CN104587606A - TMS (transcranial magnetic stimulation) system and method controlled by electroencephalogram signals - Google Patents

Abstract

The invention provides a TMS (transcranial magnetic stimulation) system and a TMS method controlled by electroencephalogram signals. The TMS system controlled by the electroencephalogram signals comprises an electroencephalogram signal gathering module, an ARM (advanced RISC machine) processor, an LCD (liquid crystal display) touch screen, a power amplifier and a stimulating coil, wherein the ARM processor comprises an electroencephalogram signal analysis module and a stimulating signal generation module, and the LCD touch screen comprises a display module and a key module. The work method of the TMS system controlled by the electroencephalogram signals includes the steps that the electroencephalogram signal gathering module obtains the electroencephalogram signals generated at time periods which are respectively 30s after starting of an activity in a corresponding activity area of the cerebral cortex and 30s before finishing of the activity in the corresponding activity area of the cerebral cortex, the electroencephalogram signal analysis module is used to perform band pass filtering so as to extract signals at alpha and beta frequency bands, and calculate a falling range of energy of the electroencephalogram signals before and after the activity, and accordingly a group of stimulation parameters are provided; the stimulating signal generation module generates stimulating signals according to the set stimulation parameters, the stimulating signals are output after digital to analog conversion, and then the stimulating coil is driven by the power amplifier, magnetic stimulation is performed on the activity area of the cerebral cortex, and therefore the purpose of relieving fatigue is achieved.

Description

Transcranial Magnetic Stimulation System and Method Controlled by EEG Signals

technical field

The invention belongs to the field of rehabilitation medical equipment, and relates to a transcranial magnetic stimulation system controlled by electroencephalogram signals.

Background technique

Fatigue is a common phenomenon in people's rehabilitation training and even in daily life. It mainly manifests as premature exhaustion after physical and mental activities, and it is difficult to start or maintain active sports. Patients may need to spend more effort to complete it easily before the onset activity. In task-based physical rehabilitation training, patients have different degrees of fatigue, which affects the tolerance and durability of training, so eliminating or relieving fatigue is of great significance to rehabilitation medicine.

Magnetic stimulation technology has been widely used in neurological disease treatment and brain function research because of its non-invasive and painless. At present, the commonly used transcranial magnetic stimulation (TMS) uses time-varying current to flow into the coil to generate high-intensity time-varying pulsed magnetic field, thereby generating induced electric field and induced current in biological tissue to excite the tissue. Due to the use of a strong magnetic field of 1-3Tesla, the requirements for equipment are very high, and it needs to be operated by professionals. TMS is generally used in hospitals. Due to the potential risk of inducing epilepsy, for safety reasons, the stimulation time is generally It should not be too long.

Extremely low-frequency magnetic fields are also used for transcranial magnetic stimulation. Extremely low-frequency magnetic fields refer to low-frequency magnetic fields with a magnetic field frequency of several Hz to tens of Hz, and the magnetic field strength generated by them is generally tens of mT. Due to the low strength of the magnetic field, it can be used for a long time in clinical diagnosis and treatment. The general stimulation time is tens of minutes to one hour, and the treatment course is one or two weeks. The low-frequency weak magnetic field can be used in family and community rehabilitation treatment.

Existing stimulation systems mostly select relevant stimulation parameters based on doctors’ experience, such as stimulation waveform, stimulation intensity, stimulation frequency, and placement of electrode coils. They cannot quantify the stimulation effect and dynamically adjust it according to the quantitative results. Empirical parameter settings and traditional stimulation modes are difficult to meet individualized treatment needs, which can easily lead to over-stimulation or under-stimulation, and cannot achieve effective or optimal therapeutic effects. Individualized treatment mode has urgent market demand and important research significance.

Contents of the invention

In order to solve the above problems, the present invention provides a transcranial magnetic stimulation system and method controlled by EEG signals, which utilizes the user's own EEG signals to set personalized stimulation parameters, excite the cerebral cortex, and improve the central system's response to muscle movement. Driving ability, relieve fatigue.

In order to achieve the above object, a kind of transcranial magnetic stimulation system controlled by EEG signals provided by the present invention is characterized in that it comprises an EEG signal acquisition module, an ARM processor, an LCD touch screen, a power amplifier and a stimulating coil in sequence, and the LCD touch screen is connected to to the ARM processor; the EEG acquisition module includes an EEG amplification module and an A/D converter; the ARM processor includes an EEG analysis module and a stimulation signal generation module; the LCD touch screen includes a display module and button module; the stimulation coil is a figure-eight coil;

The EEG signal acquisition module includes an EEG amplification module and an A/D converter, which is used to collect the EEG signals of the motor area of the cerebral cortex at the beginning of the movement 30s and 30s before the end of the movement, through the EEG amplification module and the A/D After the converter, it is sent to the ARM microprocessor for processing.

