computed tomographic

An interactive3D visualization and manipulation tool for effective assessment of angiogenesis and arteriogenesis using computed tomographic angiography
Li Shen a,c,Ling Gao b,Zhenwu Zhuang b,Ebo DeMuinck b,
Heng Huang c,Fillia Makedon c,and Justin Pearlman b
a Image and Pattern Analysis Laboratory,Department of Computer and Information Science,
University of Massachusetts Dartmouth,North Dartmouth,MA02747,USA
b Angiogenesis Research Center,Departments of Radiology and Cardiology,
Dartmouth Medical School,Lebanon,NH03756,USA
c Dartmouth Experimental Visualization Laboratory,Department of Computer Science,
Dartmouth College,Hanover,NH03755,USA
ABSTRACT
This paper presents IVM,an Interactive Vessel Manipulation tool that can help make effective and efficient as-sessment of angiogenesis and arteriogenesis in computed tomographic angiography(CTA)studies.IVM consists of three fundamental components:(1)a visualization component,(2)a tracing component,and(3)a measure-ment component.Given a user-specified threshold,IVM can create a3D surface visualization based on it.Since vessels are thin and tubular structures,using standard isosurface extraction techniques usually cannot yield satisfactory reconstructions.Instead,IVM directly renders the surface of a derived binary3D image.The image volumes collected in CTA studies often have a relatively high resolution.Thus,compared with more complicated vessel extraction and visualization techniques,rendering the binary image surface has the advantages of being effective,simple and fast.IVM employs a semi-automatic approach to determine the threshold:a user can adjust the threshold by checking the corresponding3D surface reconstruction and make the choice.Typical tracing software often defines ROIs on3D image volumes using three orthogonal views.The tracing component in IVM takes one step further:it can perform tracing not only on image slices but also in a3D view.We observe that directly operating on a3D view can help a tracer identify ROIs more easily.After setting a threshold and tracing an ROI,a user can use IVM’s measurement component to estimate the volume and other parameters of vessels in the ROI.The effectiveness of the IVM tool is demonstrated on rat vessel/bone images collected in a previous CTA study.
Keywords:Computed tomographic angiography,3D surface visualization,region of interest,vessel extraction
1.INTRODUCTION
Computed tomographic angiography(CTA)has been used to investigate therapeutic arteriogenesis of local fresh bone marrow cell(FBMC)in a rat ischemia hindlimb model.1,2One key component in the assessment process is to localize a region of interest(ROI)and quantify arteriogenesis in such an ROI.In our previous study,1,2the Vitrea2software3is used to create a3D volume visualization of an image stack,which aims to provide some hints for an expert to define an ROI by tracing each2D slice of the stack.In the quantification step,a modified ImageJ software4is used by a technician to manually calculate the area of arteriogenesis in each2D slice and Send correspondence to Li Shen.E-mails:lshen@,{ling.gao,zhenwu.zhuang,ebo.demuinck,heng.huang,fillia.makedon,justin.pearlman}@
Copyright2005Society of Photo-Optical Instrumentation Engineers.This paper will be published in SPIE Medical Imaging2005:Visualization,Image-Guided Procedures,and Display,Proc.5744and is made available as an electronic reprint(preprint)with permission of SPIE.One print or electronic copy may be made for personal use only.Systematic or multiple reproduction,distribution to multiple locations via electronic or other means,duplication of any material in this paper for a fee or for commercial purposes,or modification of the content of the paper are prohibited.
(a)binary object(b)rendering using matlab command isosurface Figure1.(a)A binary volume B,whose surface is composed of a set of square faces.(b)Surface rendering of the same object B using matlab command“isosurface(B,0.5)”,where undesired disconnectedness exists if either18-connectivity or26-connectivity is assumed.
then generate thefinal volume measure by summing up all the2D areas.This is effective but time-consuming and tedious.In addition,tracing a desired ROI in each single image slice is not an easy and trivial task,even with a3D visualization of the whole image volume available.In this work,we develop IVM,an Interactive Vessel Manipulation tool that can overcome the above problems.IVM is specifically designed to help make effective and efficient assessment of angiogenesis and arteriogenesis in CTA studies.
