Detecting the symmetry axis of the brain for stroke patients

Method development, application and analysis

Thesis of bachelorproject ‘Physics and Astrophysics’, size 12 EC, executed between 07-08-2010 and 01-09-2010

Author: Sanne Joon (5863732)

Supervisor: Dr. Henk Marquering Second corrector: Prof. Dr. Ed van Bavel

25-10-2010

AMC, University of Amsterdam,

department of Biomedical Physics faculty of Science

Abstract

Stroke is the rapid loss of brain function due to blood disturbance in the brain. It is one of the most deadly diseases in the world and demands rapid handling. The optimal treatment for stroke depends on the cause of the infarct, thrombus location and thrombus extent. The position and size thrombus can be determined on a CT angiography in which contrast agent is administered.

In order to enhance thrombi detection and to detect bleeding in the brain, the symmetry of the brain is investigated. The symmetry axis is determined using the shape of the skull from CT images. A model of the skull is defined as superimposed Gaussians and is fitted on the skull shape data.

The model is tested on CT scans from eight patients, from which two have had craniotomy surgery. For model validation, the calculated symmetry angles are compared with manually determined symmetry axes.

For non craniotomy patients, the model agrees well with the observer symmetry angles, with the exception for patients for which the skull shaped deviates too much from an ellipsoid.

For craniotomy patients, the model fails for the slices where the largest part of the craniotomy is visible. Fortunately, the lower slices due seem to give reasonably accurate symmetry angle.The model cannot detect the symmetry angle for craniotomy patient data sets with a missing image part.

The interobserver and intraobserver variance are both smaller than the difference between method symmetry angle and observer symmetry angle. Nevertheless, the described model produces accurate approximations of the symmetry axis of the brain.

Contents

Introduction 5

1 Stroke 6 1.1 Types of stroke 6 1.2 Treatment 8 1.3 Clot location and extent correlated with infarct size 9 1.4 Diagnosis 10

2 Goal 13 2.1 Concept 13 2.2 Problem statement 13 3 Method development 14 3.1 Raw image processing 14 3.2 Skull contour 16 3.3 Superimposed Gaussian 16

3.4 Manual symmetry axis determination 18 3.5 Distance from calculated to validated symmetry line. 18

4 Results 4.1 Center of mass 19

4.2 Obtained symmetry angles 19 4.3 Model validation 22 4.4 Interobserver variance 24 4.5 Intraobserver variance 26

5 Discussion 27

6 Conclusion 28

References 29

Appendix 30

Introduction A  stroke or cerebrovascular accident (CVA) is the rapidly developing loss of brain functions due to disturbance in the blood supply to the brain. A stroke can cause paralysis, loss of speech, loss of memory and eventually death. Stroke is the leading cause of adult disability in the United States and Europe and is the third most common cause of death in developed countries, exceeded only by coronary heart disease and cancer.

In the US, each year, approximately 795.000 people experience a stroke. Approximately 610.000 of these are first attacks, and 185.000 are recurrent attacks. On average, every 40 seconds, someone in the United States has a stroke. A quarter of the people older than 45 will have a stroke and the risk of recurrent stroke within five years of a first stroke is between 30% and 40%.*

About 25% of stroke patients die within a year and approximately 25% will fully recover. Among those who have survived a stroke for six months or longer, 48 percent have hemi paresis, 22 percent cannot walk, 24 to 53 percent report complete or partial dependence when participating in daily activities,12 to 18 percent are aphasic, and 32 percent are depressed.

The reason why stroke is such a severe disease, is that the brain is completely unprepared when blood flow is cut off. In other parts of the body, blood deprived cells can survive up to an hour without dying because of fat and sugar reserves. But because the brain has many tasks, for example keeping memories and motor functions, there is no room for these reserves. This means that the oxygen and glucose deprived brain cells stop working after a few seconds and start dying after five minutes. Most cells die between three to four hours.

On average, each minute: 1.9 million neurons, 4 billion synapses and 12 km of myelinated fibres are destroyed. This means that compared with the normal rate of neuron loss in brain aging, a brain suffering from a stroke ages 3.6 years each hour without treatment. So for treating stroke it applies that every second counts.

The previous data concludes that there is a small period of time after stroke onset when a significant portion of threatened brain is possibly salvageable. The extent of the period depends on different factors and can vary in some cases from a few minutes to greater than 12 hours. For most people, intervention is usually most effective if performed in less than 6 hours after onset.

*Stroke statistics between western countries are approximately similar.

1 Stroke

1.1 Types of Stroke

The word stroke refers to a clinical syndrome of vascular origin, typified by disturbance of cerebral functions lasting more than 24 hours or leading to death. There are two main types of stroke: ischemic stroke and hemorrhagic stroke, which account for 99% of strokes occurring. The remaining percent can for example be caused by systemic hypo perfusion: the general decrease in blood supply.

Ischemic stroke is caused by interruption of the blood supply due to a blood clot (thrombus) blocking the artery and takes account for almost 87% of all stroke cases. There are various reasons why this may happen: thrombosis, embolism and dissection. About 30 to 40 percent of all ischemic strokes have no obvious explanation and are termed cryptogenic (of unknown origin).

Thrombosis is the obstruction of a blood vessel by a locally formed blood clot. This will occur when the artery suffers from atherosclerosis; plaque formed in the artery because of high blood pressure and high fat content in the blood. The roughness of the plaque makes it more likely for the blood to stick together and form a thrombus.

Sometimes a clot breaks off and travels through the bloodstream until it gets stuck in a narrowing artery or due to embranchment of the arteries. The obstruction of a blood vessel due to a clot formed somewhere else in the body is called an embolism.

Figure 1a: Plaque causes blood to clot together until it obstructs the blood flow. b: Clots can also break off and block vessels downstream. [1]

If the disturbance in the arteries is caused by a blood clot that is quickly dissolved, no permanent tissue death occurs and symptoms will last less than 24 hours. This is called a transient ischemic attack (TIA).

Ischemic stroke can also be caused by the splitting of the blood vessel wall, called dissection. Usually, this occurs where the artery bends or where atherosclerosis takes place. At the bend point or at the rough surface of the plaque, a piece of the vessel lining peels off and takes hold of the blood. Eventually the blood can push the lining against the other side of the vessel and stops blood flow completely.

Figure 2: Illustration of stroke caused by a dissection. Step 1: a piece of lining detaches from the vessel. Step 2: Blood clots together because of the rough plaque. Step 3: The dissected artery wall touches the other side of the artery what stops the blood flow. [1]

Hemorrhagic stroke is caused by the interruption of the blood supply due to rupture of a weakened blood vessel. There are two main types of bleedings: intracerebral hemorrhage and subarachnoid hemorrhage. Of all strokes approximately 10% are intracerebral hemorrhage and about 3% are subarachnoid hemorrhage strokes. A stroke caused by a blood vessel that breaks inside the substance of the brain is called intracerebral hemorrhage. Subarachnoid hemorrhage is caused by bleeding just outside the brain, but still inside the skull. A common case of this type of hemorrhage develops in the form of an aneurism between a Y-dissection of the arteries.

Figure 3: An intracerebral hemorrhage in the form of a bursting aneurysm. [1]

1.2 Treatment

For each type of stroke there are different treatments. In some cases using the wrong treatment is deadly, so it is very important to determine the type of stroke quickly.

