CN104720836A - Contrast medium concentration determining method and computerized tomography equipment - Google Patents

Abstract

The invention provides a contrast medium concentration determining method and computerized tomography equipment. The method includes: selecting interested areas in target object base line images; setting X ray projection angles according to the positions of the selected interested areas; performing monitoring scanning on target objects according to the set X ray projection angles after contrast media is injected into the target objects to obtain sampling data; determining the contrast medium concentration corresponding to the interested areas according to the obtained sampling data. By the method, the amount of X ray radiation radiated to the target objects can be reduced, and the sampling rate of monitoring scanning can be increased.

Description

Contrast concentration defining method and computerized tomography equipment

Technical field

The present invention relates to medical treatment and affect diagnostic field, more particularly, relate to a kind of contrast concentration defining method and computerized tomography (CT, Computed Tomography) equipment.

Background technology

Computerized tomography (CT) equipment generally includes scanning means and control device.Scanning means comprises X-ray generator and X-ray receiving system.Under control of the control means, X-ray generator produces X-ray, and by the x-ray bombardment of generation to destination object to be scanned, X-ray receiving system receives the X-ray through destination object, and convert the X-ray of reception to the signal of telecommunication, thus destination object is scanned.In addition, CT equipment also comprises and receives the signal of telecommunication changed by X-ray receiving system and the display device generating the scanogram that the image processing apparatus of the scanogram of destination object and display generate.

In order to highlight the position that may occur pathological changes in scanogram, contrast agent can be injected to destination object, then, supervision scanning being carried out to destination object, with the contrast concentration in real time monitoring destination object, thus help to determine whether there is diseased region.

But, in order to carry out real time monitoring to contrast concentration, needing repeatedly to monitor scanning to destination object, therefore, having irradiated a large amount of X-ray radiation dosage to destination object.Therefore, a kind of minimizing is needed to irradiate the CT equipment of the radiation dose to destination object when monitoring contrast concentration.

Summary of the invention

The object of exemplary embodiment of the present invention is to overcome above-mentioned and/or other problem of the prior art.Therefore, exemplary embodiment of the present invention provides contrast concentration defining method and computerized tomography (CT) equipment that a kind of X-ray radiation dosage that can reduce to be radiated destination object also can increase the sample rate monitoring scanning.

According to exemplary embodiment, provide a kind of contrast concentration defining method, described method comprises: in the baseline image of destination object, select area-of-interest; Position according to the area-of-interest selected sets X-ray projectional angle; After injecting contrast agent to destination object, the X-ray projectional angle according to setting carries out supervision scanning, to obtain sampled data to destination object; The contrast concentration corresponding with area-of-interest is determined according to the sampled data obtained.

According to another exemplary embodiment, provide a kind of computerized tomography (CT) equipment, described CT equipment comprises: scanning means, comprise X-ray generator and X-ray receiving system, X-ray generator is constructed to produce X-ray, and by the x-ray bombardment of generation to destination object, X-ray receiving system, be constructed to receive the X-ray through destination object, and convert the X-ray of reception to the signal of telecommunication, X-ray receiving system comprises multiple passage; Control device, be constructed to gated sweep device and prescan is carried out to destination object, to obtain baseline image, and be constructed to after injecting contrast agent to destination object, according to X-ray projectional angle gated sweep device, supervision scanning is carried out to destination object, with the contrast concentration that the area-of-interest determined with select in baseline image is corresponding, wherein, X-ray projectional angle is set according to the position of the area-of-interest selected.

By detailed description below, accompanying drawing and claim, other characteristic sum aspects can become clear.

Accompanying drawing explanation

Be described for exemplary embodiment of the present invention in conjunction with the drawings, the present invention may be better understood, in the accompanying drawings:

Fig. 1 shows computerized tomography (CT) the equipment schematic block diagram according to exemplary embodiment;

Fig. 2 show for illustration of setting X-ray projectional angle step and determine the diagram of step of the passage corresponding with area-of-interest;

Fig. 3 shows the curve chart of the sampled data obtained by scanning destination object according to exemplary embodiment;

Fig. 4 shows the curve chart of the contrast concentration corresponding with area-of-interest according to exemplary embodiment;

Fig. 5 shows the block diagram of the contrast concentration defining method according to exemplary embodiment.

