velocity and
muscular activity after different vibration protocols in
Friedreich's ataxia patients. Ten patients received whole
body vibration treatments with random combination of
frequency and protocol. Femoral artery blood flow veloci-
ty, vastus lateralis and vastus medialis electromyography,
and rate of perceived exertion were registered. Peak blood
velocity was increased. Electromyography amplitude was
increased and frequencies decreased during the application
of whole body vibration. The results suggest that whole
body vibration is an effective method to increase blood
flow in patients with Friedreich's ataxia [8].
Other study partly aimed to determine the effects
of vibration on leg blood flow after intense exercise.
Twenty-three participants performed an exercise tests fol-
lowed by a recovery period using whole-body vibration or
a passive control in the seated position and blood flow was
assessed. Results showed that whole body vibration de-
creased pulsatility index in the popliteal artery following
maximal exercise and was effective to increase perfor-
mance in a later exercise tests [9, 10].
The aim of this study was to identify Eigenfre-
quencies of novel legs’ vibration machine depending on
different human weight and make an experiment identify-
ing blood circulation changes in foot using thermovision
camera.
2. Materials and methods
2.1. Computer modelling
Comsol Multiphysics software with the structural
mechanics module were used for calculations. The Struc-
tural Mechanics Module is tailor-made to model and simu-
late applications and designs in the fields of structural and
solid mechanics. The module is dedicated to the analysis of
mechanical structures that are subject to static or dynamic
loads. The eigenfrequency analysis was computed for the
natural frequencies of the unloaded and loaded structures.
Rectangle solid model of 0.485 m length and
0.004 m thickness was designed. Glass epoxy material
properties with density of 2000 kg/m3, Young’s modulus
of 17 KPa and Poisson’s ratio of 0.32 was assigned to the
model [11]. Model was fixed on left end. Imitating motors’
weight load was set on the right end with vertical direction
and on the top of the model legs weight imitating load was
prescribed. Loads of leg mass of 25.02 kg (Fig. 1, blue
arrows along beam’s length of vertical down direction) and

202
motors bulk mass of 6.43 kg (red arrow of vertical down
direction) were added to the beam model at relevant places
as on vibrational training machine.
Fig. 1 Glass epoxy beam model with legs mass load (blue
arrows) and motors weight load (red arrow), fixed
edge is by dotted red line
Designed model could be easily adjustable con-
sidering variations of input parameters such as length,
width or load either material. The model is simplified and
requires minimal time resources for making high amount
of calculations. This model will be used for further studies
on purpose of identifying eigenfrequency values of differ-
ent heights of vibrating glass epoxy plate. 3D model was
rejected due to the low efficiency of the use of time for
calculations.
2.2. Experimental setup
Vibration motors that could be find in the market
are specific and it would be difficult to adopt in this re-
search area. For this reason unbalanced mass was designed
on SolidWorks software with parameters given on Table 1.
Two identical unbalanced masses were made from the
steel. These masses were made with the aim to induce vi-
brations and generate force to glass epoxy plate by mount-
ing and fixing them on the motor’s rotor. Main parameters
of these masses are given in Table 1.
Table 1
Unbalanced mass parameters
Parameter
Value
Bulk mass
616,8 g
Mass without unbalance
212,92 g
Unbalance mass
403,88 g
Diameter
66 mm
Diameter without unbalance
36 mm
Two DOGA D.C. motors (Table 2) with mounted
unbalanced masses were used to create beating phenome-
non and higher force comparing to one vibration motor.
Revolutions per minute of each motor were controlled by
changing supplied voltage on power suppliers. Two vibra-
tions with slightly different frequencies (supplied voltage
values) induce the beats phenomenon. It is well known that
beats occur when two frequencies are close together.
Transfer of energy takes place in the coupled system which
could induce vibration in the primary system instead of
suppressing them. The coupled equations of motion with-
out damping in both systems can be obtained from Eq. 1
by setting damping in each system equal to zero.
2
11
12
22
2
10
0
10
0
xx
xx
µ αµ ω
αω

+ 
  
+=

 
  
  
 