Methods to treat ischemic stroke are:- intravenous thrombolysis - intra-arterial thrombolysis- thrombectomy - angioplasty and stenting- therapeutic hypothermia

Trombolysis is the removal of the blockage by breaking the clot down. This is realised by a clot-dissolving drug called tissue plasminogen activator (tPA). The drug will only be administered if stroke onset is less than three hours: at three hours after onset time the risks of tPA outweigh any benefit seen that the damage to the brain is mostly done. It is a valuable and effective treatment, but it has some risks, e.g. it can aggravate bleeding which can result to an intracerebral hemorrhage. The thrombolysis can be administered through the veins, or locally in the artery, close to the thrombus.

Removing the thrombus mechanically is called a thrombectomy. This is accomplished by inserting a catheter into the artery with a corkscrew-like device that grabs the clot, which is then withdrawn from the artery (see Figure 4). Mechanical thrombectomy is useful for patients who are unable to receive thrombolytic drugs or when thrombolysis is ineffective. Mechanical thrombectomy is not an option if the thrombus is too large.

Angioplasty and stenting are techniques to mechanically widen a narrowed or obstructed blood vessel. Angioplasty is preferred for clots caused by atherosclerosis. An empty balloon is inserted in the narrowed artery and crushes the stored fat at inflation. A stent is a self expanding metallic cylinder and used to counteract a disease-induced, localized flow constriction.

Therapeutic hypothermia is the invasive or non-invasive cooling of the arteries by using cooling catheters or waterblankets respectively. Hypothermia correlates positively with lower clotting, so this method focuses mainly on ischemic strokes. Most of the data for this treatment is limited to animal studies.

Figure 4: A thrombectomy: a catheter with a corkscrew-like device is inserted into the artery. The corkscrew ensnares the clot, which is then withdrawn from the body. [American Journal of Neuroradiology 27:1177-1182, June-July 2006]

Hemorrhagic strokes are hard to treat. Eventually the bleeding will stop because of increasing pressure and clot formation in the skull, but the effects of the bleeding must be treated. The hemorrhage will be treated with medication to stimulate clot formation and minimize brain swelling. In order to determine the type of medication, hemorrhagic patients get a neurosurgical evaluation to detect the cause of the bleeding.

Sometimes surgery is acquired if the localised collection of blood in the brain is bigger than 3 cm: a catheter will be passed into the brain to close off blood vessels.

1.3 Clot location and extent correlated with infarct size

We can conclude that there are many different types of stroke with each situation demanding its own treatment. It is important to take the type of stroke and its cause into account. Furthermore, it is also important to determine the location and extent of the thrombus in order to decide the optimal treatment.

The largest strokes occur when one of the four trunk arteries supplying the brain is completely blocked and there is no compensation from the other side to make up for the loss. This is however rare, because most people have great collateral flow from one side to the other, which can even result in only a small stroke. For example when the left vertebral artery is blocked, the right vertebral artery and carotid arteries still pump blood into the circle of Willis, so the loss of flow will be limited (see Figure 5).

Figure 5: The effects of an occlusion in one of the four main arteries can be compensated by the other three vessels due to collateral flow. A blockage in one of the cerebral arteries is often more severe, because there is no cross circulation possible. [Southwestern medical center, Dallas: www.utsouthwestern.edu]

Clot extent, location and artery type are important factors in determining the clinical outcome. For an acute middle cerebral artery infarct specifically, a clot burden score (CBS) has been developed to give a prediction of final damage. The CBS is a scoring system to define the extent and position of the thrombus in the MCA area by location and is scored on a scale from 1 to 10. CT angiography scans of the middle cerebral artery show where the thrombus is located.

A score of two is subtracted is the clot is found in the in each of the supraclinoid internal carotid arteries (ICA), the proximal half of the MCA trunk and the distal half of the MCA trunk (M1 segment). A score of 1 is subtracted if the thrombus is found in the infraclinoid internal carotid arteries (ICA), the anterior cerebral artery (ACA) and for each affected MCA branch (M2 segment). See Figure 6 for an illustration of the CBS.

Figure 6: The thrombus can be partially or completely occlusive. A. a score of 10 is normal, there is no clot.

B. occlusion of the internal carotid arteries resulting to a score of 7 C. thrombus in the distal M1 and M2 branch produces a CBS of 6 D. occlusion of the supraclinoid ICA, proximal M1 and ACA gives a score of 5. [7]

CBS is a useful indicator for predicting clinical outcomes. Results show that there is a positive correlation between clot size, place (e.g. main arteries, branches of main arteries) and final infarct volume. This means for example that is very likely that a thrombus with large extent and/or located in a main artery causes a large final infarct volume. CBS can help determine the type of treatment, e.g. the option for executing a mechanical thrombectomy.

1.4 Diagnosis

Patients suspected of stroke will get a physical examination, blood test and a CT scan to determine the cause and type of stroke. A CT scan generates a 2D or 3D image where each voxel has a intensity representing the density of the imaged human body; e.g. bone, brain tissue and water. These values are called Hounsfield units (HUE) and vary from -1024 to 1024 with water = 0 HU.

Because every minute counts, fast interpretation of CT images is needed to determine treatment. A noncontrast scan (NCCT) is performed to all patients before treatment to exclude haemorrhage or a large infarction, which are both situations where the use of tPA is very dangerous: For diagnosing hemorrhagic stroke using a NCCT scan, the specificity (percentage of healthy people who are correctly identified as not having the condition) is close to 100%.

The sensitivity (percentage of diseased people who are correctly identified as having the condition) for diagnosing hemorrhagic stroke using a NCCT is equal to 89%. For diagnosing ischemic stroke using a NCCT scan the specificity is equal to 96%, but more important: the sensitivity is equal to 16%, which means that most ischemic strokes are not visible on a NCCT.

Narrowing the window width of HU values from the NCCT is proven to help detect the place of infarct, but sensitivity only raises to approximately 20%.[6]

For ischemic stroke, discovering the location and extent of thrombus is very hard using a NCCT scan. Therefore it is unclear who could be qualified for tPA treatment or a mechanical thrombectomy. When there is suspicion that the patient is suffering from ischemic stroke, a contrast fluid can be administered to visualize the blood flow (CTA scan).

CT angiography (CTA) can be performed in the same imaging session as NCCT scanning without delaying treatment. This type of imaging provides data about the openness of vessels and tissue perfusion, which helps identifying the location and extent of ischemic stroke.

Figure 6: Patient with a basilar artery (fig. 5) occlusion. Upper row: early NCCT, with a small indication of infarct in the left PCA territory, Middle row: CTA-SI, hypo attenuation (darker areas of brain tissue) in multiple areas. Lower row: follow-up NCCT, additional ischemic change. The follow up NCCT confirms the territory of infarction seen on the CTA-SI. [Extent of Hypo attenuation on CT Angiography Source Images Predicts Functional Outcome in Patients With Basilar Artery Occlusion: stroke.ahajournals.org]

A disadvantage of CTA is the administration of contrast agent, which can give a mild to life threatening allergic reaction to the patient, shortness of breath and encourage blood clot formation.

2 Goal

We want to develop a program that processes the NCCT images to increase the sensitivity for diagnosing ischemic stroke. Furthermore, we want to come to automated methods for the thrombus size detection in CTA images.

2.1 Concept

All infarcts are caused by stroke in the main arteries or branches of these arteries. Although the brain is not perfectly even on both sides, the main vessels and branches do appear to be symmetrical (fig. 5).