Detailed description of the invention

Below will describe the specific embodiment of the present invention, and it is pointed out that in the specific descriptions process of these embodiments, in order to carry out brief and concise description, this description can not all do detailed description to all features of the embodiment of reality.Should be understandable that; in the actual implementation process of any one embodiment; as in the process of any one engineering project or design object; in order to realize the objectives of developer; in order to meet that system is correlated with or that business is relevant restriction; usually can make various concrete decision-making, and this also can change to another kind of embodiment from a kind of embodiment.In addition, it will also be appreciated that, although effort done in this development process may be complicated and tediously long, but for those of ordinary skill in the art relevant to content disclosed by the invention, some designs that the basis of the technology contents of disclosure exposure is carried out, manufacture or production etc. changes just conventional technological means, not should be understood to content of the present disclosure insufficient.

Unless otherwise defined, the technical term used in claims and description or scientific terminology should be in the technical field of the invention the ordinary meaning that the personage with general technical ability understands." first ", " second " that use in patent application specification of the present invention and claims and similar word do not represent any order, quantity or importance, and are only used to distinguish different ingredients.The similar word such as " one " or " one " does not represent that quantity limits, but represents to there is at least one." comprise " or the similar word such as " comprising " mean to appear at " comprising " or " comprising " before element or object contain the element or object and equivalent element thereof that appear at " comprising " or " comprising " presented hereinafter, do not get rid of other elements or object." connection " or " being connected " etc. similar word be not defined in physics or the connection of machinery, be also not limited to direct or indirectly connect.

Fig. 1 shows computerized tomography (CT) the equipment schematic block diagram according to exemplary embodiment.As shown in fig. 1, scanning means 100 and control device 200 can be comprised according to the CT equipment of exemplary embodiment.

Scanning means 100 can comprise X-ray generator 110 and X-ray receiving system 130.X-ray generator 110 can produce X-ray, and can by the x-ray bombardment of generation to destination object.X-ray receiving system 130 can receive the X-ray through destination object, and can convert the X-ray of reception to the signal of telecommunication.Here, X-ray receiving system 130 can comprise multiple passage.Although do not illustrate, can also comprise according to the CT equipment of exemplary embodiment and receive the signal of telecommunication changed by X-ray receiving system and the display device generating the scanogram that the blood processor of the scanogram of destination object and display generate.

Control device 200 can scan by gated sweep device 100 pairs of destination objects.Such as, before injecting contrast agent to destination object, control device 200 can carry out prescan by gated sweep device 100 pairs of destination objects, thus obtains baseline image.In addition, after injecting contrast agent to destination object, control device 200 can carry out supervision scanning by gated sweep device 100 pairs of destination objects, with the contrast concentration that the area-of-interest determined with select in baseline image (ROI) is corresponding, this will be explained in more detail below.In other words, according to exemplary embodiment, CT equipment can contrast concentration change in time in the part corresponding with ROI of real time monitoring destination object, thus determines whether there is diseased region in the part corresponding with ROI.Therefore, compared with carrying out monitoring with traditional entirety to destination object the CT equipment that scans, can by carrying out monitoring that scanning reduces the X-ray radiation dosage of the radiation direction destination object when supervision contrast concentration for monitoring contrast concentration in the part corresponding with ROI according to the CT equipment of exemplary embodiment.

According to exemplary embodiment, in order to monitor the contrast concentration in the part corresponding with ROI, control device 200 can carry out gated sweep device 100 pairs of destination objects according to X-ray projectional angle and carry out supervision scanning.Here, X-ray projectional angle can be set according to the position of the area-of-interest selected.

Fig. 2 show for illustration of setting X-ray projectional angle step and determine the diagram of step of the passage corresponding with ROI.

As shown in Figure 2, first, operator manually can select ROI in baseline image.Although be depicted as by ROI in fig. 2 and have round-shaped, but exemplary embodiment is not limited thereto, and the shape of ROI can change as required, and such as, ROI can have rectangular shape.