(1)
The modal frequencies of this system are given
by:
( )
( )
22
12
1,2 2
1
21
ωω µ
ωµ αµ
+ + ±∏
=+−
(2)
The coupling parameter α in the mass matrix is
responsible for the beat phenomenon.
Table 2.
DOGA D.C. motor parameters
Parameter
Value
Bulk mass
2,6 kg
Nominal voltage
24 V
Nominal Torque
0,75 Nm
Nominal speed
1000 rpm
Nominal current
5,5 V
Investigated leg mass calculations were based on
Plagenhoef et al. (1983) studies [12]. Total leg weight is
equal to 16.68% of total male weight and 18.43% of total
female weight. Calculations of leg mass depending on dif-
ferent body weight were made and can be found in
Table 3. These values are necessary for executing
eigenfrequency analysis on Comsol Multiphysics software.
Table 3
Leg mass calculations
Body weight
Leg mass
55 kg (female)
20,273 kg
60 kg (female)
22,116 kg
65 kg (female)
23,959 kg
70 kg (female)
25,802 kg
75 kg (male)
25,02 kg
80 kg (male)
26,688 kg
85 kg (male)
28,356 kg
90 kg (male)
30,024 kg
95 kg (male)
31,692 kg
100 kg (male)
33,36 kg
Experimental setup is presented in Fig. 2. Train-
ing machine (Fig. 2, (1)) model was designed with Solid-
Works software. Machine was developed with the ability
of changing plate’s angle where tested person’s legs are
fixed. The glass epoxy plate was chosen as vibrating part
because of its cyclic durability of the flexural strength. The
plate was covered with a foam for a better comfort reason.
Plate’s length can be adjustable depending on human’s
height or leg’s length. Motors were adjusted to give an
inward rotation to unbalanced masses so creating force to
vertical direction. Motors were fixed motionlessly next to
each other. Beating phenomenon enables to induce suffi-
cient force by using low voltage and small size motors for
making vibrational movement of adequate displacement.
Vibrations’ data was gathered from Robotron 00032 with
low frequency acceleration sensor KB12 with resolution of
300 mV per 1 m/s2 and processed with Picoscope 3424 in

203
Picoscope PC software. Motors were supplied by Digimess
HY3020 power suppliers (1ch, 30V, 20A, adjustable).
Fig. 2 Experimental setup: 1 - Legs vibrating machine with
motors and unbalanced masses; 2 - Acceleration
sensor KB12; 3 - Power suppliers (0-30V/20A, ad-
justable); 4 - Robotron 00032; 5 - Picoscope 3424;
6 - PC with Picoscope 6 software
Legs vibrational training machine was developed
with the aim to eliminate negative effects of standing hu-
man vibrations that are described on various studies. For
example on ISO 2631-1 guidelines on Mechanical vibra-
tion and shock – Evaluation of human exposure to whole-
body vibration is written that long-term high-intensity
whole-body vibration indicates an increased health risk to
the lumbar spine. It is noted that this may be due to the
biodynamic behaviour of the spine: horizontal displace-
ment and torsion of the segments of the vertebral column.
Furthermore whole-body vibration exercise may worsen
certain endogenous pathologic disturbances of the spine.
Developed legs’ vibrating machine eliminates negative
vibrational excitation effects that are caused by standing
position. Further studies are planned for physiological pa-
rameters measurement after affecting human in prescribed
protocol of vibrations using developed legs’ vibrating ma-
chine.
Fig. 3 High-sensitivity infrared thermal imaging camera
FLIR-t62101
Vibrational excitation influence is widely defined
in previous studies mentioned in the Introduction chapter.
To identify vibrational excitation influence on foot blood
flow high-sensitivity infrared thermal imaging camera was
used (Fig. 3). Four points on right foot (Hallux toe, Long
toe, right point on the foot and left point on the foot) were
monitored before and after experiment and temperature
difference was registered by making thermal images.
3. Results
First, eigenfrequency analysis of epoxy glass plate
was made with Comsol multiphysics software. Primary
calculations were made without adding leg mass and after
then prescribing legs weight of 75 kg weight male (equal
to tested person). Eigenfrequency of glass epoxy beam
without leg mass load was equal to 9.05 Hz (Fig. 4). After
adding leg mass of 25.02 kg and motors bulk mass of
6.43 kg eigenfrequency value decreased to 3.28 Hz
(Fig. 5).
Fig. 4 Eigenfrequency value of first vibration mode
without load
Fig. 5 Eigenfrequency value of first vibration mode with
load
Further calculations with aim to identify frequen-
cy range of different weight male and female persons were
made by changing legs mass load on beam regarding to
Table 3. Frequency values from 3.47 to 3.25 Hz for fe-
males at 55 to 70 kg weight range and frequency range
from 3.28 to 3.02 Hz for males at 75 to 100 kg range were
calculated and are given in Table 4.