We hypothesize that direct comparison of the healthy half with the diseased half enhances the diseased areas.

Figure 7: Mirror matching to detect thrombus position and extent. [vessel disease map, AMC]

2.2 Problem statement

For the comparison of the two brain halves, they need to be identified. We cannot assume that the vertical axis is the symmetry axis, because the scanning is performed while the patient is suffering: It is common the patients head is tilted in an arbitrary direction.

We therefore need to determine the symmetry axis- or plane- of the brain that can be used as a reference from where the main arteries can be found and compared. Here, we aim at a robust approximation of the symmetry axis as an initial step. The aim is not necessarily to pin point this axis perfectly, but to at least have a very good resemblance to the actual angle and spatial coordinates. It is expected that the symmetry axis is similar for all slices.

3 Method development

The detection of the symmetry axis of the brain is based upon the skull contour in 2D CT images. First the center of mass of each image is calculated, subsequently we determine the distance from the contour point to the center of mass. These distances as a function of angle are used to find the angle belonging to the symmetry axis of the shape of the skull.

The algorithms that were developed were implemented in the program MeVislab and used for image processing and extracting information from the images. MeVislab is a GUI program based on VisualC++. Originlab is used for further data analysis.

3.1 Raw image processing

Our first goal is to determine the contour of the skull. The input images obtained from the CT scanner need to be processed in order to be useful for our method. Because we want to calculate the center of mass and find the contour of the skull, we need to convert the image in a way that the head can be distinguished from the background.

The 3D image acquired by the scanner can be represented as a series of 2D slices. Slices used for this research are 5 millimetre thick axial slices. With MeVislab, all the individual slices can be gathered into one 3D file using the module dicomimport.

The HU values of the images are negative for air (< -1000 HU) and fat (–30 to –70 HU) , zero for water and positive for muscle (20–40 HU), blood (60–100 HU) and bone/metal (>1000 HU). This implies that a threshold (between -1000 and -70 HU) is sufficient to distinct the head from background. A threshold result in a an image with only two different grey values.

Figure 8: A CT image slice before and after threshold in MeVislab.

Figure 8 shows that a simple determination of the transition between foreground and background color does not directly produce an outer contour of the skull: air filled parts of the body such as the inner nose also result in a foreground and background transition.

Mathematical morphology may appear the logic method to remove the holes in the skull image. However, the holes appeared too large to be removed by standard mathematical closing approaches.

We here propose to use connected components analysis of the image. A connected component is a volume in the 3D picture defined by adjacent voxels of the same grey value. The connected component analysis result in an image in which each connected component has a different grey value. In the MevisLab application, the smallest volume gets the highest value and the largest volume the smallest value. It is also possible to enter a threshold of certain volume size for which the smaller connected components get a grey value equal to zero. The minimum cluster size chosen is 50ml. Because we graphically divided the 3D image in 2D slices, the connected components are visualized in 2D.

In our images, the thresholded head is the largest connected component and thus gets value zero. The background has an arbitrary value greater than zero. With simple mathematical operations we end up with a final image with foreground pixels with a value equal to 5 and background pixels equal to zero (see Figure 9). With this image, it is possible to accurately determine the outer contour of the skull.

Figure 9: Scheme in MeVislab: Modules used for processing CT images. Output image is skull contour area with constant value.

3.2 Skull ContourThe center of mass is a module that calculates the mean location of all the mass in a system. Because our processed image only consists of fore-and background pixels, we rather call it center of geometry. This means:

; (eq. 3.1)

The linearity in 3D for xcm and ycm coordinates will be tested by making an XYZ-plot of the coordinates as a function of height, representing the different slices, and performing a linear fit through the xcm-coordinates in mm as a function of height in mm and a linear fit through the ycm-coordinates in mm as a function of height in mm for a non-craniotomy patient.

Figure 10: Scheme in MeVislab: Center of mass and Skullcontour modules. White dots on output image show the distance from COM to the edge of the foreground.

SkullContour is a module that finds the distance between the center of mass and the edge of the skull as a function of angle. This module determines the background pixel that is closest to the center of mass as a function of the angle. The white dots in the output window in Figure 10 show the result of this module. Length in mm as function of angle, θ, is written to disk.

Since the program calculates the length from center of mass to the skull edge, we add up the lengths with angle equal to θ with lengths equal to θ+π. This gives all the distances through the center of mass from skull to skull edge for variable angles α with range 0 to π rad.

3.3 Superimposed Gaussian

We hypothesized that the angle corresponding to the highest value for the length is equal to the symmetry angle, because when approximating the shape of the skull with an ellipsoid, the length in the anterior direction is the largest. Hence this should enable us to automatically find the line of symmetry.

This ellipsoid approximation no longer holds for scans with a nose: the nose is curved too much for the algorithm to work. Because we know the symmetry line must intersect the nose area, this is a problem for the theory described above.

Figure 11: Lengths found for different angles using skullcontour. It shows that for either graph the highest value for length is not corresponding to the symmetry angle. A: data obtained from slice in fig. 10. (nose height), the biggest length value is not found by the algorithm. B Skullcontour graph from a slice higher up the brain; the dip in the graph caused by the shape of the back of the head.

If the highest length value is not given, the wrong symmetry angle will be given (see Figure 11). This problem is solved by fitting all data with a Gaussian graph to simulate a maximum length. It is important that the fit is suitable for each slice, because the volume of scanning may differ: some scans start from the mouth up, some from the nose up.

Although it is not necessary to precisely find the symmetry angle for each slice, it is still important to obtain a fit as good as possible because these slices cannot automatically be disregarded due to the difference in scanning volume.

The contour data is fitted to a superimposed Gaussian fit:

(eq. 3.2)

With:- l, the length of the skull contour to the center of mass- α, the angle- αs, the symmetry angle- y0, a constant representing the minimal distance of the skull contour - Ai, area under Gaussian curve with [0≤A2≤6]- wi, width of Gaussian with [0≤w2≤0.2]

Initial conditions: y0 = 135 mm, A1 = 135 rad·mm w1 = 1,5 rad, A2 = 2,7 rad·mm and w2 = 0,15 rad

A2 and w2 have certain intervals, so that the superimposed Gaussian simulates the shape of a nose if these values are positive. If the slice originates from a higher part of the head, A2 and w2 converge to 0.

Because of these limits, the initial spike suitable for a graph like 11A, will disappear if fitted on a graph like 11B.

3.4 Manual symmetry axis determination

To validate our symmetry detection method, two ‘observers’ manually determined symmetry axes in a series of CT images showing the brain structures in the best possible contrast. During the instruction, it was explained that a line had to be drawn in the best possible mirror position. This prevents observers from trying to draw a line so that on each side there is an even amount of brain area, which could be wrong, taking swollen tissue into account.

The CT images were shown on a computer, such that the coordinates chosen by the observers were saved on disk. The participator can mark a line by clicking on desired starting and end point of the line. This has been done for eight images per stroke patient and for multiple patients suffering from ‘normal stroke’ or stroke involving a craniotomy due to swelling.

This enables us to determine the accuracy of our automated method. Moreover, the inter- and intraobserver variability is determined to see whether the difference fall within the manual variance.

3.5 Distance from calculated to validated symmetry line.

The distance from the model symmetry line to the symmetry line drawn by the observers is defined by the distance of the line perpendicular to the model line from the center of mass to the observer line.

