IN
DEGREE PROJECT MEDICAL ENGINEERING,
SECOND CYCLE, 30 CREDITS ,
STOCKHOLM SWEDEN 2017
Translation of Clinical Rupture
Risk Factors for the
Biomechanics-based AAA Simulations
VIKTOR WINTHER
Abstract
The abdominal aorta is the largest blood vessel in the abdomen and the main supplier of blood to the lower body. An abdominal aortic aneurysm (AAA) is an unnatural enlargement of the abdominal aorta, which is a serious condition with a high risk of mortality. If the aneurysm exceeds a certain diameter or growth rate, surgical interventions are justified. Use of a diameter-based criterion has been proven to be inaccurate though since some smaller aneurysms can rupture whilst some larger aneurysms remain quiescent. A biomechanical rupture risk assessment (BRRA) that utilizes the finite element method can be used to evaluate the risk of aneurysm rupture. The BRRA calculates the stresses in the aneurysm based upon CT scans and patients blood pressure. Comparing the stresses with the strength of wall in the aneurysm makes it possible to evaluate the risk of rupture. If the stress exceeds the strength, the aneurysm will rupture. To calculate the strength of the vessel wall, a strength equation is used. The strength equation consists of risk factors such as family history, gender, intra luminal pressure and aneurysm diameter. To individualize the assessment further it would be possible to identify and use other risk factors.
Rupture risk factors were searched for through two spate literature searches. To identify the risk factors the search utilized keywords such as “rupture risk factors” and “abdominal aortic aneurysm” together with “peak wall stress” or “wall stress”. The search also used a state of the art article from previous research, which contained a list of risk factors that could be searched for. For a factor to be used in this study they had to be global risk factors. Instead of increasing the risk of rupture in a localised point in the aneurysm, a global factor affects the aneurysm uniformly throughout its entirety. The search focused on statistical trials that evaluate the factors impact on wall stress or wall strength. An AAA wall strength equation was constructed based on the rupture risk factors that were identified. This equation was translated into the Finite element analysis program (FEAP) to evaluate its behaviour. A statistical analysis was performed in Matlab using data from the program A4CLINICS developed by VASCOPS gMBh. Using 41 patients along with known patient characteristics and CT scans Biomechanical rupture risk assessment (BRRA) was conducted using the new strength equation. The assessment resulted in a new peak wall rupture index (PWRI). The resulting data was separated into two groups based upon their volume growth rate, one fast growing and one slow growing group. This separation was done for both the VASCOPS strength equation and the new one. Pearson correlation testing was used to test the correlation between both strength equations and volume growth or diameter growth. To evaluate the sensitivity of the strength equation, receiver operating characteristics (ROC) curves were also used.
The PWRI in fast and slow groups were not different (p-values of 0.1257 for VASCOPS and 0.0679 for the new equation). The Pearson correlation coefficients showed a higher correlation between new PWRI and volume growth compared to diameter growth. The new PWRI had a higher sensitivity for predicting the volume growth compared to the diameter growth. Initial volume and diameter had the highest sensitivity of all predictors.
Sammanfattning
Buk aortan är det största blod kärlet i bukhålan och står för blodtillförseln till underkroppen. Ett onaturligt förstorat blodkärl, ett så kallat aneurysm som uppstår i buk aortan är ett allvarligt tillstånd med hög mortalitets risk. Om diametern på aneurysmet överstiger en viss längd eller att diametern växer med en viss hastighet så är kirurgiska åtgärder bestyrkta för att förhindra att det brister. Användandet av diametern som utvärderings metod har visat sig vara felaktigt eftersom mindre aneurysmer kan brista medan större inte gör det. En biomekanisk utvärderings program, ett så kallat ”biomechanical rupture risk assessment” (BRRA) , som använder finita element metoden kan istället användas för att utvärdera risken för att ett aneurysm brister. Med hjälp av BRRA kan de tryck belastningar som sker i aneurysmet beräknas baserat på patient specifika CT-bilder och blodtryck. Genom att jämföra tryckbelastningarna på blodkärlets vägg med hållfastheten i kärlväggen är så kan en risk för att aneurysmet brister fås fram. Om tryck belastningen på kärlväggen är högre än
hållfastheten så kommer aneurysmet att brista. För att beräkna hållfastheten i kärlväggen så används en så kallad hållfasthetsekvation. Denna ekvation använder sig utav risk parametrar såsom
aneurysmer inom familjen, kön, intra luminalt tryck och aneurysmets diameter. För att kunna specificera utvärderingen ytterligare så kan identifierandet och användandet av flera sådana riskparametrar vara en lösning.