Then, X-ray projectional angle can be set like this, that is, make the region corresponding with X-ray projectional angle correspond to target arterial (such as, aorta) in ROI and not overlapping with the tremulous pulse outside ROI.Such as, operator can move (such as, rotate) for limiting the graticule of X-ray projectional angle, target arterial in ROI is corresponded to (such as to make the X-ray projectional angle limited by graticule while making graticule crossing with the periphery of ROI, aorta) and not overlapping with the tremulous pulse outside ROI, as shown in Figure 2.

After setting X-ray projectional angle, control device 200 can carry out supervision scanning according to projectional angle gated sweep device 100 pairs of destination objects after being filled with contrast agent to destination object of setting.Specifically, control device 200 can rotate to the position corresponding with the projectional angle of setting by gated sweep device 100, then, scanning means 100 can be made no longer to rotate, and carries out supervision scanning simultaneously.Therefore, with carry out monitoring compared with traditional CT equipment of scanning while rotating, CT equipment according to exemplary embodiment can monitor scanning more frequently to the specific part of destination object within the same time, therefore can increase the sample rate of contrast concentration.Such as, according to the sample rate of the CT equipment of current exemplary embodiment can be 984 times or the higher of sample rate of traditional CT equipment.

By such supervision scanning, can obtain multiple sampled data, wherein, each sampled data includes the multiple data obtained by the multiple Air conduct measurement in x-ray detection device 130.Therefore, according to exemplary embodiment, control device 200 can determine the passage corresponding with area-of-interest in X-ray sensing apparatus according to the position of ROI and X-ray projectional angle, thus in sampled data, determine the data corresponding to the passage corresponding with area-of-interest.

Such as, the passage corresponding with area-of-interest can be determined according to following formula:

$r1=a\tan \left(\frac{x1-\mathrm{xv}1}{y1-\mathrm{yv}1}\right)-\mathrm{\θ}$

$r2=a\tan \left(\frac{x2-\mathrm{xv}2}{y2-\mathrm{yv}2}\right)-\mathrm{\θ}$

$c1=\mathrm{Ccenter}+r1\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

$c2=\mathrm{Ccenter}+r2\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

In formula, (x1, y1) be the coordinate of the pixel in the upper left corner of ROI, (x2, y2) be the coordinate of the pixel in the lower right corner of ROI, the distance at the position of the destination object of SID corresponding to the center from X-ray generator to baseline image, the coordinate of the center pixel of baseline image is (x01, y01), θ be setting X-ray projectional angle (namely, the anglec of rotation of X-ray generator 110), (xv1, and (xv2 yv1), yv2) vertical line through the center of baseline image and the coordinate of intersection point of graticule limiting X-ray projectional angle is respectively, Ccenter is the middle numbering in the numbering of the passage of X-ray sensing apparatus 130, Cmax is the maximum numbering in the numbering of the passage of X-ray sensing apparatus 130, rh be from X-ray generator 110 be transmitted into X-ray sensing apparatus 130 in the middle of numbering passage X-ray and be transmitted into from X-ray generator 110 X-ray sensing apparatus 130 maximum numbering passage X-ray between angle, c1 and c2 is respectively the lowest number of the passage corresponding with area-of-interest and maximum numbering.

Fig. 3 shows the curve chart of the sampled data obtained by scanning destination object according to exemplary embodiment.

In the ongoing illustrated embodiment, determine that the passage corresponding with ROI is shown in figure 2 from the 480th passage to the 520th passage by above formula.Therefore, in curve chart shown in Figure 3, the data corresponding with ROI are confirmed as by with the data obtained to the 520th passage from the 480th passage, wherein, transverse axis represents channel number, and the longitudinal axis represents the degree decayed because object blocks during the X-ray of launching from X-ray generator 110 incides each passage of x-ray detection device 130.