204
Table 4
Eigenfrequency value differ depending
on body mass and gender
Body mass, kg
Gender
Eigenfrequency,
Hz
55
Female
3.47
60
Female
3.39
65
Female
3.32
70
Female
3.25
75
Male
3.28
80
Male
3.22
85
Male
3.17
90
Male
3.11
95
Male
3.06
100
Male
3.02
Next experiments with legs vibrating machine
identifying working frequencies were executed. Beating
phenomenon was induced during vibrational excitation in
order to establish higher force. Knowing the importance of
higher displacement amplitudes, frequency value has to be
as close to eigenfrequency value as possible for each leg
mass mean. Experiment was conducted with 75 kg weight
person. Voltage values were chosen according to tested
person’s vibrational excitation impact feeling. Beating
phenomenon frequencies ranging from 0.5 Hz to 4.8 Hz
were registered (Figs. 6-11).
Fig. 6 Voltage: 7.8-7.4 V; beating frequency: 0.5 Hz; force
to legs: 44.68 N
Fig. 7 Voltage: 10.7-9.6 V; beating frequency: 1.168 Hz;
force to legs: 78.12 N
Low voltage causes low revolution per minute
number and lower force mean. Glass epoxy plate and feet
displacement is significantly smaller comparing to fre-
quency values that are close to eigenfrequencies. That
means minor influence on stimulating foot blood circula-
tion. Therefore higher voltage values were used for further
investigations (Figs. 8-11). In all of them clear beating
phenomenon could be defined from diagrams. It is im-
portant to note that natural frequencies of the motors has
not been felt by tested person.
Fig. 8 Voltage: 11.2-13.8 V; beating frequency: 2.217 Hz;
force to legs: 117.78 N
Fig. 9 Voltage: 15.1-10 V; beating frequency: 4.844 Hz;
force to legs: 137.10 N
Fig. 10 Voltage: 16.9-12.4 V; beating frequency: 4.152 Hz;
force to legs: 116.30 N
Fig. 11 Voltage: 16.9-13.9 V; beating frequency: 3.311 Hz;
force to legs: 180.2 N.
Voltage values of 16.9 V and 13.9 V (Fig. 11)
were chosen for further experiments to register vibrational
excitation influence on blood circulation at foot. The fre-
quency of 3.311 Hz were the closest value to eigenfre-
quency value that was calculated at Comsol multiphysics
software. Motors with unbalanced masses working on
these voltage values generate 180.2 N force.
Temperature was monitored on four points: two

205
on different toes (Hallux and Long) and two points on feet
(one on the left and one on the right). Temperature changes
were recorded right after the exercise and after resting 3
and 5 minutes. Peak temperature rise values were regis-
tered after resting 3 minutes after the vibrational excitation.
Temperature rise of 0.7 C on Hallux toe (Fig. 12), 1 C on
Long toe (Fig. 13), 0.9 C on right foot point (Fig. 14) and
1.5 C on left foot point (Fig. 15) were captured.
Fig. 12 Hallux toe temperature before (left) and after
(right) vibrating legs
Fig. 13 Long toe temperature before (left) and after (right)
vibrating legs
Fig. 14 Right foot point temperature before (left) and after
(right) vibrating legs
Fig. 15 Left foot point temperature before (a) and after (b)
vibrating legs
4. Conclusions
1. Beam natural frequencies without leg’s weight
load were 9.05 Hz and assessing 75 kg male’s legs weight
– 3.28 Hz. This value is close to determined frequency
range from earlier experiments with highest impact cardio-
vascular parameters and liquid (blood) properties changes.
2. Eigenfrequency values of 3.47-3.25 Hz for fe-
males (weight: 55-70 kg) and 3.28-3.02 Hz (weight: 75-
100 kg) for males were calculated. These values indicates
different working regimes and supplied voltage parameters
depending on human weight and will be implemented in
device control algorithm.
3. Experiment with legs vibrating machine was
conducted to identify working regimes and necessary volt-
ages for each motor to generate eigenfrequency value of
3.28 Hz for 75 kg weight male. 16.9 V and 13.9 V supply
voltage for each motor respectively generated beating vi-
brations of 3.311 Hz. Thermal analysis of the feet was exe-
cuted at this frequency range. Further experiments to iden-
tify cardiovascular parameters changes will be conducted
on identified working frequencies.
4. Vibrational effect assessing experiment was
made on 3.311 Hz beating vibrations registering tempera-
ture changes on four points of the foot. Temperature raise
of 0.7 C on Hallux toe, 1 C on Long toe, 0.9 C on right
foot point and 1.5 C on left foot point were registered.
These values are very close to earlier experimental results
of exciting human hand and monitoring temperature
changes [13].
5. Acknowledgement
This research work was funded by EU Structural
Funds project "In-Smart" (Nr. VP1-3.1-ŠMM-10-V-02-
012), ministry of education and science, Lithuania.
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M. Venslauskas, V. Ostasevicius, V. Jurenas
NOVEL TRAINING MACHINE FOR STIMULATION
OF BLOOD CIRCULATION IN FEET
S u m m a r y
The aim of the current work was to identify vibra-
tional machine glass epoxy plate eigenfrequencies, numer-
ically identify working regimes on different input parame-
ters and investigate the blood flow in foot after vibrational
excitation using high-sensitivity infrared thermal imaging
camera. Novel training machine has been designed for this
purpose. Two vibrating motors rotating on different revo-
lution per minute value were used to induce beating phe-
nomenon and create sufficient force. Comsol Multiphysics
model was designed for eigenfrequency analysis of ma-
chines’ vibrating glass epoxy plate. Natural frequency of
3.28 Hz has been observed on loaded beam. Experiments
with training machine were executed with the purpose of
identification of beating phenomenon induction regimes on
vibrating frequencies close to calculated eigenfrequencies
values. Motors supplied by 16.9 V and 13.9 V respectively
created beating frequency of 3.311 Hz and generated force
to legs of 180.2 N. After that foot temperature was regis-
tered. Temperature raise of 0.7 C on Hallux toe, 1 C on
Long toe, 0.9 C on right foot point and 1.5 C on left foot
point were noted.
Keywords: vibrations, blood circulation, beating pheno-
menon.
Received April 13, 2015
Accepted May 13, 2015