Två litteratursökningar genomfördes för att identifiera potentiella riskparametrar. För detta syfte användes sökord såsom rupture risk factors” och “abdominal aortic aneurysm” tillsammans med “peak wall stress” eller “wall stress”. Sökningen inkluderade även tidigare artiklar som innehöll listade riskparametrar som kunde sökas efter. För att en parameter skulle användas i denna studie behövde den vara en global parameter vilket innebär att hela aneurysmet påverkas uniformt och inte endast ett specifikt område. Sökningen fokuserade på statistiska studier som presenterade parametrarnas påverkan på antingen tryckbelastningarna.
Baserat på resultaten från litteratur sökningen så skapades en ekvation som beräknade kärlväggens hållfasthet. Ekvationen implementerades i finita element programmet FEAP för att utvärdera ekvationens funktionalitet. Efter att ekvationen utvärderats kunde statistiska simuleringar genomföras i Matlab med hjälp av data från programmet A4CLINICS utvecklat av VASCOPS gMBh. Simuleringarna inkluderade 41 patienter tillsammans med personlig medicinsk data och CT-bilder och en BRRA genomfördes med den nya hållfasthetsekvationen. Resultatet blev ett index värde som talar om risken för att aneurysmet brister, ett ”peak wall rupture index” (PWRI) för varje patient.
Resultaten delades upp i två grupper baserat på tillväxthastigheten för aneurysmets volym, en snabbt växande grupp och en långsamt växande grupp. Grupperingen gjordes för den gamla BRRA och den nya hållfasthetsekvationen. Illustrering av denna gruppering gjordes med hjälp av lådagram. För att utvärdera sensitiviteten och specificiteten användes en ”receiver operating characteristics ” kurva. T-test visade att grupperingen an snabb och långsam tillväxt hade genererat två separata grupper med p-värde 0.1257 för VASCOPS PWRI och p-värde 0.0679 för den nya PWRI. Pearsons korrelations koefficient visade en högre korrelation mellan den nya PWRI och volym tillväxten jämfört med diameterns tillväxt. Den nya PWRI hade en högre sensitivitet att förutse volym tillväxt jämfört med diameter tillväxt.
Acknowledgement
I am very grateful that I was given the opportunity to write my master’s thesis about a medical
technology that has an important role in vascular medicine and to help in the process of improving it. I would like to express my sincere thanks to my supervisor at the Department of solid Mechanics at the Royal school of Technology, KTH professor Tomas Christian Gasser. He has taught me about many things about solid mechanics and also about the work needed when developing and improving a medical device. He have also encouraged me with a positive attitude during the times when things haven’t been going as smoothly as one can hope for and have given me lots of feedback. I would also like to thank Christopher Miller who has been a huge help for me when learning about Finite Element Analysis program. He has also been a huge help in answering many of my questions about simulations and finite element analysis as well as providing lots of feedback on my report. Moritz Lindquist I am grateful to for helping me obtain data for the statistical simulations. I also want to thank my
supervisor at KTH, Svein Kleiven, for all the help during this process.
Keywords: Abdominal aortic aneurysm, Rupture risk, Peak wall stress, Rupture index, Wall stress, Wall
strength, Rupture risk factors, Biomechanical rupture risk assessment, Biomechanics
Nomenclature
Abbreviations
AAA Abdominal aortic aneurysm
BRRA Biomechanical rupture risk assessment WRI Wall rupture index
PWRI Peak wall rupture index
RRED Rupture risk equivalent diameter FEAP Finite element analysis program ROC Receiver operating characteristics COPD Chronic Obstructive Pulmonary Disease
HR Hazard ratio
Table of Contents
1.