Figure 12: The distance from the calculated (green) to the validated (blue) symmetry line is defined as the distance perpendicular to the calculated center of mass between these lines.

4 Results

4.1 Center of Mass

A set of center of mass (CM) positions is plotted in 3D (see Figure 13). The range of the x- and y-axis are chosen to represent the dimensions of the CT images. The standard deviations, σi are: σx = 0.30 mm and σy = 0.54 mm.

Figure 13: A: The center of mass values for each slice with thickness 5mm seen in the YZ-plane point of view; σy = 0,54 mm B: The center of mass values seen in the XZ-plane point of view; σx = 0,30 mm

4.2 Symmetry angles

A Gaussian fit seems to work especially well for skullcontour graphs similar to fig. 11B, but less for the graphs with resemblance to fig. 11A.

The algorithm is accurate for analyzing data from more dorsal slices, because the curve is approximately constant. Unfortunately the upper part of the head is approximately round and therefore the symmetry axis cannot be determined in these slices.

The skull contour data is plotted as a function of the angle for each slice in Origin, which subsequently is fitted with a superimposed Gaussian curve. Figure 14 shows the benefit of using a superimposed Gaussian over a normal Gaussian fit, when the slice is at the height of the nose. For craniotomy patients this method can be helpful since the head loses its ellipsoidal shape

Because of this improvement, the given symmetry angle value can be improved with approximately 0.04 rad for slices in the nose areas for non craniotomy patients and 0.1 ~ 0.2 rad for craniotomy patients, depending on the location of the craniotomy

Figure 14: Example of the skull contour at a height in which the nose is included in the scan. For this type of slice (see also figure 11A), the superimposed Gaussian fit gives a better approximation of the angle that defines the symmetry line from the center of mass to the nose.

Figure 15: The superimposed Gaussian fit gives a slightly better approximation of the angle that defines the symmetry line from the center of mass to the nose.

Since the Gaussian fit is based on the ellipsoidal form of the skull, it is not reliable for craniotomy patients (figures 17, 18b). This implies that for these patients only the lower slices containing the nose can reliably find the symmetry angle. Figure 16 and 18a show that the superimposed Gaussian is especially helpful for determining the symmetry angle for a craniotomy patient:

Figure 16: Especially for craniotomy patients, the superimposed Gaussian fit gives an improved approximation of the symmetry angle.

Figure 17: Because the head loses its ellipsoidal shape due to craniotomy, the Gaussian fit indicates the wrong angle of symmetry. (also see figure 17b)

Figure 18a: The red line indicates the line of symmetry found by a Gaussian fit, the green line shows the symmetry line obtained by the superimposed Gaussian. The swelling can slightly be observed in the lower slides of the brain. (see also figure 15 at α ≈ 2 rad.) b: The red line indicates the symmetry line found by a Gaussian fit: the superimposed Gaussian turns into this simple form automatically when there is no sign of the nose in the slice. The arrows indicate the places where skull bone is removed due to the large swelling. Seeing the craniotomy, it is impossible to find the line of symmetry on this slice using our method.

The method is tested with eight patients of which two treated with craniotomy. The model is also tested on two scans taken at a later time, from which one is a craniotomy patient. Figure 14 and 15 are originated from patient one, while figures 16, 17 and 18 are obtained from dataset 8b. Tables 1a and 1b in the appendix contain all the obtained symmetry angles and corresponded errors calculated by the program Origin. If a superimposed Gaussian fit was possible, it is integrated in the data. Patient numbers indicated with a star show the derived angles from craniotomy patient CT images.

For every patient, the symmetry angle result is shown for the 4th and 16th CT image in the appendix.

4.3 Model validation

Visual evaluation confirmed that the model approximately indicates the symmetry angle (fig. 15 and 18a). To quantify the accuracy in the obtained angle, all data sets are examined by two observers, from who one is an expert. Data sets from patient 1 and 2 are also examined by three extra observers in order to investigate interobserver variance. One observer (not the expert) examined CT images from patient 1 three times, to determine the intra observer variance.

Table 2 in the appendix shows the found symmetry angles, αs , by the expert observer and observer 2 for all patients and the absolute difference in αs with the model data. The observer uncertainty, u(αs), is equal to 0.04 rad. We defined: if equation 4.1 is true, then the model and observer data are in conflict and the model needs to be adjusted for that type of slice or patient data.

(eq. 4.1)

Every third slice of a image data set is examined. We only evaluated the admission scans skipping data for patient 7b and 8b. It is notable that the difference in symmetry axes for craniotomy patient 2 are large. This is due to the more round shape in these areas, where the model fails to find the correct symmetry angle.

The seemingly great calculated distances from method symmetry line to validated symmetry line for patient two result from the definition of this distance; which is the distance from the center of mass perpendicular to the method symmetry line (figure 12). When the method and validated symmetry angles vary so greatly, this is a poor approximation of the actual distance from method to validated symmetry line.

Figure 19 shows an example of three different symmetry lines . The green, blue and pink lines are the lines for the angles obtained by the method, expert and second observer respectively.

Figure 19: Example of the determined symmetry axes . The green line is determined by the method with αs = 1,760 rad, the blue line is found by the expert with αs = 1,762 rad and center of mass distance 2,9 mm. The pink line is found by the second observer with αs = 1,756 rad and center of mass distance 3,1 mm.

This figure indicates that the main difference originates from the calculated center of mass. The angle obtained by the expert is more accurate than the one found by the second observer.

4.4 Inter observer variance

Table 3a in the appendix contains the obtained symmetry angles by the model and the five observers for patient 1. The center of mass distance and conflict result is also listed.

The symmetry angles are all not in conflict with the angle obtained by the method. In overall the absolute difference in angle for the expert is not necessarily smaller than of the other observers. Still, the average deviation is slightly smaller for the expert compared to the other observers. This means the expert is most consistent in determining the angle, which implies these constant chosen angles are the best approximation for the actual symmetry angle.

The average deviation is the average of the absolute deviations from the data points, in this case the observer symmetry angles, with respect to their average value. We explore if the chosen symmetry angles will lie between 98% confidence bands, which are defined by the average angle minus three times the average deviation1 and the average angle plus three times the average deviation1.

The error for the drawn symmetry line is 0.04 rad which indicates that an observer can distinguish angle differences of this magnitude and/or cannot draw the line precisely as they want to. All the average deviations1 times three for the data set of patient one are smaller than 0.04 rad, which indicates there are no relevant differences between observers.

The obtained method and observer symmetry angles as a function of slice number giver the following graph:

Figure 20: The average symmetry angle for all slices is obtained by fitting a straight line with slope =0 through the method data points. This gives αs ≈ 1,732 with uncertainty u(αs) ≈ 0,003

The inter observer variance for this patient data is smaller than the averaged variance between observers and model data.

In this graph (figure 20) it is visualized that the angles calculated from the lower slice numbers lie nearest to the determined observer angles. The ‘dip’ in angle caused by the slices 7 to 14 is due to the transition of a superimposed Gaussian form to a regular Gaussian form, the model is not specially designed for these type of slices.

Regarding that the range of possible values for the symmetry angle is about one radian, these results are tolerably accurate.

Table 3b from the appendix contains the obtained symmetry angles by the model and the five observers for patient 2, who is treated with craniotomy.