Then, control device 200 can determine the contrast concentration corresponding with ROI according to the data obtained by the passage corresponding with area-of-interest in the sampled data obtained.Such as, control device can calculate the contrast concentration corresponding with ROI according to following formula:

$D\left(n\right)=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_n\left(i\right)-B$

$B=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_p\left(i\right)$

In formula, P _ni () represents the sampled data obtained by No. i-th passage by carrying out destination object monitoring scanning n-th time, P _pi () represents the sampled data obtained by No. i-th passage by carrying out prescan to destination object, B is the baseline value carrying out prescan to destination object and obtained by the passage corresponding with area-of-interest, D represents the contrast concentration corresponding with area-of-interest when carrying out monitoring scanning for n-th time to destination object, n and i is natural number.

Therefore, the contrast concentration of ROI during each supervision scanning can be determined by repeatedly monitoring scanning, thus contrast concentration is monitored over time.Such as, according to exemplary embodiment, curve chart as shown in Figure 4 can be obtained, wherein, Fig. 4 shows by carrying out monitoring scanning 40 times and obtains the contrast concentration corresponding with ROI curve chart over time, wherein, transverse axis represents the number of times monitoring scanning, contrast concentration corresponding with area-of-interest when the longitudinal axis represents that each supervision scans.

According to exemplary embodiment, CT equipment only can carry out supervision to the part corresponding with area-of-interest (ROI) of destination object when carrying out contrast concentration and monitoring and scan, instead of supervision scanning is carried out to the entirety of destination object, thus the X-ray radiation dosage being radiated destination object can be reduced, and the sample rate monitoring scanning can be increased.

Fig. 5 shows the block diagram of the contrast concentration defining method according to exemplary embodiment.Hereinafter, for brevity, the repeatability omitted for same or similar element or feature is described.

As shown in Figure 5, first can select in the baseline image of destination object area-of-interest (ROI) (S510).Here, prescan can be carried out to destination object, to obtain baseline image.

After have selected ROI, X-ray projectional angle (S530) can be set according to the position of the ROI selected.Such as, operator can rotate the graticule limiting X-ray projectional angle, corresponds to the target arterial in area-of-interest and not overseas with region of interest tremulous pulse is overlapping to make the region corresponding with X-ray projectional angle.

After injecting contrast agent to destination object, supervision scanning can be carried out, to obtain sampled data (S550) according to the X-ray projectional angle of setting to destination object.Such as, after control X-ray generator moves to the position corresponding with X-ray projectional angle, while X-ray generator can be made to keep current location constant, supervision scanning is carried out to destination object.Here, X-ray generator is identical with the X-ray generator 110 described with reference to Fig. 1, therefore no longer will carry out repeated description to it.

After obtaining sampled data, the contrast concentration (S570) corresponding with ROI can be determined according to the sampled data obtained.Such as, the passage corresponding with ROI in X-ray sensing apparatus can be determined according to the position of area-of-interest and X-ray projectional angle.In one exemplary embodiment, the passage corresponding with ROI can be determined according to following formula:

$r1=a\tan \left(\frac{x1-\mathrm{xv}1}{y1-\mathrm{yv}1}\right)-\mathrm{\θ}$

$r2=a\tan \left(\frac{x2-\mathrm{xv}2}{y2-\mathrm{yv}2}\right)-\mathrm{\θ}$

$c1=\mathrm{Ccenter}+r1\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

$c2=\mathrm{Ccenter}+r2\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

Here, X-ray sensing apparatus can be identical with the X-ray sensing apparatus 130 described with reference to Fig. 1, therefore no longer will carry out repeated description to it.

Then, the contrast concentration corresponding with ROI can be determined according to the data obtained by the passage corresponding with ROI in the sampled data obtained.Such as, the contrast concentration corresponding with area-of-interest can be calculated according to following formula:

$D\left(n\right)=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_n\left(i\right)-B$

$B=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_p\left(i\right)$

Therefore, the contrast concentration of ROI during each supervision scanning can be determined by repeatedly monitoring scanning, thus contrast concentration is monitored over time.Such as, according to exemplary embodiment, contrast concentration curve chart over time corresponding with ROI as shown in Figure 4 can be obtained, wherein, carry out 40 times and monitored scanning.