Introduction
1.1.
Backgrounds……….………1
1.2.
Aim ………..………..…………..1
2.
Method
2.1.
Literature search………..………2
2.1.1.
Strength equation………2
2.2.
Finite element simulations……….6
2.2.1.
Simulating ring model of AAA……….6
2.2.2.
Simulation of individual case………6
2.3.
Statistical study of fast and slow growth………..7
2.3.1.
Dividing patients into fast and slow volume growth……...7
2.3.2.
Receiver operating characteristics………7
2.3.3.
Pearson correlation analysis……….8
3.
Results
3.1.
Strength equation………..………..9
3.2.
Individual case simulation………..……….9
3.3.
Simulations in A4CLINICS………..……….11
3.4.
PWRI in fast and slow growth ………..…………..11
3.5.
Receiver operating characteristics………..…….12
3.6.
Pearson correlation………..………..14
4.
Discussion and Conclusions
4.1.
Literature search………..……….15
4.2.
Strenght equation………..………..15
4.3.
Simulations in A4CLINICS………..………..16
4.4.
Conclusion………..………17
5.
References………..………..……….18
Appendix A, Literature study
Appendix B, Simulation plots
1. Introduction
1.1 Background
The abdominal aorta is located in the abdomen, close to the spine. This is the largest blood vessel in the abdominal cavity and supplies the abdomen with blood. The blood vessel can be described as a cylinder with two layers, an inner layer consisting of intra luminal thrombus (ILT) and an outer layer, which is the vessel wall [1]. A permanent enlargement of the abdominal aorta by 50 % and more is termed an abdominal aortic aneurysm (AAA). Patients diagnosed with AAA are often men over the age of 65 and AAA has a mortality rate of 1.3 % [4].
Surgical and endovascular interventions are performed to prevent AAA from rupture. Currently such interventions are performed if the abdominal aortic diameter exceeds 55 mm or its growth rate is greater than 10 mm/year. However, recently the initial aneurysm volume and volume growth of an AAA has been proven to be better predictors of rupture risk compared to the diameter criteria of 55 mm [31]. Based on this, a more individualised intervention criterion could be better suited to identifying those patients in need of invasive surgical intervention. Factors such as age, gender and shape of the aorta can all affect the aneurysm in different ways and the risk of it rupturing. As such, a risk assessment procedure that is capable of interpreting such individual factors is more desirable. The biomechanical rupture risk assessment (BRRA) evaluates the risk of rupturing in the AAA by using finite element analysis to compute wall stress and strength. If the wall stress exceeds the wall strength somewhere in the aorta, it ruptures [3]. In previous studies it has been proven that relating the wall strength to the wall stress is a better predictor of rupture risk on an individual level [6, 7]. A strength equation quantifies the wall strength of the aneurysm. Computation of wall strength and wall stress provides the biomechanical indices; peak wall stress (PWS) and peak wall rupture index (PWRI). By using said indices it is possible to evaluate the risk of potential ruptures more accurately compared to measuring the largest abdominal aortic diameter. To further improve the BRRA, more individual risk factors should be integrated. For example, drugs, genetic background, lifestyle, etc. may affect aortic wall mechanical properties. The robustness of BRRA diagnostic information could be improved further through the quantification of such risk factors and their subsequent implementation into the risk assessment.
1.2 Aim
2.1 Method
2.1.1 Literature search
A literature review was performed in Pubmed to identify rupture risks that could be implemented into a rupture risk assessment. The review investigated 85 studies out of which data from 18 were used. The state of the art article by T. Christian Gasser [2] was used as an introduction to the project as well as background for the literature search. The article presents the BRRA and explains its clinical application. It further explains how the system A4CLINICS developed by VASCOPS GmbH performs BRRA.