The symmetry angles originating from the lower slices are overall not in conflict with the angle obtained by the method, but all the data resulting from the area above the nose is in conflict for all observers, this is due to the loss of ellipsoidal shape caused by the craniotomy.

Half of the average deviation1 multiplied by three is larger than the observer angle uncertainty. This is mainly caused by the non-expert observers, seeing that the average deviation2 is the same for the expert, but higher for the other observers compared with the average deviation2 from patient data 1.

Figure 21: The average symmetry angle for all slices is obtained by fitting a straight line with slope =0 through the method data points. This gives αs ≈ 1,669 with uncertainty u(αs) ≈ 0,022

There is a prompt change in the symmetry angle as a function of slice number, caused by the impossible superimposed Gaussian from slice 13 and up. Also for this data set the inter observer variance is smaller than the variance between method data points, which is logical since the model fails for the last half of the slices.

4.5 Intra observer variance

Observer 2 examined the images from patient 1 three times. Average deviation1 is the average deviation for the same slices between sets and average deviation2 is the average deviation of the different slices per set.

With the values of the average deviation for the same slices between sets, we can check if the drawing error value of 0.04 rad is a good estimate for drawing the symmetry line, or maybe the observers are more confused because of the image, resulting in a larger drawing error.

sliceno. 1 4 7 10 13 16 19 22 25 28 avg.dev.2

▼ 3 · avg.dev.

> 0.04 ? ▼Model data

symmetry angle αs (rad) 1.787 1.748 1.739 1.741 1.760 1.763 1.763 1.769 1.790 1.785 0.0146 no

error u(rad) 0.009 0.011 0.011 0.005 0.005 0.004 0.004 0.004 0.004 0.006

Set 1 symmetry angle αs (rad) 1.783 1.763 1.766 1.781 1.756 1.757 1.747 1.752 1.791 1.777 0.0126 noabs. difference αs (rad) 0.004 0.015 0.027 0.040 0.004 0.006 0.016 0.017 0.001 0.008conflict? no no no no no no no no no noCM distance (mm) 0.1 0.8 0.9 4.1 3.1 0.8 1.3 2.0 1.0 0.0

Set 2 symmetry angle αs (rad) 1.789 1.762 1.737 1.744 1.757 1.752 1.740 1.755 1.788 1.807 0.0189 yesabs. difference αs (rad) 0.002 0.014 0.002 0.003 0.003 0.011 0.023 0.014 0.002 0.022conflict? no no no no no no no no no noCM distance (mm) 2.6 2.2 0.8 1 1.7 1.1 0.6 0.2 1.1 0.8

Set 3 symmetry angle αs (rad) 1.749 1.764 1.758 1.733 1.762 1.739 1.744 1.758 1.784 1.809 0.0158 noabs. difference αs (rad) 0.038 0.016 0.019 0.008 0.002 0.024 0.019 0.011 0.006 0.024conflict? no no no no no no no no no noCM distance (mm) 1.0 0.1 0.1 0.0 2.8 0.4 0.9 2.1 3.1 1.0

average deviation1 (rad) 0.016 0.001 0.011 0.019 0.003 0.007 0.002 0.002 0.003 0.0143 · avg.dev. > 0.04 ? yes no no yes no no no no no yes

Table 4: Data sets resulting from three image examinations with obtained symmetry angles for patient 1 compared. There are quite a few differences in symmetry angle This observer is quite constant overall, with exception to slice 1, 10 and 28 of data set 2.

All the separate slice angles are not in conflict with the obtained symmetry angle by the method, but the average angle deviation1 of slice 1, 10 and 28 and the average deviation2 of data set 2 are somewhat larger than the error limit. Still this is just a slight difference, and a smaller intra observer variance for the expert is expected seen the average deviations2 for patient data 1 and 2 in tables 3a and b.

5 Discussion

We have presented a method to calculate the symmetry axis in NCCT images based upon the contour of the skull to potentially improve diagnosis and treatment decision support.

Regarding the skull contour results, the top half or a small part of the image is not visible for some patients, causing a skull contour with a large dip in the graph. This is the case considering slice one of patient data 6. The results could improve by fitting an ellipse on the image before calculating the skull contour for big missing pieces.

A smaller missing image part, which is common at the tip of the nose, can prevent the connected components module from filling the holes. This could be solved by using mathematical morphology first. However, this may alter the charactering shape.

Because the model seems to give accurate values for the slices of types A and B in figure 11, a more accurate angle could be obtained by only taking these slices into account. (see graph 19) It is still difficult to determine this segment, so the graph needs to be recognized by the program.

An easy solution is defining results having larger values for B and q than some limit to be the skull contour division of type 11A. A way to eliminate the ‘transition’ slices segment between the divisions of type 11A and B, is to make a precise fit of the skull contour and state that all graphs with more than three extreme values and B and q values lower than some limit will not be taken into calculation.

For non-craniotomy patients, there is a loss of the ellipsoidal shape of the skull in the top slices due to the shrinking of the image when going upwards. This is shown in table 2 for patients 3 and 6. This causes only a handful of obtained angles to be in conflict with the observer results.

For craniotomy patients, the model fails consequently for the slices where the largest part of the swelling is visible. Fortunately, angles obtained from the lower slices lie within the error range. This data however will get lost if all the found angles are averaged, so the filtering of the type A slices is especially convenient for craniotomy patients.

There are also some differing values for the symmetry angle for patient 4 in the second table. The images of patient 4 in the appendix show the skull looks less like a perfect ellipsoid compared to the other (non craniotomy) patients. So for patients with a skull shaped that looks less like a perfect ellipsoid, the model can determine the wrong angle.

In the unfortunate case of a craniotomy patient data set with a missing image part, there has to be relied on the slices containing the craniotomy. We cannot extract the symmetry angle for these slices with our model.

Looking at the intra observer data it would be more accurate to substract the estimated drawing error from this data, but only if there are results available of more observers that have examined the same patient multiple times and one of these observers being an expert.

6 Conclusion

We have presented a method to estimate the symmetry line in NCCT scans based upon thresholding and connected component analysis. The method makes use of the distance from the center of mass in the image to the contour of the skull. The first and second half of these distances are added together and subsequently fitted with a superimposed Gaussian.

Regarding the center of mass, the data points seem to form an approximate straight line and can therefore be regarded accurate.

The skull contour calculation works fine, with the exception that sometime some parts of the nose are not found by the algorithm (figure 11A). This is solved by a superimposed Gaussian model that fits on the added skull contour.

The model is designed to find the symmetry angle seems to work acceptable for non-craniotomy patients, seen that most of the obtained angles are not in conflict with the angles found by the observers.

For patients with a skull shaped that do not resemble a ellipsoid, the model may yield an inaccurate angle.

For craniotomy patients, the model fails for the slices where the largest part of the craniotomy is visible (table 3b, figure 18b, figures 2B and 8bB of the appendix). Fortunately, the lower slices due seem to give reasonably accurate symmetry angle.

Looking at the intra observer data, the drawing error value of 0.04 rad gives a good indication of the uncertainty between multiple observations of the same imageset.

The inter observer and intra observer variance are both smaller than the difference between method symmetry angle and observer symmetry angle. Nevertheless, the presented approach gives a good estimation of the symmetry axis.

