PROCESS FOR THE DETERMINATION OF THE CROSS-SECTIONAL AREA AND VOLUME OF AN OBJECT

Abstract

A process for the determination of the cross-sectional area and volume of an object including the steps of a. Providing a container having a closed bottom, an open top, a side wall, a tap at a reference height, b. Providing a flowable medium having a surface in the container, c. Providing at least one measuring means for measuring a height of the surface of the flowable medium in the container relative to the reference height, d. Providing an object having a vertical Z-axis relative to the X,Y plane of the surface and positioning the object in the container, the object being at least partly submerged in the flowable medium, e. Providing calculating means for calculating the cross-sectional area and/or volume of the object in the X,Y plane relative to a position on the Z-axis, f. Opening the tap in the container to allow the flowable medium to flow out of the container, g. Measuring the height of the surface of the flowable medium relative to the reference height as a function of time (h(t)) during the outflow of the flowable medium, h. Calculating the cross-sectional area of the object (A.sub.o) as a function of the height relative to the reference height based on the determined height of the surface as a function of time (h(t)) during the outflow of the flowable medium in step f). A device for measuring the cross-sectional area and volume of an object.

Claims

1. A process for the determination of a cross-sectional area (A.sub.o) as a function of a height of an object, comprising the steps of: a. Providing a container having a closed bottom, an open top, a side wall, a tap at a reference height, b. Providing a flowable medium having a surface in the container, c. Providing at least one measuring means for measuring a height of the surface of the flowable medium in the container relative to the reference height, d. Providing an object having a vertical Z-axis relative to a X,Y plane of the surface and positioning the object in the container, the object being at least partly submerged in the flowable medium, e. Providing calculating means for calculating the cross-sectional area and/or volume of the object in the X,Y plane relative to a position on the Z-axis, f. Opening the tap in the container to allow the flowable medium to flow out of the container, or removing the flowable medium by using a pump, or adding flowable medium to the container, g. Measuring the height of the surface of the flowable medium relative to the reference height as a function of time (h(t)) during the outflow or inflow of the flowable medium, h. Calculating the cross-sectional area of the object (A.sub.o) as a function of the height relative to the reference height based on the determined height of the surface as a function of time (h(t)) during the outflow or inflow of the flowable medium in step f).

2. The process according to claim 1, further comprising calculating a volume of any defined segment of the object based on to the height of the object relative to the reference height.

3. The process according to claim 1, correcting the cross-sectional area (A.sub.o) of the object as a function of height for an offset of the object relative to the reference height in a vertical direction of the object.

4. The process according to claim 1, wherein the container is cylindrical.

5. The process according to claim 1, wherein the flowable medium is a liquid.

6. The process according to claim 1, wherein the object is a part of a human body.

7. The process according to claim 1, wherein the container is cylindrical and comprises one tap, the means for measuring the height is a pressure sensor and the flowable medium is water.

8. The process according to claim 1, wherein the calculation of the cross-sectional area of the object is based on a non-stationary mass balance equation and the Bernouilli equation.

9. The process according to claim 4, wherein an equation is used for the determination of a cross-sectional area, wherein the equation is $A_{\mathrm{cs}}*\frac{.Math..Math.h}{.Math..Math.t}=-C_c.Math.C_f.Math..Math..Math.r^2.Math.\sqrt{2.Math.g.Math.h}.Math.\left(t\right)$ wherein A.sub.cs=cross-sectional area of the annular space between the object and the wall of the container $\frac{.Math..Math.h}{.Math..Math.t}=\mathrm{difference}.Math..Math.\mathrm{quotient},.Math.\mathrm{change}.Math..Math.\mathrm{in}.Math..Math.\mathrm{height}.Math..Math.\mathrm{of}.Math..Math.\mathrm{the}.Math..Math.\mathrm{flowable}$ $\mathrm{medium}.Math..Math.\mathrm{in}.Math..Math.\mathrm{the}.Math..Math.\mathrm{container}.Math..Math.\mathrm{as}.Math..Math.\mathrm{function}.Math..Math.\mathrm{of}.Math..Math.\mathrm{time}$ r=radius of the tap opening, C.sub.c=factor correcting for contraction side effects, C.sub.f=factor correcting for friction side effects, g=acceleration due to gravity h(t)=height of the flowable medium as function of time and t=time.

10. A device for performing the process according to claim 1, wherein the device comprises a container comprising a closed bottom, an open top, a side wall and at least one tap and at least one means for measuring the height of a flowable medium in the container.

11. The device according to claim 10, wherein the at least one means for measuring the height is selected from a pressure sensor, a conduction sensor, a balance, a weighing scale, an altimeter, a tape measure and optical means.