The search for rupture risk factors was divided into two parts, one focusing on the references and list of rupture risk factors from the state of the art article and one individual search using keywords. From the reference list in the state of the art article [2], relevant articles were located and used as material in the literature study. Keywords that were often used in the articles were abdominal aortic aneurysm, rupture risk, peak wall stress, rupture index, wall stress, wall strength, rupture risk factors, biomechanical rupture risk assessment, and biomechanics. The first search focused on specific rupture risk factors that were listed in the state of the art article. A total list of all rupture risk factors that were searched for is in appendix C, Table 1. The search was performed following the flow chart in search A in figure 1. The key words “Rupture risk factor” and “Abdominal aortic aneurysm” was combined with one search for each specific risk factor listed in table 1, appendix C.
A second search using keywords was performed. The second search was performed according to search B in figure 1. “Rupture risk factor” and “Abdominal aortic aneurysm” was the main keywords. To these “PWS”, “Wall strength” or “Wall stress” was added. To further specify “rupture index” or “BRRA” was added to the search term to comply with the software that was used.
In order for them to be included, the risk factors had to have been shown to have a global impact on the aneurysm and that they have a direct impact on either the wall strength or the wall stress. For the consideration of statistical studies quantifying rupture risk, there had to be more than 100 patients that had participated in the study.
2.1.2 Strength equation
The risk rupture factors from studies were presented as statistical risk of rupturing or as hazard ratio (HR). The rupture risk factors were used to construct a strength equation representing the wall strength of the aneurysm. A HR is used in relation to a control group and will function as relative risk of rupturing [8]. A control patient was therefore constructed with a wall strength of 570 MPa to implement the HR[9, 10]. The rupture risk factors had a proportional relation with this strength. For example, a HR of 1.05 will reduce the wall strength to 95% of its original value. All risk factors are combined into creating a single strength equation representing a specific patient AAA wall strength. Table 1 lists the rupture risk factors identified from the literature. The variables BMI and age each has a baseline value corresponding to a control patient. BMI is set at 23 kg/m2 for a normal weighted person [30]. Cholesterol and forced expiratory volume was set to be binary since the data which the simulations are built on did not contain specific values for these two variables. The strength equation with all parameters was constructed as follows [22, 26, 27]:
𝑊𝐴𝐿𝐿 𝑆𝑇𝑅𝐸𝑁𝐺𝑇𝐻
= 570
(1.18
𝑎𝑛𝑔𝑒𝑜𝑡𝑒𝑛𝑠𝑖𝑛× 1.5
𝑠𝑒𝑥× 2
𝑠𝑚𝑜𝑘𝑖𝑛𝑔× 1.035
𝑎𝑔𝑒× 0.98
𝑏𝑚𝑖× 0.92
𝑐ℎ𝑜𝑙𝑒𝑠𝑡𝑒𝑟𝑜𝑙× 1.32
𝑚𝑎𝑝× 0.62
𝑓𝑒𝑣× 1.11
𝑝𝑝× 1.47
𝑑𝑝× 1.36
𝑐𝑎𝑙𝑐𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛× 1.28
𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠)
⁄
Each parameter is constructed as (a)(b) where (a) denotes the HR or relative risk and (b) represents the rupture risk factors value. Giving (b) a value of 0 will remove the parameter from the equation since (a)0 = 1. The binary rupture risk factors sets (b) to either 1 or 0. The variable rupture risk factors such as BMI and age give (b) a patient specific value. If no information exists about a factor, a value of 0 is given to (b) to remove its effect from the equation.