2.METHODS
IVM consists of three fundamental components:(1)a visualization component,(2)a tracing component,and(3) a measurement component.The key technique behind these components is a simple and effective vessel/bone extraction algorithm based on isosurface construction.In this section,wefirst present this algorithm,and then describe the IVM system.
2.1.Fast algorithm for isosurface construction
A gray-level image volume can be represented by a three dimensional matrix of intensity values.Each element of this matrix is called a voxel.We can use f(x,y,z)to describe such a matrix,where(x,y,z)specifies the voxel coordinates and f(x,y,z)specifies the voxel intensity.To visualize structures embedded in a3D volume, isosurface construction is often used,where isosurfaces are surfaces within a volume that have the same parameter value.Isosurfaces can be extracted using simple thresholding approach as well as the standard Marching Cubes algorithm.5
Given a user-specified threshold,IVM creates a3D surface visualization of vessel/bone structures after thresholding an image volume.Since vessels are thin and tubular structures,using standard isosurface extrac-tion techniques(e.g.,the Marching Cubes algorithm5or the matlab routine)usually cannot yield satisfactory reconstructions;see Figure1for an example.To overcome this problem,IVM directly renders the surface of a derived binary3D image set.Figure1(a)shows a sample binary image rendered using this approach,where its surface is composed of a set of square faces.Note that our image volume has a relatively high resolution:its voxel size is0.19×0.19×0.85mm3and its dimensions are512×512×100.Thus,compared with more complicated vessel extraction and visualization techniques,6rendering the binary image surface has the advantages of being not only effective but also simple and fast.
2.1.1.Concepts and notation
We introduce some concepts and notation that will be used in the rest of the paper.Let
V f={(x,y,z,f(x,y,z))|x∈[1,n1],y∈[1,n2],z∈[1,n3]}
Figure2.Voxel(x,y,z),its corners,and faces.
be an n1×n2×n3data volume,where f(x,y,z)specifies the intensity value of voxel(x,y,z).Let
S={(x,y,z)|x∈[1,n1],y∈[1,n2],z∈[1,n3]}
be the space of voxel(integer)coordinates for V f.For convenience,in this paper,we use V b to denote a binary volume,where b(x,y,z)is a binary function defined on S;and use V f to denote a gray-level intensity volume, where f(x,y,z)takes integer values between0and255.
We interpret each voxel(x,y,z)∈S as a cube extending from x−0.5to x+0.5,y−0.5to y+0.5,and z−0.5to z+0.5.Thus,all possible voxel corners can be collected into a vertex set
C={(x−0.5,y−0.5,z−0.5)|x∈[1,n1+1],y∈[1,n2+1],z∈[1,n3+1]}.
We index each voxel corner(x−0.5,y−0.5,z−0.5)∈C as
I(x−0.5,y−0.5,z−0.5)=(x−1)∗(n2+1)∗(n3+1)+(y−1)∗(n3+1)+z.
This indexing scheme creates a bijective mapping between C and[1,(n1+1)∗(n2+1)∗(n3+1)].
Now based on the complete set C of voxel corner vertices and the indexing scheme I,for each voxel(x,y,z)∈S,we can define its six faces as follows(see Figure2):
a=I(x−0.5,y−0.5,z−0.5)
left(x,y,z)=(a,e,h,d)b=I(x+0.5,y−0.5,z−0.5)
right(x,y,z)=(c,g,f,b)c=I(x+0.5,y+0.5,z−0.5)
bottom(x,y,z)=(a,d,c,b),where d=I(x−0.5,y+0.5,z−0.5).
top(x,y,z)=(e,f,g,h)e=I(x−0.5,y−0.5,z+0.5)
front(x,y,z)=(a,b,f,e)f=I(x+0.5,y−0.5,z+0.5)
rear(x,y,z)=(c,d,h,g)g=I(x+0.5,y+0.5,z+0.5)
h=I(x−0.5,y+0.5,z+0.5) For simplicity,we use surface(V b)to denote the surface of a binary volume V b.Let V f be our input CTA
scan,which is a3D intensity volume.Let V t
f be the result of thresholdin
g V f using threshold t,and so V t
f
is a
binary image.Thus,one task of the IVM tool is to visualize surface(V t
f )for each possible t efficiently enough so
that one can use IVM to interactively select an appropriate threshold for best visualization and segmentation of a structure.To achieve this goal,wefirst present a simple surface extraction algorithm for a binary volume and then propose an efficient algorithm for extracting all the isosurfaces from a3D image by varying the threshold (i.e.,isovalue).