According to exemplary embodiment, contrast concentration defining method only can carry out supervision to the part corresponding with area-of-interest (ROI) of destination object when carrying out contrast concentration and monitoring and scan, instead of supervision scanning is carried out to the entirety of destination object, thus the X-ray radiation dosage being radiated destination object can be reduced, and the sample rate monitoring scanning can be increased.

Be described above some exemplary embodiments.It should be understood, however, that and can make various amendment.Such as, if if described technology is combined by different way with the assembly in the execution of different orders and/or described system, framework, equipment or circuit and/or is substituted by other assembly or its equivalent or supplement, then suitable result can be realized.Correspondingly, other embodiments also fall in the protection domain of claim.

Claims (15)

1. a contrast concentration defining method, described method comprises:

Area-of-interest is selected in the baseline image of destination object;

Position according to the area-of-interest selected sets X-ray projectional angle;

After injecting contrast agent to destination object, the X-ray projectional angle according to setting carries out supervision scanning, to obtain sampled data to destination object;

The contrast concentration corresponding with area-of-interest is determined according to the sampled data obtained.

2. the method for claim 1, wherein described method also comprises:

Prescan is carried out to destination object, to obtain baseline image.

3. the method for claim 1, wherein, in the step of setting X-ray projectional angle, the graticule of rotation restriction X-ray projectional angle, corresponds to the target arterial in area-of-interest to make the region corresponding with X-ray projectional angle and not overseas with region of interest tremulous pulse is overlapping.

4. the method for claim 1, wherein, carrying out monitoring in the step of scanning, after control X-ray generator moves to the position corresponding with X-ray projectional angle, supervision scanning is carried out to destination object, wherein, X-ray generator produces X-ray, and by the x-ray bombardment of generation to destination object.

5. the method for claim 1, determine that the step of the contrast concentration corresponding with area-of-interest comprises:

The passage corresponding with area-of-interest in X-ray sensing apparatus is determined according to the position of area-of-interest and X-ray projectional angle, wherein, the reception of X-ray sensing apparatus is produced by X-ray generator and passes the X-ray of destination object, and the X-ray of reception is converted to the signal of telecommunication.

6. method as claimed in claim 5, wherein, determine the passage corresponding with area-of-interest according to following formula:

$r1=a\tan \left(\frac{x1-\mathrm{xv}1}{y1-\mathrm{yv}1}\right)-\mathrm{\θ}$

$r2=a\tan \left(\frac{x2-\mathrm{xv}2}{y2-\mathrm{yv}2}\right)-\mathrm{\θ}$

$c1=\mathrm{Ccenter}+r1\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

$c2=\mathrm{Ccenter}+r2\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

Wherein, (x1, y1) be the coordinate of the pixel in the upper left corner of area-of-interest, (x2, y2) be the coordinate of the pixel in the lower right corner of area-of-interest, θ is the X-ray projectional angle of setting, (xv1, and (xv2 yv1), yv2) be vertical line through the center of baseline image and the coordinate of intersection point of graticule limiting X-ray projectional angle, Ccenter is the middle numbering in the numbering of the passage of X-ray sensing apparatus, Cmax is the maximum numbering in the numbering of the passage of X-ray sensing apparatus, rh is transmitted into angle between the X-ray with the passage of middle numbering of X-ray sensing apparatus and the X-ray with the passage of maximum numbering being transmitted into X-ray sensing apparatus from X-ray generator from X-ray generator, c1 and c2 is respectively the lowest number of the passage corresponding with area-of-interest and maximum numbering.

7. method as claimed in claim 5, wherein, determine that the step of the contrast concentration corresponding with area-of-interest also comprises:

The contrast concentration corresponding with area-of-interest is determined according to the data obtained by the passage corresponding with area-of-interest in the sampled data obtained.

8. method as claimed in claim 7, wherein, calculates the contrast concentration corresponding with area-of-interest according to following formula:

$D\left(n\right)=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_n\left(i\right)-B$

$B=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_p\left(i\right)$

Wherein, P _ni () represents the sampled data obtained by No. i-th passage by carrying out destination object monitoring scanning n-th time, P _pi () represents the sampled data obtained by No. i-th passage by carrying out prescan to destination object, B is the baseline value carrying out prescan to destination object and obtained by the passage corresponding with area-of-interest, D represents the contrast concentration corresponding with area-of-interest when carrying out monitoring scanning for n-th time to destination object, n and i is natural number.