References:

[1]  John R. Marler, Stroke For Dummies (2005) John Wiley & Sons IncISBN: 978-0-7645-7201-2

[2] J. Mackay, G. Mensah, The Atlas of Heart Disease and Stroke (2004) ISBN: 978-9241562768

[3] American Heart Association, The American Heart Disease and Stroke Statistics 2010 update (2010) Dallas, TXonline ISSN: 1524-4539

[4] Henk Marquering, Medusa – an extensive use case, AMC Dept. of Biomedical Physics and Engineering (june 2010), powerpoint presentation

[5] I.Y.L. Tan, A.M. Demchuk, J. Hopyan, L. Zhang, D. Gladstone, K. Wong, M. Martin, S.P. Symons, A.J. Fox, R.I. Aviv, CT Angiography Clot Burden Score and Collateral Score: Correlation with Clinical and Radiologic Outcomes in Acute Middle Cerebral Artery Infarct (jan 2009) American Society of Neuroradiology.

[6] R. Gonzalez, et al, Acute Ischemic Stroke - Imaging and Intervention (2006) SpringerISBN-13 978-3-540-25264-9

[7] M. Sonka, V. Hlavec, R. Boyle, Image Processing, Analysis and Machine Vision, (1999) PWS Publishing

Appendix:

Obtained symmetry angles (rad)Patient ► 1 2* 3 4 5Slice ▼ angle error angle error angle error angle error angle error 0 1.790 0.010 1.537 0.011 1.521 0.020 1.641 0.020 1.549 0.018

1 1.787 0.009 1.512 0.012 1.538 0.022 1.619 0.019 1.524 0.0152 1.784 0.009 1.512 0.017 1.553 0.017 1.589 0.016 1.500 0.0103 1.766 0.008 1.545 0.017 1.559 0.017 1.694 0.013 1.478 0.0124 1.748 0.011 1.612 0.012 1.583 0.017 1.682 0.009 1.486 0.0085 1.768 0.017 1.576 0.012 1.554 0.016 1.698 0.008 1.486 0.0086 1.738 0.009 1.594 0.010 1.554 0.015 1.729 0.010 1.486 0.0097 1.739 0.011 1.582 0.007 1.548 0.013 1.723 0.007 1.493 0.0098 1.746 0.009 1.580 0.005 1.547 0.012 1.728 0.009 1.496 0.0099 1.743 0.009 1.573 0.005 1.550 0.012 1.729 0.009 1.490 0.00910 1.741 0.005 1.578 0.005 1.566 0.011 1.723 0.009 1.477 0.00811 1.743 0.005 1.574 0.007 1.562 0.009 1.723 0.008 1.471 0.00712 1.750 0.005 1.590 0.010 1.573 0.007 1.721 0.007 1.469 0.00613 1.760 0.005 1.782 0.016 1.580 0.005 1.718 0.005 1.469 0.00414 1.761 0.005 1.770 0.011 1.578 0.004 1.722 0.005 1.474 0.00415 1.765 0.005 1.749 0.010 1.575 0.004 1.728 0.005 1.478 0.00416 1.763 0.004 1.760 0.011 1.587 0.004 1.734 0.006 1.482 0.00317 1.763 0.004 1.788 0.012 1.595 0.004 1.741 0.006 1.485 0.00318 1.765 0.004 1.813 0.012 1.597 0.005 1.745 0.005 1.491 0.00219 1.763 0.004 1.819 0.013 1.594 0.005 1.738 0.005 1.495 0.00220 1.763 0.004 1.815 0.012 1.590 0.004 1.730 0.004 1.503 0.00221 1.766 0.004 1.807 0.011 1.588 0.004 1.725 0.004 1.510 0.00322 1.769 0.004 1.813 0.011 1.591 0.004 1.725 0.004 1.514 0.00323 1.786 0.003 1.816 0.010 1.599 0.004 1.735 0.004 1.518 0.00324 1.794 0.003 1.848 0.010 1.602 0.004 1.737 0.003 1.521 0.00225 1.790 0.004 1.857 0.010 1.606 0.004 1.726 0.004 1.495 0.00226 1.770 0.004 1.870 0.010 1.610 0.004 1.691 0.006 1.449 0.00427 1.757 0.006 1.866 0.010 1.631 0.004 1.884 0.023 1.391 0.00628 1.785 0.006 1.829 0.013 1.659 0.003 1.605 0.025 1.275 0.01029 1.754 0.005 1.805 0.016 1.781 0.010 1.643 0.018 1.380 0.01230 1.795 0.019

avg. angle 1.732 ±0.003 1.669 ±0.022 1.586 ±0.003 1.711 ±0.004 1.478 ±0.002

Table 1a: obtained symmetry angles using the superimposed Gaussian fit.

Obtained symmetry angles (rad)Patient► 6 7a 7b 8a 8b*

Slice ▼ angle error angle error angle error angle error angle error 0 1.535 0.014 1.471 0.010 1.634 0.011 1.141 0.010 1.483 0.011

1 -- -- 1.470 0.011 1.643 0.011 1.153 0.022 1.502 0.0142 1.629 0.015 1.476 0.012 1.654 0.013 1.134 0.008 1.651 0.0203 1.615 0.015 1.491 0.014 1.657 0.010 1.135 0.010 1.608 0.0174 1.527 0.010 1.493 0.012 1.659 0.009 1.138 0.012 1.528 0.0275 1.551 0.008 1.490 0.014 1.654 0.013 1.135 0.006 1.646 0.0166 1.555 0.006 1.487 0.009 1.676 0.010 1.137 0.007 1.658 0.0177 1.556 0.003 1.491 0.007 1.645 0.009 1.138 0.009 1.676 0.0138 1.554 0.002 1.493 0.005 1.642 0.004 1.122 0.017 1.697 0.0139 1.554 0.001 1.501 0.005 1.639 0.004 1.121 0.019 1.686 0.00910 1.553 0.001 1.502 0.005 1.648 0.005 1.130 0.017 1.689 0.00911 1.553 0.001 1.503 0.006 1.654 0.005 1.145 0.014 1.678 0.00912 1.553 0.002 1.499 0.006 1.664 0.006 1.164 0.010 1.680 0.00913 1.557 0.002 1.500 0.007 1.669 0.010 1.176 0.007 1.691 0.00914 1.554 0.002 1.506 0.008 1.671 0.009 1.179 0.006 1.708 0.00815 1.552 0.003 1.506 0.007 1.676 0.008 1.186 0.005 1.727 0.00816 1.549 0.003 1.506 0.005 1.677 0.006 1.183 0.004 1.736 0.00817 1.548 0.003 1.507 0.004 1.683 0.005 1.186 0.004 1.739 0.00918 1.547 0.003 1.510 0.004 1.679 0.004 1.191 0.004 1.741 0.00919 1.547 0.003 1.513 0.004 1.681 0.004 1.193 0.005 1.753 0.00920 1.552 0.003 1.510 0.003 1.688 0.004 1.201 0.006 1.773 0.00921 1.478 0.005 1.501 0.003 1.692 0.004 1.212 0.006 1.791 0.00922 1.458 0.006 1.492 0.004 1.691 0.004 1.227 0.005 1.825 0.00923 1.426 0.006 1.487 0.003 1.690 0.003 1.216 0.004 1.884 0.01024 1.373 0.006 1.489 0.003 1.694 0.003 1.203 0.004 1.940 0.01225 1.323 0.006 1.489 0.003 1.697 0.003 1.184 0.004 1.998 0.01526 1.254 0.009 1.488 0.003 1.701 0.003 1.180 0.006 2.086 0.01727 1.164 0.016 1.487 0.003 1.700 0.003 1.206 0.006 2.181 0.01928 1.713 0.005 1.481 0.003 1.709 0.002 1.194 0.008 2.344 0.02229 1.751 0.005 1.462 0.003 1.713 0.002 1.096 0.007 2.442 0.023

avg. angle 1.378 ±0.002 1.493 ±0.001 1.673 ±0.001 1.167 ±0.023 1.785 ±0.026

Table 1b: Symmetry angles using the superimposed Gaussian fit (The symmetry angle for slice 1 from patient number six could not be obtained due to holes in the processed image overlapping with the background ).