Note that the object voxels touching the border of the data volume often require a special treatment. Therefore,in this study,we make sure that all border voxels belong to the background by padding additional background layers to the volume if necessary.Therefore,in the rest of this paper,we only need to consider voxel coordinates x from2to n1−1,y from2to n2−1,and z from2to n3−1.For convenience,we use S interior={(x,y,z)|x∈[2,n1−1],y∈[2,n2−1],z∈[2,n3−1]}to denote the set of these voxel coordinates.
Algorithm 1Surface extraction for a binary object
Input :Binary image V b
Output :surface =surface (V b )
Begin
1:surface =∅
2:for each voxel (x,y,z )∈S interior such that b (x,y,z )=1do
3:if b (x −1,y,z )=0then 4:surface =surface {left(x,y,z )}
5:if b (x +1,y,z )=0then 6:surface =surface {right(x,y,z )}
7:if b (x,y −1,z )=0then 8:surface =surface {front(x,y,z )}
9:if b (x,y +1,z )=0then 10:surface =surface {rear(x,y,z )}
11:if b (x,y,z −1)=0then 12:surface =surface {bottom(x,y,z )}
13:if b (x,y,z +1)=0then 14:surface =surface {top(x,y,z )}
15:return surface End
2.1.2.Surface extraction for a binary volume
Given a 3D binary image V b ,it is easy to construct its surface.Algorithm 1shows a straightforward approach for surface construction of a binary object.Note that some notation used in Algorithm 1is defined in Section 2.1.1.The correctness of Algorithm 1is obvious,since the surface of a binary object can be defined as a set of all the square voxel faces whose two incident voxels are different.Algorithm 1organizes the four nodes of each voxel face on the surface mesh in a counterclockwise order if one looks at it from the outside.
We use matlab to implement Algorithm 1.Although a for-loop is involved in the description of Algorithm 1,it is easy to see that different iterations of the loop (i.e.,Lines 3-14)can actually run in parallel.This is because each iteration corresponds to the processing of a single different voxel.Thus,in our implementation,we do not need to use any for-loop,which is known very inefficient in matlab.Instead,we use vector and matrix operations to achieve a much better performance.
In addition,a surface structure is usually defined by a set of vertices and a set of ing a complete set of all voxel corners as the vertex set for a surface,it is enough for Algorithm 1to focus only on the creation of faces.In the actual implementation,we can employ a sparse vector to denote if a vertex index (∈I )is used in the final surface (V b );and then use this information to remove unnecessary vertices when rendering the surface.
2.1.
3.Surface extraction for an intensity volume
As mentioned before,the surface visualization strategy employed in IVM aims to allow adjustable thresholds.Thus,given a 3D intensity image V f ,IVM should be able to extract its isosurfaces for all possible thresholds (i.e.,isovalues).Given a user-specified threshold t ,one naive solution to visualize the desired isosurface is to first threshold V f using t ,and then use Algorithm 1to construct the surface for binary object V t f .
However,since our CTA scans are large-scale image volumes (with dimensions of 512×512×100),as reported later,the average running time (±standard deviation)for creating a single isosurface for a typical image volume is 27.8±0.4seconds.This is obviously not ideal for an interactive ing an alternative offline method,we need 7074seconds (1.96hours)to create all possible isosurfaces for that image volume.Therefore,the above naive solution is relatively inefficient.In order to accelerate the generation of isosurfaces for all the isovalues,we introduce a simple but effective data structure and then present an efficient rendering algorithm based on the structure.
The key observation for our algorithm is that the surface of V t
f is composed of exactly all the square voxel
faces u that satisfy the following condition:f(x1,y1,z1)<t≤f(x2,y2,z2),where(x1,y1,z1)and(x2,y2,z2)are two incident voxels of u.In other words,we have
surface(V t f)={u|f(x1,y1,z1)<t≤f(x2,y2,z2),v inci(u)={(x1,y1,z1),(x2,y2,z2)},u∈all voxel faces}, where v inci(u)is the set of two incident voxels of u.