Risk factor Measurement Baseline Value Reference
Age Patients age, measured in years 75 year HR 1.035/year [14, 24, 25]
Angiotensin inhibitor Patient have been treated with angiotensin inhibitor - HR 0.82 [14, 16] Body mass index Patients body mass index, measured in kg/m2 23 kg/m2 HR 0.98 per kg/m2 [14, 25] Calcification Abdominal aortic calcification (AAC) score. 0 AAC-score Stress increase 36% [18, 5, 21] Cholesterol Cholesterol in blood, measured in mmol/L 5mmol/L HR 0.92 per mmol/L [25, 17, 24]
DP increase 10% Diastolic blood pressure, measured in mmHg 120 mmHg HR 1.47 [14, 20]
FEV Maximum vital lung capacity, measured in litres 5 L HR 0.62/L [25, 23]
MAP increase 10% Mean arterial pressure, measured in mmHg 90 mmHg HR 1.32 [14, 24]
Sex If patient is male or female, yes or no - 50 % higher risk for women [14,19,20,5,25]
Smoking If the patient is smoking, yes or no - 2 times higher risk [15,24,25]
PP increase 10% Systolic-Diastolic pressure, [mmHg] 40 mmHg HR 1.11 [14]
Wall stiffness decrease 10% Pulse wave velocity (PWV), m/s 8 PWV 28% higher risk [17,20]
2.2 Finite Element Simulations
The trial simulations to test the strength equation were performed using the program FEAP, (finite element analysis program). FEAP is constructed using the Microsoft visual studio 2012 and Intel parallel studio XE 2015. In FEAP one can create model geometries, translate them into a discrete mesh, and apply various boundary and loading conditions to the structure. Such information is prescribed in an input file that is loaded into and interpreted by FEAP to solve the desired problem.
2.2.1 Simulating ring model of AAA
In order to verify the implementation of the strength model and evaluate how it behaves, a trial simulation was performed. The goal was to create a simplified model representing a small section the abdominal aorta. A ring was constructed in an input file with two layers, an inner layer representing an intra luminal thrombus and an outer layer that represents the vessel wall. An illustration of this model can be seen in figure 2. The luminal surface of the inner layer is exposed to a pressure in the radial direction, simulating the pressure acting on the vessel wall in the aorta.
Figure 2: Ring geometry with two layers to mimic cylindrical segment of abdominal aorta with inner layer intra luminal thrombus and outer layer being the vessel wall.
The applied blood pressure deforms the ring. FEAP has a number of predefined material models that describes the stress and strain behaviour of solid materials. In this study a Yeoh model [10,11] was used, which is a third order polynomial model that is used to describe stress and strain in rubber-like materials. This constitutive model was used for the ring to simulate the deformation in an aortic vessel. For the specific values for Yeoh model parameters, see input file for ring simulation in appendix D.
To solve the non-linear deformation problem the pressure was incremented. Pressure starts at zero and is increased during specific time steps. The time steps start at 0.001 seconds, each step representing an increased pressure. After every tenth cycle, the time step is increased tenfold.
2.2.2 Simulation of individual case.
(CT) scan. The simulation was performed as for the ring model, using pressure increments starting at a time step of 0.001 sec to solve the non-linear problem.
To evaluate the impact of the various rupture risk factors under investigation, each risk factor was first assessed individually. Subsequently, the risk factors were then investigated in a number of combinations, such that every factor was evaluated together with the other risk factors. The combinations was constructed of first two risk factors after which number of risk factors included increased until all were used is the same simulation.
2.3 Statistical study of fast and slow growth
The next step in evaluating the equation was the simulation of patient data. Patients that were included had been diagnosed with AAA and had undergone at least two CTA study between the years 2009 and 2013. The data was provided by the Department of Vascular surgery at the Karolinska University Hospital in Stockholm, Sweden.
The data consisted of 41 cases (32 males and 9 females). Each set of data contained CT scans and a description of the patient’s medical characteristics. Unfortunately, the calcification and wall strength risk factors were not recorded for each patient; as a result, they were excluded from the simulations. The patient characteristics provide the necessary information to perform BRRA simulation using VASCOPS A4CLINICS. The strength equation was coded into A4CLINICS along with an interface to add potential risk factors.
2.3.1 Dividing patients into fast and slow volume growth
Following the simulations for each patient, the VASCOPS PWRI using the standard BRRA risk factors was outputted and also the new PWRI, which integrates, further risk factors into the framework. Every patient had unique simulations based on their characteristics. The statistical calculations were performed using the software Matlab R2014b. To test the statistical behaviour of the obtained PWRI values, the data was arranged into two groups based upon the volume growth rate; those that had a fast growth rate and those with a slow growth rate. The separation of patients was based upon the median volume growth rate of all 41 patients. A patient that had a volume growth above the median was classified as having a fast growing aneurysm, whilst if the volume growth was below the median, the patient was assigned to the slow growing aneurysm group. The predicted PWRI values in both groups were illustrated using boxplots. Too evaluate if there was a discernible difference between the arrived at PWRI for both groups, a t-test was performed. The t-test evaluated the hypothesis that the two groups had unequal mean values and a p-value was generated in order to evaluate the statistical significance of the results. Statistical significance is defined by a p-value of less than 0.05.