9. a computerized tomography equipment, comprising:

Scanning means, comprise X-ray generator and X-ray receiving system, X-ray generator is constructed to produce X-ray, and by the x-ray bombardment of generation to destination object, X-ray receiving system, be constructed to receive the X-ray through destination object, and convert the X-ray of reception to the signal of telecommunication, X-ray receiving system comprises multiple passage;

Control device, be constructed to gated sweep device and prescan is carried out to destination object, to obtain baseline image, and be constructed to after injecting contrast agent to destination object, according to X-ray projectional angle gated sweep device, supervision scanning is carried out to destination object, with the contrast concentration that the area-of-interest determined with select in baseline image is corresponding, wherein, X-ray projectional angle is set according to the position of the area-of-interest selected.

10. computerized tomography equipment as claimed in claim 9, wherein, X-ray projectional angle is set to the region corresponding with X-ray projectional angle and corresponds to the target arterial in area-of-interest and not overseas with region of interest tremulous pulse is overlapping.

11. computerized tomography equipment as claimed in claim 9, wherein, control device is configured to making after the X-ray generator of scanning means moves to the position corresponding with X-ray projectional angle further, and gated sweep device carries out supervision scanning to destination object.

12. computerized tomography equipment as claimed in claim 9, wherein, control device is also constructed to the passage corresponding with area-of-interest determined according to the position of area-of-interest and X-ray projectional angle in X-ray sensing apparatus.

13. computerized tomography equipment as claimed in claim 12, wherein, control device is constructed to determine the passage corresponding with area-of-interest according to following formula:

$r1=a\tan \left(\frac{x1-\mathrm{xv}1}{y1-\mathrm{yv}1}\right)-\mathrm{\θ}$

$r2=a\tan \left(\frac{x2-\mathrm{xv}2}{y2-\mathrm{yv}2}\right)-\mathrm{\θ}$

$c1=\mathrm{Ccenter}+r1\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

$c2=\mathrm{Ccenter}+r2\×\frac{(C\max -\mathrm{Ccenter})}{\mathrm{rh}}$

Wherein, (x1, y1) be the coordinate of the pixel in the upper left corner of area-of-interest, (x2, y2) be the coordinate of the pixel in the lower right corner of area-of-interest, θ is the X-ray projectional angle of setting, (xv1, and (xv2 yv1), yv2) vertical line through the center of baseline image and the coordinate of intersection point of graticule limiting X-ray projectional angle is respectively, Ccenter is the middle numbering in the numbering of the passage of X-ray sensing apparatus, Cmax is the maximum numbering in the numbering of the passage of X-ray sensing apparatus, rh is transmitted into angle between the X-ray with the passage of middle numbering of X-ray sensing apparatus and the X-ray with the passage of maximum numbering being transmitted into X-ray sensing apparatus from X-ray generator from X-ray generator, c1 and c2 is respectively the lowest number of the passage corresponding with area-of-interest and maximum numbering.

14. computerized tomography equipment as claimed in claim 12, wherein, control device is constructed to determine the contrast concentration corresponding with area-of-interest according to the data obtained by the passage corresponding with area-of-interest in the sampled data obtained.

15. computerized tomography equipment as claimed in claim 14, wherein, control device is constructed to calculate the contrast concentration corresponding with area-of-interest according to following formula:

$D\left(n\right)=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_n\left(i\right)-B$

$B=\underset{i=c1}{\overset{c2}{\mathrm{\Σ}}}{P}_p\left(i\right)$

Wherein, P _ni () represents the sampled data obtained by No. i-th passage by carrying out destination object monitoring scanning n-th time, P _pi () represents the sampled data obtained by No. i-th passage by carrying out prescan to destination object, B is the baseline value carrying out prescan to destination object and obtained by the passage corresponding with area-of-interest, D represents the contrast concentration corresponding with area-of-interest when carrying out monitoring scanning for n-th time to destination object, n and i is natural number.