The ARM processor includes an EEG signal analysis module and a stimulation signal generation module, and the EEG signal analysis module is used to preprocess the EEG signal, calculate alpha and beta frequency band energy, and provide a reference for magnetic stimulation output Signal; the stimulation signal generating module is used to generate a stimulation signal according to the set stimulation parameters, perform D/A conversion and output it.

The working method of described EEG signal analysis module comprises:

Step 1, use a band-pass filter to extract the EEG signals in the alpha (8-12Hz) and beta (13-30Hz) frequency bands, square the EEG amplitude and take the average as the EEG signal energy, and compare the alpha before and after this exercise And the downward trend of beta frequency band energy, that is, calculate the percentage PERa and PERb of the EEG alpha and beta frequency band energy 30s before the end of the exercise and the EEG alpha and beta frequency band energy 30s before the exercise start, take per=min[PERa,PERb];

Step 2, calculate the reference values of parameters such as stimulation frequency, stimulation intensity and stimulation duration according to per, set the step size of a certain adjustment parameter as ss, the number of adjustable gears as d, and the adjustment factor as n, then this adjustment parameter The reference value of

$\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; ss</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; d</span>}\\ {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}& \mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, S _min refers to the minimum gear set by this kind of adjustment parameter, S _max refers to the maximum gear set by this kind of adjustment parameter, the adjustment factor n is a function of per, and the calculation method is as follows

$\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; CEILING</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 50</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 50</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 50</span>}<span\; class="notranslate">\; \%</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

CEILING() in the above formula is an upward rounding function.

The LCD touch screen includes a display module and a button module, the display module is used to display stimulation parameters and prompt information; the button module is used to manually adjust recommended parameters and choose to start or stop magnetic stimulation.

The power amplifier is used to amplify the power of the signal output by the stimulation signal generating module, so as to drive the stimulation coil.

The stimulating coil is fixed above the corresponding motor area of the cerebral cortex, and converts the stimulating signal into an alternating magnetic field, thereby generating an induced electric field and an induced current inside the brain, so as to excite the brain tissue and relieve fatigue. The 8-shaped coil adopts a multi-layer winding method, and consists of two circular coils with an inner radius of 2cm and an outer radius of 2.6cm, and is wound with an enamelled copper wire with a diameter of 0.35mm, and the magnetic field focusing range is 0.25mm. cm2, the spatial resolution of the magnetic field is 5mm, and the stimulation depth is 1.5-2cm.

The working method of the transcranial magnetic stimulation system controlled by EEG signals provided by the present invention includes:

Step 1, place the EEG electrodes, select the appropriate leads, and use the EEG signal acquisition module to collect the EEG signals 30s before the start of the exercise and 30s before the end of the exercise;

Step 2, the EEG signal analysis module, calculates the decline rate of the EEG alpha and beta frequency band energy of this exercise, and then calculates a set of recommended stimulation parameters;

Step 3: Display the recommended information on the LCD touch screen, manually adjust the recommended parameters on the button module, and then choose to start magnetic stimulation. The stimulation signal generation module generates stimulation signals according to the set stimulation parameters, and outputs them through D/A conversion, and then through power amplification, drives the stimulation coil fixed above the corresponding motor area of the cerebral cortex, and performs magnetic stimulation on the motor area of the cerebral cortex.

Compared with the prior art, the EEG signal-controlled transcranial magnetic stimulation system provided by the present invention calculates the energy changes in the alpha and beta frequency bands by collecting the user's own EEG signals, and formulates personalized magnetic stimulation parameters. to relieve fatigue; adopt low-frequency, low-intensity methods, so that magnetic stimulation can be used conveniently, safely and effectively; the eight-shaped stimulation coil of the present invention has good focus and stimulation depth, which meets the design requirements; the cluster stimulation used way, the coil generates less heat, and the excitability of the cerebral cortex lasts longer after stimulation. The present invention can not only be used to alleviate limb movement fatigue in rehabilitation training, but also can be popularized and applied to other functional rehabilitation and sports medicine, and is suitable for use in families and communities.

Description of drawings

Fig. 1 is a block diagram of the magnetic stimulation system of the present invention

Fig. 2 is a schematic diagram of the stimulation coil of the present invention

Fig. 3 is the magnetic field distribution figure of the present invention

Fig. 4 is a stimulation pattern figure of the present invention

Fig. 5 is the stimulus effect figure of the present invention

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

The block diagram of the transcranial magnetic stimulation system of the present invention is shown in Figure 1, which consists of an EEG signal acquisition module, an ARM processor, an LCD touch screen, a power amplifier and a stimulation coil. The magnetic stimulation system is under the control of EEG signals. The ARM processor generates cluster stimulation pulse signals of different intensities and frequencies. After being amplified by the power amplifier, an alternating magnetic field is generated in the coil. Through spatial coupling, it acts on the motor cortex of the brain. Inductive currents are generated in the body to stimulate corresponding tissue cells and cause energy changes in the alpha or beta bands of EEG signals.