2.3.2 Receiver operating characteristics
volume and diameter is used as a reference. ROC was constructed for diameter growth and volume growth. A threshold value representing the optimal value is needed to compute ROC. The threshold was set to 15 % for the relative volume growth and 5 % for the relative diameter growth. If the growth rate exceeds 15 % for the volume growth, then the aneurysm is classified as fast growth [28, 29]. If the relative growth rate for the diameter exceeds 5 %, the aneurysm is considered fast growing [28, 33]. Four predictors were plotted, VASCOPS PWRI, new PWRI, initial aneurysm volume and initial aneurysm diameter. A control line is also added to represent the sensitivity and specificity for a set of randomized numbers would provide.
2.3.3 Pearson correlation analysis
3. Results
3.1 Strength equation
Simulations using the cylindrical model resulted in a deformation that mimicked the deformation within an arterial blood vessel. Simulations using the ring model in the finite element simulations section resulted in plausible deformation.
3.2 Individual case simulation
The peak wall stress for the individual patient reached 322 kPa, strength values below this stress value would indicate high rupture risk. An example of simulations using a patient-specific aneurysm geometry can be seen in figure 3. This plot shows the rupture indexes distributed over the aneurysm for a patient where smoking has been added to the simulation as a risk factor. As can be seen in the plot, the arrow indicates the location of the maximum rupture index, which has a magnitude of 1.13. The resulting wall stress and wall strength values followed closely with magnitudes observed in previous studies values [9].
Figure 3: Distribution of the smoking rupture risk index over the entire aneurysm geometry, arrow indicating PWRI.
3.3 Simulations in A4CLINICS
An example of the plots outputted by VASCOPS software for visualisation purposes can be seen in figure 5. Grey areas indicate patients bone and the coloured region represents the risk index of aneurysm wall. The arrow identifies the area where the highest PWRI is measured.
Figure 5: Visualisation of the Rupture risk index outputted by VASCOPS A4CLINICS software. Image from [35] with the permission to use by T. Christian Gasser.
3.4 PWRI in fast and slow growth
3.5 Receiver operating characteristics
First analysis predicted the diameter growth. All predictors are close to the randomized line, which suggests low sensitivity. The diameter and volume have the largest area beneath their curve as showcased in Table 2. All predictors are close to 0.5. VASCOPS PWRI has the lowest sensitivity.
Figure 6: A ROC-curve showing the sensitivity when using the diameter growth as a control parameter. The PWRR from the new and old equations are plotted together with the initial aneurysm volume and maximum aneurysm diameter.
Second analysis predictions were made on the volume growth. All of the predictors are clearly above the randomized line, which indicates higher sensitivity, compared to predicting diameter growth, figure 7. The new PWRI has a higher sensitivity compared to the VASCOPS PWRI when viewing the area beneath the lines in table 2. Neither of the PWRI reaches the same predictive values as the initial diameter or volume though. Diameter has higher sensitivity than both equation but the initial aneurysm volume has the largest area, indicating highest sensitivity.
False positive rate (1-Specificity)
Figure 7: a ROC-curve showing the sensitivity using volume growth as control parameter. The PWRR from the new and old equations are plotted together with initial aneurysm volume and maximum aneurysm diameter. Sensitivity in ROC plots based on the area beneath curves. Initial volume and diameter has the highest values, indicating highest sensitivity. Prediction of volume growth had the highest sensitivity.
Predictor Diameter growth Volume growth
New PWRI 0.5331 0.7033
VASCOPS PWRI 0.4988 0.6495
Initial Volume 0.6483 0.7608
Initial Diameter 0.6189 0.7488
Table 2: Area below each predictor’s line for cases where diameter growth and volume growth is used as a
control parameter.