With the above observation,we develop a data structure that enables efficientfindings of neighboring voxel values.Thus,we can make full use of efficient vector and matrix operations provided by matlab and avoid the use of expensive for-loops.This data structure consists of six additional3D volumes,
f left,f right,f front,f rear,f bottom,f top,
which store the neighboring voxel values for six different directions respectively:
f left(x,y,z)=f(x−1,y,z)
f right(x,y,z)=f(x+1,y,z)
f front(x,y,z)=f(x,y−1,z)
f rear(x,y,z)=f(x,y+1,z)
f bottom(x,y,z)=f(x,y,z−1)
f top(x,y,z)=f(x,y,z+1)
where(x,y,z)∈S interior.Since most of voxel values in our CTA scans are zeros,we can use a sparse vector to store each of these3D volumes to save space and time costs.
Now we can present Algorithm2,which extracts all possible isosurfaces for a3D image volume.The pre-computation of f left,f right,f front,f rear,f bottom,f top enables possible parallel processing of iterations of the inner for-loop(i.e.,Lines5−16).Thus,the inner for-loop can be replaced by some vector and matrix operations in a matlab implementation to improve the performance.Therefore,only the outer for-loop is needed in the implementation for creating all the isosurfaces for a3D volume.
Using Algorithm2,IVM can create these isosurfaces in two different manners:(1)run Algorithm2offline, store the results,and load the results when necessary;and(2)create any desired isosurface on thefly when the tool is being used.
2.2.IVM system and components
The IVM system contains three parts:(1)a visualization component,(2)a tracing component,and(3)a measurement ing these components,IVM can perform the following tasks:•Interactive selection of an appropriate threshold for semi-automatic segmentation of structures of interest in a3D image volume,where the selection is supported by a3D surface reference model.
•Determination of a region of interest(ROI)in a3D volume by performing tracing in a3D view and/or on
a set of2D image slices.
•Volume assessment for task-relevant structure parts constrained by an ROI.
Although IVM is originally designed for effective assessment of arteriogenesis using computed tomographic an-giography,it is a general3D image visualization and manipulation tool that can also be applied to other computer vision and medical image analysis problem.Figure3shows the interface of the IVM system,which includes a control panel(a),a3D surface viewer(b),and an image stack browser(c).The rest of this section provides a brief description of the IVM functionalities.
Algorithm 2Extracting all possible
isosurfaces
for
a
3D image volume
Input :3D image volume V f
Output :surface t =surface (V t f ),for all 0<t <255
Begin
1:Compute f left ,f right ,f front ,f rear
,f bottom ,f top
2:for t =1;t <255;t ++do
3:surface t =∅
4:for each voxel (x,y,z )∈S interior do
5:if f left (x,y,z )<t ≤f (x,y,z )then
6:surface t =surface t {left(x,y,z )}
7:if f right (x,y,z )<t ≤f (x,y,z )then 8:surface t =surface t {right(x,y,z )}
9:if f front (x,y,z )<t ≤f (x,y,z )then
10:surface t =surface t {front(x,y,z )}
11:if f rear (x,y,z )<t ≤f (x,y,z )then
12:surface t =surface t {rear(x,y,z )}
13:if f bottom (x,y,z )<t ≤f (x,y,z )then 14:surface t =surface t {bottom(x,y,z )}
15:if f top (x,y,z )<t ≤f (x,y,z )then 16:surface t =surface t {top(x,y,z )}
17:return surface 1,surface 2,...,surface 254
End
(a)Control panel (b)Surface viewer 010*******
400500
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450
500
Slice 55/100Volume = 60.004687 mm 3 (t=220)
(c)Image viewer
Figure 3.IVM interfaces:(a)control panel,(b)surface viewer,(c)image viewer.
2.2.1.Surface and image visualization
Visualization is a basic functionality of the IVM system.IVM is designed for processing high resolution3D image volumes,and it can visualize a3D volume using both an image viewer(Figure3(c))and a surface viewer (Figure3(b)).The image viewer displays axial slices one at a time,and the image slider in the control panel (Figure3(a))can be used to select different axial slices.
The surface viewer displays the surface of a thresholded volume using the current threshold setting.The threshold slider in the control panel can be used to adjust the threshold.Accordingly,the3D surface visualization is updated in the surface viewer.The new surface can be either loaded from a pre-computedfile or computed on thefly.The“Create”button in the control panel can be used to create pre-computed surfaces and save them in afiing the surface threshold slider,one can interactively evaluate the surface rendering results and pick the most appropriate threshold value for the extraction of structures of interest(vessels and bones in this study). In the surface viewer,one can rotate the3D visualization to select a satisfactory viewing angle.