12. The device according to claim 10, wherein the container comprises a flowable medium and an object.

13. The process according to claim 1, further including the step of assessing tissue edema.

14. The process according to claim 13, wherein the tissue edema in an arm or a leg is assessed.

15. The process according to claim 5, wherein the liquid is water.

16. The process of claim 6, wherein the part of the human body is an arm or leg.

17. The process according to claim 2, correcting the cross-sectional area (A.sub.o) of the object as a function of height for an offset of the object relative to the reference height in a vertical direction of the object.

18. The process according to claim 7, wherein an equation is used for the determination of a cross-sectional area, wherein the equation is $A_{\mathrm{cs}}*\frac{.Math..Math.h}{.Math..Math.t}=-C_c.Math.C_f.Math..Math..Math.r^2.Math.\sqrt{2.Math.g.Math.h}.Math.\left(t\right)$ wherein A.sub.cs=cross-sectional area of the annular space between the object and the wall of the container $\frac{.Math..Math.h}{.Math..Math.t}=\mathrm{difference}.Math..Math.\mathrm{quotient},.Math.\mathrm{change}.Math..Math.\mathrm{in}.Math..Math.\mathrm{height}.Math..Math.\mathrm{of}.Math..Math.\mathrm{the}.Math..Math.\mathrm{flowable}$ $\mathrm{medium}.Math..Math.\mathrm{in}.Math..Math.\mathrm{the}.Math..Math.\mathrm{container}.Math..Math.\mathrm{as}.Math..Math.\mathrm{function}.Math..Math.\mathrm{of}.Math..Math.\mathrm{time}$ r=radius of the tap opening, C.sub.c=factor correcting for contraction side effects, C.sub.f=factor correcting for friction side effects, g=acceleration due to gravity h(t)=height of the flowable medium as function of time and t=time.

19. The process according to claim 9, further including the step of assessing tissue edema.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0092] The present invention is further elucidated referring to FIGS. 1, 2, 3, 4A, 4B, 5A, 5B, 6, 7 and 8 in which:

[0093] FIG. 1 illustrates the device for the determination of the cross-sectional area and/or the volume of an object.

[0094] FIG. 2 illustrates a side view of a container comprising a flowable medium.

[0095] FIG. 3 illustrates a side view of a container comprising a flowable medium and a leg of a person.

[0096] FIGS. 4A and 4B illustrate a side view of a container comprising a flowable medium and a leg of a person at different stages of the measurement.

[0097] FIGS. 5A and 5B illustrate the cross-section of the container and body at a height H and H (see FIGS. 4A and 4B).

[0098] FIG. 6 illustrates the height of a water column in a deflating cylindrical container as function of time. The following assumptions are made: R=0.15 m, r=0.005 m, C.sub.c=0.62 and C.sub.f=0.73.

[0099] FIG. 7 is a representation of the height of a water column in a deflating cylindrical container. The lower curve in FIG. 7 represents the results of a container containing a leg of a shop-window dummy. The upper curve in FIG. 7 represents the reference wherein the container contained no object.

[0100] FIG. 8 represents a graph of the radius of the leg versus the height of the leg (1) This graph was compared with some measurements using a tailor tape (2).

DETAILED DESCRIPTION OF THE INVENTION

[0101] In FIG. 1 the device 1 for the determination of the cross-sectional area and/or the volume of an object is shown. The device comprises a cylindrical container 2. The container has an open top 3, a side wall 4 and a closed bottom 5. On the container a scale 7 can be provided so that the (change of the) height of flowable medium 12 in the container 2 can be read. The container is provided with an outlet preferably comprising a tap 8. The container 2 has a volume 6, which is larger than the total volume of the body part which will be inserted in the container 2 and the volume of flowable medium 12. The flowable medium 12 has a surface 13 which defines the X,Y-plane.

[0102] The cylindrical container 2 can be provided with a pressure sensor 9. Above the container 2 an altitude sensor 11 can be provided that can determine the height of the surface 13 of the flowable medium 12. The container 2 can also been placed on a weighing scale 10.

[0103] The device 1 optionally contains one or more taps and/or measuring means.

[0104] FIG. 2 shows a side view of the device 1, comprising the container 2 having side wall 4, bottom 5 and opening 3 with tap 8. The container 2 is provided with a scale 7, a pressure sensor 9, a weighing scale 10 and an altitude sensor 11. The X-axis and the Y-axis lie in the plane of the surface 13 of the flowable medium 12. The Z-axis is perpendicular to the X and Y axis. The container (2) is filled to a level H with flowable medium 12. The cross sectional area of the flowable medium 12 is defined by A.