False positive rate (1-Specificity)
3.6 Pearson correlation
All predictors show a higher correlation to the volume growth compared to the diameter growth, see table 3. For the new PWRI there is a much higher correlation to the volume growth compared to the diameter growth. The VASCOPS PWRI has slightly higher correlation values compared to the new PWRI when viewing the volume growth. With the diameter growth there is a larger difference in correlation for the new and VASCOPS PWRI. Initial diameter and initial volume has the strongest correlation with the colume growth.
Predictor
Diameter growth
Volume growth
New PWRI
0.0058
0.2224
VASCOPS PWRI 0.2043
0.2376
Initial Volume
0.2930
0.5601
Initial Diameter 0.2898
0.509
4. Discussion and Conclusions
4.1 Literature search.
The objective of the literature search was to identify rupture risk factors. A search was performed with specific risk factors as focus. From T.C. Gassers article [2] a list of risk factors with a documented impact on the wall strength was obtained. Focusing on each factor the search phrase combined rupture risk factor with AAA and each specific risk factor separately. Knowing which risk factors exist and specifying the search according to these increases the likelihood of finding articles that could be included in the study. A second objective search was also performed based on keywords. If only one search were performed, there was a risk that the study would only replicate previous results. Therefore a second search was carried out.
The objective was to evaluate other factors and their combined risks. Values for diameter, ILT and history of aneurysm were not of interest in this study. These values are difficult to implement into the simulations since they are local parameters. The ILT changes within the aneurysm and will not have the same value in the whole aneurysm. The parameter sex was used since this is a global parameter and also one of the largest risk factors. Therefore it was included in this study. Diameter is already used in the existing equation and was therefore not included.
4.2 Wall Strength equation
The strength equation is constructed of several different separate factors. Each factor affects the AAA in different ways. The COPD and smoking have a similar impact on the aneurysm. Smoking affects the lungs, which makes them incapable of transporting oxygen to the blood. In order that sufficient oxygen is transported throughout the body, the physiological response is to increase blood pressure. This will then increase the stress in the aneurysm and hence increase the risk of rupture. COPD will also decrease the lungs functionality and as such will lead to a similar increase in blood pressure [19, 25]. The difference in gender is dependent on the body proportions and women will have a higher risk of ruptured AAA compared to men [19, 5]. Calcification increases maximum PWS and alters stress distributions, which leads to an increased risk of rupture [5, 21]. ACE inhibitors increase the systemic collagen synthesis and reduce the stiffness of the wall. This drop in stiffness reduces the risk of the wall rupturing [16]. Ageing has the opposite effect, as the elastin content of the vessel lessens with age, the vessel wall becomes stiffer. This creates less elasticity that can dampen the force impact when stress is exerted on the wall [17]. Each factor in the strength equation is known to have a documented individual effect on aneurysm development.
Wall stiffness as well as calcification were risk factors that weren’t included due to insufficient data. The factor calcification can be classified as a global factor if it occurs uniformly. The problem is though that calcifications can also be very localized. It is therefore a complicated factor to apply in the study since it is not exclusively a global parameter. The factor wall stiffness is a global parameter but the problem is in measuring this clinically. Often to evaluate the wall stiffness there is a need to retrieve and test tissue samples. The BRRA is meant to reduce the amount of invasive interventions, which is why wall stiffness needs an improved method of measuring.
4.3 Simulations in A4CLINICS
The box plots representing the separation of fast and slow volume growth displayed in Figure 4, show a difference between the groups for both the VASCOPS PWRI case (old strength equation) and the new PWRI (new strength equation). If the wall strength equation is related to growth then each groups PWRI should indicate their level of growth rate. A faster growth should have higher PWRI and vice versa. The boxplots however cannot be used to draw this conclusion without knowledge pertaining to how statistically significant the results are. A t-test was therefore performed to test the hypothesis that the two groups have unequal mean values. If the hypothesis were rejected, then the separation of patients into two groups would present as infeasible. The t-tests suggest that for both the new PWRI and the VASCOPS PWRI that the hypothesis cannot be rejected. This indicates that there are two separate groups based on the PWRI. However, the p-value for the VASCOPS PWRI was 0.1257, almost double that of the p-value observed for the new PWRI, which was 0.0679. Despite the hypothesis being met, it is not with a high enough statistical significance to reliably separate the dataset into two groups. However, the new PWRI approaches statistical significance and if there were be an increased population in a future simulation, the new PWRI may reach statistical significance.