Users can define an ROI using either the3D surface viewer or the2D image viewer.The ROI boundary is displayed in a different color(e.g.,green in Figure3).For the3D surface viewer,if one clicks“Preview(3D)”button in the control pattern,the structure within the ROI will be rendered in a different color(e.g.,green in Figure3(b)).This helps one determine if his/her definition of the ROI is appropriate.
2.2.2.Interactive tracing
After setting the threshold using the IVM visualization component,a satisfactory segmentation result of the structure of interest in the3D volume is available.Now the next step is to define an ROI in the3D space to localize task-relevant structure parts.Typical tracing softwares(e.g.,CTMRedit7and TROI8)usually define ROIs on3D image volumes using three orthogonal views.The tracing component in IVM takes one step further: it can perform tracing not only on image slices but also in a3D surface view.We observe that directly operating on a3D view can help a tracer identify ROIs more easily.
The tracing functionality on image slices is standard.One can define a2D contour on each slice,and a series of these contours from all the slices form the surface model of an ROI.We observe that,for a few neighboring slices,their ROI traces are often very similar.Thus,to avoid tracing each individual slice and save duplicated efforts,the IVM control panel provides“Copy2D ROI”button,whose functionality is to copy the ROI on the current slice to a set of user-specified image slices.
For tracing in a3D surface view,several standard views(e.g.,axial,coronal,sagittal)are provided by a popup menu in the control ing this menu,one can select to trace on the xy(axial),yz(coronal),or zx (sagittal)plane;or directly rotate the3D surface tofind an appropriate view for tracing.In this study,we use the coronal view to define an ROI.The tracing results on coronal view put constraints on y and z,but not on x.If additional tracing is performed on the xy or zx planes of a3D view,more constraints on x,y and z values can be placed on the ROI.
To introduce moreflexibility,an ROI can be projected onto each2D image slice.For example,Figure3(b) shows an ROI in a3D view,and Figure3(c)shows the projection of this ROI onto a2D slice.If necessary,each ROI on a2D slice can be adjusted by re-tracing the2D image slice.
2.2.
3.Effective measurement
After setting a threshold and tracing an ROI,a user can use the IVM’s measurement component to estimate the volume of vessels in the ROI.For example,the title part of Figure3(c)shows the estimated volume for the structure parts inside the ROI,which are those green vessels shown in Figure3(b).The future extension of IVM will be able to estimate multiple other parameters such as vessel diameter distributions and fractal dimensions.
The effectiveness of the measurement depends on a good selection of the threshold and an accurate definition of the ROI.IVM aims to achieve both goals.On one hand,IVM employs a semi-automatic approach to determine the threshold:a user can adjust the threshold by checking the corresponding3D surface reconstruction and then pick the best one.On the other hand,IVM allows one to operate directly on a3D view as well as traditional 2D image view,which can help a tracer identify ROIs more easily and effectively.
(a)Threshold =100(b)Threshold =220
Figure 4.3D surface visualizations of rat bones:(a)the threshold is set as 100;(b)the threshold is set as 220.Rat bones are extracted by thresholding its 3D image volume,where image intensity values range from 0to 255.A user can adjust the threshold value to an appropriate one by checking its corresponding visualization.
3.RESULTS
Rat vessel/bone images collected in our previous study 1,2are used to demonstrate the functionalities of the IVM tool.Figure 4shows 3D surface visualizations of rat bones using IVM.Rat bones are extracted by thresholding its 3D image volume,where image intensity values range from 0to 255.Figure 4(a)and Figure 4(b)show two rendering results after setting the thresholds as 100and 220,respectively.
Using IVM,a user can adjust the threshold to an appropriate value by checking its corresponding surface visualization.The threshold slider in the control panel is used to adjust the threshold.Our fast isosurface construction algorithm,Algorithm 2,is used to construct the surface of a thresholded volume.This can be done in two ways:(1)the surface can be created on the fly when one is using the IVM tool;(2)all possible isosurfaces of a given volume can be created offline and thus one just need to load the results when using the IVM tool.