[0105] FIG. 3 shows a side view of a container 2 according to FIG. 2. A person P is standing with one leg L in the container. The container is filled with flowable medium 12 in the container 2 to level H. The Z-axis is illustrated by the arrow Z on the leg L of the person P.

[0106] FIGS. 4A and 4B illustrate a side view of a container 2 according to FIG. 3. The container 2 comprises a flowable medium 12 and a leg L of a person P. During the measurement flowable medium 12 is removed via the tap 8. FIGS. 4A and 4B show the container 2 at different stages of the measurement. According to FIG. 4A the height of the flowable medium 12 is lowered to height H and according to FIG. 4B the height of the flowable medium 12 is further lowered to height H.

[0107] FIGS. 5A and 5B illustrate a cross sectional view of a container 2 comprising a leg L at height Va according to FIG. 4A and height Vb according to FIG. 4B. At height Va the leg L has a cross sectional area A. At height Vb the leg L has a cross sectional area A. The annular space A in FIGS. 5A and 5B is equal to the cross-sectional area A.sub.cs. Comparing of FIGS. 5A and 5B shows that the cross sectional area A of the leg L is larger than the cross sectional area A of the leg L.

[0108] The process for the determination of the cross-sectional area is described on the basis of FIGS. 3, 4A and 4B. FIG. 3 shows the starting point of the measurement where the flowable medium 12 has height H and the tap 8 is closed. The tap 8 is opened and the flowable medium 12 descends to a height H as shown in FIG. 4A or a height H as shown in FIG. 4B. During the outflow of the flowable medium 12 at least one of the measuring means 7, 9, 10 or 11 is used to determine the height of the flowable medium. The heights H, H and H can be used to calculate the volume of the leg between H and H, H and H or H and H. It is also possible to calculate the cross-sectional area at height H, H or H by using equation 10 as described here above.

[0109] In practice, the height differences between the individual measuring points will be smaller than in the above explanation. Thereby the measurement can become a nearly continuous measurement of the cross sectional area of the object.

[0110] Although the invention has been described in detail for purposes of illustration, it is understood that such detail is solely for that purpose and variations can be made therein by those skilled in the art without departing from the spirit and scope of the invention as defined in the claims.

[0111] It is further noted that the invention relates to all possible combinations of features described herein, preferred in particular are those combinations of features that are present in the claims.

[0112] It is noted that the term comprising does not exclude the presence of other elements. However, it is also to be understood that a description on a product comprising certain components also discloses a product consisting of these components. Similarly, it is also to be understood that a description on a process comprising certain steps also discloses a process consisting of these steps.

EXAMPLE

[0113] A cylindrical container 2 (diameter 30 cm) provided with a tap 8 and only a pressure sensor 9 according to FIG. 1 was used. During the experiments the temperature of the water remained at a constant value.

[0114] Time was monitored using a conventional watch and the water height was monitored by eye. Deflation of the container was done with only water in the container (reference) and subsequently with a leg of a shop-window dummy in the water in the container. The foot of the leg was placed on the bottom of the container and the leg touched the wall of the container at the top. The results of the test are presented by the lower curve in FIG. 7. The upper curve in FIG. 7 represents the reference.

[0115] The curves show that the rate of deflation

[00020]$\left(\frac{.Math..Math.h}{.Math..Math.t}\right)$

is higher in the presence of the leg. The curve representing the situation where the leg is present shows a slope that is steeper at any height h(t), compared to the curve of the reference container without the leg.

[0116] The set of measuring points was mathematically processed as described above, rendering

[00021]$\left(\frac{.Math..Math.h}{.Math..Math.t}\right).$

[0117] Thereafter, the cross-sectional area of the leg at any height was calculated starting from equation (10). For a cylindrical container A.sub.c=R.sup.2 and the annular space is described by .(R.sup.2R.sub.leg.sup.2), assuming the leg is perfectly cylindrical at any height. This rendered the following equation:

[00022]$.Math.\left(R^2-R_{\mathrm{leg}}^2\right)*\frac{.Math..Math.h}{.Math..Math.t}=-C_c.Math.C_f.Math..Math..Math.r^2.Math.\sqrt{2.Math.g.Math.h}$

[0118] As

[00023]$\left(\frac{.Math..Math.h}{.Math..Math.t}\right),$

at any height h was known, as well as R and r, the radius of the leg at any height could be calculated.

[0119] In FIG. 8 this calculation of the radius of the leg was compared with some measurements using a tailor tape.