Patientdata set

slice no. Model data Expert data

abs diff. conflict CMdistance

Observer 2 data

abs diff. conflict CM distance

sliceno. αs (rad) u(rad) αs (rad) αs (rad) (mm) αs (rad) αs (rad) (mm)1 1 1.787 0.009 1.771 0.016 no 0.7 1.783 0.004 no 0.1  4 1.748 0.011 1.763 0.015 no 0.3 1.763 0.015 no 0.8  7 1.739 0.011 1.756 0.017 no 0.9 1.766 0.027 no 0.9  10 1.741 0.005 1.763 0.022 no 0.1 1.781 0.040 no 4.1  13 1.760 0.005 1.762 0.002 no 2.9 1.756 0.004 no 3.1  16 1.763 0.004 1.755 0.008 no 0.6 1.757 0.006 no 0.8  19 1.763 0.004 1.756 0.007 no 1.4 1.747 0.016 no 1.3  22 1.769 0.004 1.747 0.022 no 1.3 1.752 0.017 no 2.0  25 1.790 0.004 1.769 0.021 no 2.1 1.791 0.001 no 1.0  28 1.785 0.006 1.804 0.019 no 1.0 1.777 0.008 no 0.0                   2* 1 1.512 0.012 1.636 0.124 yes 5.1 1.635 0.123 yes 6.6  4 1.612 0.012 1.646 0.034 no 3.6 1.611 0.001 no 2.2  7 1.582 0.007 1.642 0.060 no 6.9 1.625 0.043 no 6.3  10 1.578 0.005 1.647 0.069 no 7.0 1.647 0.069 no 7.2  13 1.782 0.016 1.642 0.140 yes 8.8 1.655 0.127 yes 7.0  16 1.76 0.011 1.675 0.085 yes 10.2 1.666 0.094 yes 7.7  19 1.819 0.013 1.660 0.159 yes 8.9 1.665 0.154 yes 9.8  22 1.813 0.011 1.663 0.150 yes 8.9 1.685 0.128 yes 9.9  25 1.857 0.010 1.648 0.209 yes 6.9 1.683 0.174 yes 9.3  28 1.829 0.013 1.659 0.170 yes 7.6 1.680 0.149 yes 8.2

3 1 1.554 0.014 1.540 0.014 no 1.7 1.544 0.010 no 0.5  4 1.577 0.005 1.560 0.017 no 0.1 1.573 0.004 no 0.9  7 1.566 0.005 1.535 0.031 no 2.2 1.551 0.015 no 1.1  10 1.568 0.009 1.537 0.031 no 1.6 1.550 0.018 no 0.1  13 1.580 0.005 1.552 0.028 no 0.3 1.571 0.009 no 1.5  16 1.587 0.004 1.530 0.057 no 1.7 1.541 0.046 no 0.5  19 1.594 0.005 1.547 0.047 no 0.9 1.568 0.026 no 0.0  22 1.591 0.004 1.548 0.043 no 1.8 1.564 0.027 no 1.4  25 1.606 0.004 1.527 0.079 no 3.8 1.549 0.057 no 2.5  28 1.659 0.003 1.553 0.106 yes 0.7 1.604 0.055 no 0.6

4 1 1.619 0.019 1.665 0.046 no 0.0 1.679 0.060 no 1.9  4 1.682 0.009 1.654 0.028 no 0.1 1.656 0.026 no 0.5  7 1.723 0.007 1.635 0.088 yes 2.6 1.662 0.061 yes 0.9  10 1.723 0.009 1.662 0.061 no 1.5 1.668 0.055 no 0.0  13 1.718 0.005 1.644 0.074 no 0.7 1.664 0.054 no 0.7  16 1.734 0.006 1.652 0.082 yes 0.6 1.656 0.078 no 2.2  19 1.738 0.005 1.639 0.099 yes 1.7 1.650 0.088 no 2.3  22 1.725 0.004 1.668 0.057 no 3.2 1.665 0.060 no 2.8  25 1.726 0.004 1.659 0.067 no 1.4 1.694 0.032 yes 1.7

5 1 1.524 0.015 1.442 0.082 no 2.6 1.494 0.030 no 2.5  4 1.486 0.008 1.487 0.001 no 1.0 1.491 0.005 no 0.3  7 1.493 0.009 1.455 0.038 no 2.3 1.466 0.027 no 2.1  10 1.477 0.008 1.431 0.046 no 3.4 1.469 0.008 no 1.7

  13 1.469 0.004 1.425 0.044 no 3.2 1.467 0.002 no 2.1  16 1.482 0.003 1.427 0.055 no 3.4 1.422 0.060 no 1.3  19 1.495 0.002 1.428 0.067 no 3.3 1.452 0.043 no 1.2  22 1.514 0.003 1.447 0.067 no 1.7 1.441 0.073 no 0.9  25 1.495 0.002 1.408 0.087 no 1.3 1.412 0.083 no 1.2  28 1.275 0.010 1.363 0.088 no 0.7 1.375 0.100 no 0.2                   6 1 -- -- 1.587 -- -- -- 1.593 -- -- --  4 1.527 0.010 1.571 0.044 no 1.2 1.604 0.077 no 0.6  7 1.556 0.003 1.580 0.024 no 1.0 1.565 0.009 no 0.3  10 1.553 0.001 1.568 0.015 no 2.1 1.568 0.015 no 1.2  13 1.557 0.002 1.554 0.003 no 1.4 1.560 0.003 no 2.0  16 1.549 0.003 1.559 0.010 no 1.1 1.562 0.013 no 1.9  19 1.547 0.003 1.564 0.017 no 9.8 1.574 0.027 no 9.0  22 1.458 0.006 1.551 0.093 no 12.7 1.567 0.109 yes 11.5  25 1.323 0.006 1.415 0.092 yes 0.8 1.600 0.277 yes 1.2

7a 1 1.470 0.011 1.448 0.022 no 3.2 1.475 0.005 no 1.2  4 1.493 0.012 1.450 0.043 no 0.4 1.459 0.034 no 0.5  7 1.491 0.007 1.440 0.051 no 2.8 1.454 0.037 no 0.4  10 1.502 0.005 1.437 0.065 no 2.7 1.491 0.011 no 4.5  13 1.500 0.007 1.453 0.047 no 1.9 1.472 0.028 no 1.6  16 1.506 0.005 1.461 0.045 no 0.1 1.478 0.028 no 2.2  19 1.513 0.004 1.445 0.068 no 1.6 1.451 0.062 no 2.1  22 1.492 0.004 1.429 0.063 no 0.1 1.446 0.046 no 1.4  25 1.489 0.003 1.447 0.042 no 0.9 1.450 0.039 no 1.9  28 1.481 0.003 1.449 0.032 no 2.5 1.443 0.038 no 0.3