ARM adopts STM32F103ZET6 microprocessor, including 11 timers and built-in 12-bit ADC and DAC, used for stimulation time control, EEG signal acquisition and stimulation pulse signal generation and adjustment, built-in 512KB Flash and 64KB SRAM , it can also be used as a large-capacity storage device through SPI to expand the SD card of more than 32Gb, which is used for the storage of EEG processing and analysis programs and data.

The LCD touch screen adopts a 2.8-inch TFT LCD module, the interface is a 16-bit 80 parallel port, the resolution is 320×240, and it supports 65K color display for displaying stimulation parameters. It comes with a touch screen that can be used as a control input for manual adjustment. Recommended stimulation parameters and choose to start or stop magnetic stimulation.

The power amplifier adopts high-performance LM3886 audio power amplifier chip, the average output power is 30W under 8Ω load, it can effectively amplify the pulse signal, and the distortion is only 0.03%.

Transcranial magnetic stimulation adopts continuous plexus stimulation, and each pulse plexus is composed of 3 single pulses with a frequency of 50Hz. The gear is 12Hz, the adjustment step is 1Hz, and the number of gears is 8; the minimum gear of the magnetic field strength is 5mT, the maximum gear is 20mT, the adjustment step is 5mT, and the number of gears is 4; the minimum stimulation duration is The gear is 20 minutes, the maximum gear is 60 minutes, the adjustment step is 10 minutes, and the number of gears is 5.

Using COMSOL Multiphysics finite element analysis software, the shape and winding method of the magnetic stimulation coil are designed and the generated magnetic field is simulated and calculated. The diameter of the copper core determines the maximum current allowed to pass, and the winding method and the number of layers will affect the focus. Sex and maximum stimulation intensity, shape and size determine a series of properties such as stimulation range, stimulation shape, stimulation depth and so on. The present invention has designed the 8-shaped coil of multi-layer winding method, and Fig. 2 is its schematic diagram. The 8-shaped coil is composed of two circular coils with an inner radius of 2cm and an outer radius of 2.6cm. It is wound with an enamelled copper wire with a diameter of 0.35mm. Each circular coil has 37 layers and 15 turns per layer. The resistance value is 18.5Ω.

Figure 3 is the radial magnetic field distribution diagram of the 8-shaped coil at four different depths. The peak of the magnetic field mainly stays within the radial range of ±2cm at the tangent of the 8-shaped coil; the peak at the tangent of the coil increases with the depth It becomes gentle, gradually changing from point stimulation to regional stimulation; when the depth is shallow (<10mm), the focus is better; when the depth is large (≥20mm), the focus of the coil becomes worse. The stimulation depth meets the stimulation requirements for the cerebral cortex.

After obtaining the EEG signals of the appropriate leads, the alpha (8-12 Hz) and beta (13-30 Hz) frequency bands were extracted using a band-pass filter, and the EEG data 30 s before the end of the exercise and the EEG data 30 s after the start of the exercise were respectively extracted. The electrical signal takes 5 seconds as a period to calculate the square of the amplitude and then take the average as the energy of the alpha and beta frequency bands of the EEG signal, and then calculate the energy of the alpha and beta frequency bands of the EEG signal 30s before the end of the exercise to the energy of the alpha and beta frequency bands of the EEG signal 30s after the start of the exercise The percentages of are PERa and PERb respectively, take per=min[PERa,PERb]. Then according to per and formula (1), formula (2) to set the reference value of a group of stimulation signals including stimulation frequency, stimulation intensity and stimulation duration. When per is less than or equal to 50%, the stimulation intensity takes the maximum gear; when per is greater than 50%, the stimulation intensity will decrease according to the increase of per, based on adjusting the step size ss and the number of gears d.

Taking the task of grasping the right hand as an example, the working method of the transcranial magnetic stimulation system controlled by EEG signals provided by the present invention is described:

Step 1, the EEG signal acquisition electrodes adopt the international "10-20" electrode placement standard. According to the principle of the brain controlling the contralateral limb, select the C3 or C4 lead to collect the EEG signals 30s before the beginning of the exercise and 30s before the end of the exercise. ;