In order to show that Algorithm 2is efficient enough to allow interactive manipulation of the threshold,we have performed several experiments on a Dell Workstation PWS670with a Xeon 3.00GHz CPU and 2.00GB of RAM,which is running WinXP Professional OS and Matlab version 7.0.In the experiments,a rat vessel/bone image stack is used and its resolution is 512×512×100.Both Algorithm 1and Algorithm 2are tested on this stack for extracting isosurfaces for all possible thresholds.Figure 5shows the running times (a)and the numbers of vertices (b)and faces (c)in the resulting surfaces for all the experiments.The average running time (±standard deviation)for creating a single isosurface is 6.7±0.4seconds using Algorithm 2and 27.8±0.4seconds using Algorithm 1.Clearly,it is quite feasible if we want to create the surface on the fly using Algorithm 2,while the performance of Algorithm 1is intolerable in this case.If we employ the offline approach,the processing time for creating all possible isosurfaces in advance of interactive manipulation is 1712seconds (28.5minutes)using Algorithm 2,and it is 7074seconds (1.96hours)using Algorithm 1.
After setting the threshold,an ROI needs to be traced to localize task-relevant structure parts.Figure 6shows an example of tracing such an ROI on the yz plane of a 3D view:(a)the green contour defines the ROI by putting constraints on y and z values,and the vessel parts within the ROI are highlighted in green;(b)the ROI and the vessel surface are viewed from another angle.Note that both bones and vessels are visualized in these plots;and including bones in the visualization sometimes can help localize an ROI.In addition,tracing can also be performed on the xy and xz planes of a 3D view,and thus more contraints on x ,y and z values can be placed on the ROI.
To introduce more flexibility,an ROI can be projected onto each 2D image slice.For example,Figure 3(b)shows an ROI in a 3D view,and Figure 3(c)shows the projection of this ROI onto a 2D slice.If necessary,each
threshold
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Figure5.Experimental results of isosurface creation:running times(a)of Algorithm1and Algorithm2,number of vertices(b)and number of faces(c)in the resulting surface are shown on Y-axis,the threshold used in the experiment is shown on X-axis.A rat vessel/bone image stack is used in this experiment and its resolution is512×512×100.
(a)Tracing an ROI on the yz plane of a3D view(b)View from another angle
Figure6.Tracing an ROI on the yz plane of a3D view in order to localize task-relevant vessel parts:(a)the green contour defines the ROI by putting constraints on the y and z values,and the vessel parts within the ROI are highlighted in green;(b)the ROI and the vessel surface are viewed from another angle.Note that both bones and vessels are visualized in these plots.
ROI on a2D slice can be adjusted,since an ROI can also be defined by directly tracing2D image slices.Figure7 shows an example of defining an ROI by directly tracing a series of2D image slices.
After setting the threshold and tracing the ROI,the vessel volume can be assessed using the IVM measurement pared with the previous process that uses the Vitrea2and the ImageJ softwares for vessel measurement,this new process using IVM can get matched or even better results using much less time.On a typical image stack,it takes at least2hours for a technician to measure the vessel volume for two sides of one rat using the ImageJ software.In addition,due to a lack of3D visualization,we are not very sure if the tracing results using ImageJ are accurate ing the IVM tool,we become more confident about our selection of task-relevant ROIs with the help of the3D vessel model reference.Furthermore,the IVM tool can also help accelerate our process for vessel measurement.Now we only need about30minutes to measure two side vessels of one rat using IVM.
4.CONCLUSIONS
The contribution of this work is the design and implementation of IVM,which is a semi-automatic tool for visualizing,extracting,manipulating,and measuring vessel/bone structures embedded in CTA image volumes. Extracting vessel/bone structures and defining ROIs are two key issues in this work.Although extensive work has been done on vessel extraction,6most of studies are targeted at automatic segmentation that is a very difficult process.IVM employs an interactive and semi-automatic approach to perform vessel extraction by providing fast surface visualization to help a user select a threshold.In addition,IVM allows a user to trace ROIs not only on2D image slices but also in a3D view.To sum up,IVM is an interactive vessel manipulation tool that can help make efficient and effective assessment of angiogenesis and arteriogenesis in CTA studies.
ACKNOWLEDGMENTS
This work was supported by the Flight Attendant Medical Research Institute.
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