8a* 1 1.153 0.019 1.105 0.418 no 4.0 1.094 0.059 no 5.0  4 1.138 0.027 1.108 0.420 no 4.8 1.13 0.008 no 5.2  7 1.138 0.013 1.126 0.550 no 0.1 1.136 0.002 no 1.3  10 1.13 0.009 1.114 0.575 no 1.9 1.117 0.013 no 0.5  13 1.176 0.009 1.128 0.563 no 0.7 1.128 0.048 no 0.9  16 1.183 0.008 1.143 0.593 no 0.1 1.142 0.041 no 0.3  19 1.193 0.009 1.139 0.614 no 0.7 1.133 0.06 no 1.4  22 1.227 0.009 1.147 0.678 no 0.9 1.161 0.066 no 1.7  25 1.184 0.015 1.147 0.851 no 1.0 1.16 0.024 no 1.4  28 1.194 0.022 1.173 1.171 no 1.2 1.17 0.024 no 0.7Table 2: The obtained symmetry angles compared to the observer symmetry angles.

Data patient 1sliceno. 1 4 7 10 13 16 19 22 25 28 avg.dev.2▼

Model data

symmetry angle αs (rad) 1.787 1.748 1.739 1.741 1.760 1.763 1.763 1.769 1.790 1.785 0.0146error u(rad) 0.009 0.011 0.011 0.005 0.005 0.004 0.004 0.004 0.004 0.006

expert data symmetry angle αs (rad) 1.771 1.763 1.756 1.763 1.762 1.755 1.756 1.747 1.769 1.804 0.0100abs. difference αs (rad) 0.016 0.015 0.017 0.022 0.002 0.008 0.007 0.022 0.021 0.019conflict? no no no no no no no no no noCM distance (mm) 0.7 0.3 0.9 0.1 2.9 0.6 1.4 1.3 2.1 1.0

observer 2 data

symmetry angle αs (rad) 1.783 1.763 1.766 1.781 1.756 1.757 1.747 1.752 1.791 1.777 0.0126abs. difference αs (rad) 0.004 0.015 0.027 0.040 0.004 0.006 0.016 0.017 0.001 0.008conflict? no no no no no no no no no noCM distance (mm) 0.1 0.8 0.9 4.1 3.1 0.8 1.3 2.0 1.0 0.0

observer 3 data

symmetry angle αs (rad) 1.774 1.769 1.757 1.781 1.762 1.743 1.761 1.764 1.790 1.757 0.0102abs. difference αs (rad) 0.013 0.021 0.018 0.040 0.002 0.020 0.002 0.005 0.000 0.028conflict? no no no no no no no no no noCM distance (mm) 0.5 0.5 0.7 0.1 1.9 0.1 1.0 1.8 2.3 1.9

observer 4 data

symmetry angle αs (rad) 1.760 1.746 1.732 1.737 1.752 1.758 1.709 1.752 1.779 1.782 0.0158abs. difference αs (rad) 0.027 0.002 0.007 0.004 0.008 0.005 0.054 0.017 0.011 0.003conflict? no no no no no no no no no noCM distance (mm) 1.8 0.9 1.7 0.7 2.7 0.6 1.2 1.2 3.7 1.7

observer 5 data

symmetry angle αs (rad) 1.778 1.764 1.750 1.745 1.747 1.747 1.742 1.771 1.794 1.771 0.0147abs. difference αs (rad) 0.009 0.016 0.011 0.004 0.013 0.016 0.021 0.002 0.004 0.014conflict? no no no no no no no no no noCM distance (mm) 1.1 0.3 0.2 0.8 2.1 0.5 1.5 0.4 1.9 1.3

comparison average deviation1 (rad) 0.006 0.006 0.009 0.016 0.005 0.006 0.014 0.008 0.009 0.0123 · avg.dev. > 0.04 ? no no no no no no no no no no

Table 3a: The obtained symmetry angles compared and the observer symmetry angles. There are no striking differences between observers. Also the average deviation1 * 3 < 0.04 rad.

Data patient 2*sliceno. 1 4 7 10 13 16 19 22 25 28 avg.dev.2▼

Model data

symmetry angle αs (rad) 1.512 1.612 1.582 1.578 1.782 1.76 1.819 1.813 1.857 1.829 0.1144error u(rad) 0.012 0.012 0.007 0.005 0.016 0.011 0.013 0.011 0.010 0.013

expert data symmetry angle αs (rad) 1.636 1.646 1.642 1.647 1.642 1.675 1.660 1.663 1.648 1.659 0.0100abs. difference αs (rad) 0.124 0.034 0.060 0.069 0.140 0.085 0.159 0.150 0.209 0.170

conflict? yes no no no yes no yes yes yes yesCM distance (mm) 5.1 3.6 6.9 7.0 8.8 10.2 8.9 8.9 6.9 7.6

observer 2 data

symmetry angle αs (rad) 1.635 1.611 1.625 1.647 1.655 1.666 1.665 1.685 1.683 1.680 0.0206abs. difference αs (rad) 0.123 0.001 0.043 0.069 0.127 0.094 0.154 0.128 0.174 0.149conflict? yes no no no yes no yes yes yes yesCM distance (mm) 6.6 2.2 6.3 7.2 7 7.7 9.8 9.9 9.3 8.2

observer 3 data

symmetry angle αs (rad) 1.633 1.63 1.643 1.65 1.666 1.808 1.66 1.672 1.674 1.681 0.0166abs. difference αs (rad) 0.121 0.018 0.061 0.072 0.116 0.048 0.159 0.141 0.183 0.148conflict? yes no no no yes no yes yes yes yesCM distance (mm) 4.5 3.3 6.0 6.4 8.1 9.0 9.1 9.2 9.4 6.8

observer 4 data

symmetry angle αs (rad) 1.564 1.588 1.649 1.643 1.594 1.606 1.657 1.665 1.678 1.694 0.0366abs. difference αs (rad) 0.052 0.024 0.067 0.065 0.188 0.154 0.162 0.148 0.179 0.135conflict? no no no no yes yes yes yes yes yesCM distance (mm) 1.5 0.5 6.1 4.0 4.3 2.6 8.5 8.4 8.7 8.1

observer 5 data

symmetry angle αs (rad) 1.646 1.637 1.640 1.702 1.645 1.663 1.666 1.669 1.669 1.673 0.0152abs. difference αs (rad) 0.134 0.025 0.058 0.124 0.137 0.097 0.153 0.144 0.188 0.156conflict? yes no no yes yes no yes yes yes yesCM distance (mm) 5.4 4.3 7.2 13.0 7.8 8.6 9.1 8.4 8.3 7.0

comparison average deviation1 (rad) 0.024 0.018 0.006 0.018 0.019 0.022 0.003 0.006 0.010 0.0093 · avg.dev. > 0.04 ? yes yes no yes yes yes no no no no

Table 3b: The obtained symmetry angles compared and the observer symmetry angles for a craniotomy patient. There are quite a few differences in symmetry angle and distance.

The 4th and 16th CT images corresponding to the obtained symmetry angles by the method. The left corner of each image shows the patient number. Images 2 and 8 result from craniotomy patients. Images 2B, 4B and 8bB are in conflict with the model.

Figure 21: The obtained symmetry angles by the method for every 4th and 16th slice of all the studied patients.