Step 2, using a band-pass filter to extract the EEG signals in the alpha (8-12 Hz) and beta (13-30 Hz) frequency bands, the EEG data 30 s before the end of the exercise and the EEG signal 30 s after the start of the exercise were divided into 5 seconds. A period of calculating the square of the amplitude and taking the average as the energy of the EEG alpha and beta frequency bands, and then calculating the percentages of the EEG alpha and beta frequency band energy 30s before the end of the exercise to the EEG alpha and beta frequency band energy 30s after the exercise start are PERa and PERb, take per=min[PERa,PERb]. Assuming that PERa and PERb are 85% and 80%, respectively, then per=80%. For the recommended setting of the stimulation frequency, it is known that the minimum gear is 5Hz, the maximum gear is 12Hz, the adjustment step is 1Hz, and the number of gears is 8. First, calculate the adjustment factor of the stimulation frequency n=CEILING((80%-50 %)×2×4)=CEILING(2.4)=3, then calculate the reference value of the adjustment frequency S=5+(8-3)×1=10Hz, the recommended settings for the stimulation intensity and stimulation time are similar to the stimulation frequency, I won't repeat them here;

Step 3, view the recommended stimulation parameters through the display module, manually adjust each stimulation parameter through the button module, and choose to start magnetic stimulation, and then the stimulation signal generation module generates stimulation signals according to the set stimulation parameters, and outputs them through D/A conversion. Through power amplification, the stimulation coil fixed above the motor area of the cerebral cortex is driven to magnetically stimulate the motor area of the cerebral cortex.

Fig. 4 is the stimulation mode adopted in this embodiment. Continuous cluster stimulation is adopted, and each pulse cluster is composed of three single pulses with a frequency of 50 Hz, and the frequency between cluster stimulations is adjustable, ranging from 5-12 Hz. The advantage of this stimulation method is that the coil generates less heat, the excitability of the cerebral cortex lasts longer after stimulation, and better stimulation effects can be obtained.

Figure 5 is a diagram of the EEG signal capability of the embodiment after the end of the exercise with and without transcranial magnetic stimulation. It can be seen from the figure that: the transcranial magnetic stimulation makes no significant change in theta frequency band energy, alpha, The energy in the beta and gamma frequency bands is significantly improved; the transcranial magnetic stimulation system controlled by EEG signals provided by the invention has the beneficial effects of exciting the cerebral cortex and relieving central fatigue.

Claims (3)

1. the transcranial magnetic stimulation system of a kind of EEG signal control is characterized in that, comprises EEG signal acquisition module, ARM processor, LCD touch screen, power amplifier and stimulation coil successively, and LCD touch screen is connected to ARM processor; The EEG acquisition module includes an EEG amplification module and an A/D converter; the ARM processor includes an EEG analysis module and a stimulation signal generation module; the LCD touch screen includes a display module and a button module; The stimulating coil is an 8-shaped coil; The 8-shaped coil adopts a multi-layer winding method, and is composed of two circular coils with an inner radius of 2cm and an outer radius of 2.6cm, and is wound with an enamelled copper wire with a diameter of 0.35mm; the magnetic field focusing range is 0.25mm cm ² , the spatial resolution of the magnetic field is 5mm, and the stimulation depth is 1.5-2cm. 2. the transcranial magnetic stimulation system of EEG signal control as claimed in claim 1, is characterized in that, stimulation signal adopts continuous plexus stimulation mode, and each pulse plexus is made up of 3 single pulses with a frequency of 50Hz, and plexus stimulation The frequency, stimulation intensity and stimulation duration are adjustable: the minimum gear of the frequency is 5Hz, the maximum gear is 12Hz, the adjustment step is 1Hz, and the number of gears is 8; the minimum gear of the magnetic field strength is 5mT, the maximum gear The position is 20mT, the adjustment step is 5mT, and the number of gears is 4; the minimum gear of the stimulation duration is 20min, the maximum gear is 60min, the adjustment step is 10min, and the number of gears is 5. 3. Apply the transcranial magnetic stimulation system controlled by the EEG signal as claimed in claim 1 or 2, wherein the steps include: Step 1, use a band-pass filter to extract the EEG signals in the alpha (8-12Hz) and beta (13-30Hz) frequency bands, square the EEG amplitude and take the average as the EEG signal energy, and compare the alpha before and after this exercise And the downward trend of beta frequency band energy, that is, calculate the percentage PERa and PERb of the EEG alpha and beta frequency band energy 30s before the end of the exercise and the EEG alpha and beta frequency band energy 30s before the exercise start, take per=min[PERa,PERb]; Step 2, calculate the reference values of parameters such as stimulation frequency, stimulation intensity and stimulation duration according to per, set the step size of a certain adjustment parameter as ss, the number of adjustable gears as d, and the adjustment factor as n, then this adjustment parameter The reference value of $\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; ss</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; d</span>}\\ {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}& \mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$ Among them, S _min refers to the minimum gear set by this kind of adjustment parameter, S _max refers to the maximum gear set by this kind of adjustment parameter, the adjustment factor n is a function of per, and the calculation method is as follows $\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; CEILING</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 50</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 50</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; per</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 50</span>}<span\; class="notranslate">\; \%</span>\end{array}\right.$ CEILING () in the formula is an upward rounding function.