For future works and improvements there is a need to revise the strength equation. The true combinatory values between the rupture risk factors must be clinically tested in order to achieve a more accurate strength equation. There should also be a larger population used for simulations, which will act to increase the statistical significance of any statements and conclusions that can be drawn. The simulations should also include ruptured and non-ruptured cases. In this study the usage of volume growth was used as an evaluative method. With data consisting of ruptured and non-ruptured patient cases, it would be possible to see if the strength equation can predict the rupturing aneurysm and correlate with known outcomes.
4.4 Conclusion
5. References
[1] Bengt lindskog, 2008, medicinsk terminologi, 6th edition, Studentliteratur, Sweden.
[2] T. Christian Gasser, 2016, Biomechanical rupture risk assessment – a consistent and objective
decision-making tool for abdominal aortic aneurysm patients, AORTA, volume 4, pages 42-60
[3] Michael S.Heng, Michael J. Fagan, Jason W. Collier, Grishma Desai, Peter T. McCollum, Ian
C.Chetter, 2008, Peak wall stress measurement in elective and acute abdominal aortic aneurysms, Journal of vascular surgery, volume 47, issue 1, page 17-22
[4] Tim McGloughlin, 2011, Biomechanics and mechanobiology of aneurysms, volume 7, Springer,
USA
[5] Thomas Schmitz-Rixen, M. Keese, M. Hakimi, A. Peters, D. Böckler, K. Nelson, R. T. Grundmann. Ruptured abdominal aortic aneurysm- epidemiology, predisposing factors and biology. Langenbeck's Archives of Surgery, May 2016, Volume 401, Issue 3, pp 275–288
[6] E.M.J. van Disseldorp, N.J. Petterson, M.C.M. Rutten, F.N. van de Vosse, M.R.H.M. van Sambeek,
R.G.P. Lopata. November 2016, Patient Specific Wall Stress Analysis and Mechanical Characterization of Abdominal Aortic Aneurysms Using 4D Ultrasound. European Journal of Vascular and Endovascular Surgery, Volume 52, Issue 5, Pages 635–642
[7] A. Venkatasubramaniam, M. Fagan, T. Mehta, K. Mylankal, B. Ray, G. Kuhan, et al. 2004, A
comparative study of aortic wall stress using finite element analysis for ruptured and non-ruptured abdominal aortic aneurysms. Eur J Vasc Endovasc Surg, 28 (2) pp. 168–176
[8] Spotswood L. Spruance, Julia E. Reid, Michael Grace, and Matthew Samore, 2004 Aug, Hazard
Ratio in Clinical Trials. Antimicrob Agents Chemother., issue 48, pages 2787–2792.
[9] C. Forsell, J. Swedenborg, J. Roy, T. C. Gasser. online 2012, The quasi static failure properties of
the Abdominal Aortic Aneurysm wall estimated by mixed experimental-numerical approach. Annals of biomedical engineering,
[10] Majid Shahzada , Ali Kamranb , Muhammad Zeeshan Siddiquia , Muhammad Farhana. 2015,
Mechanical Characterization and FE Modelling of a Hyperelastic Material. Materials Research. issue 18, 918-924
[11] Aidy Ali, M. Hosseini, B.B. Sahari. 2010, A Review of Constitutive Models for Rubber-Like
Materials. American J. of Engineering and Applied Sciences, issue 3 (1): 232-239.
[12] Vorp, D A. Raghavan.M L, Muluk. S C, Makaroun. M S, Steed. D L, Shapiro. R , Webster. M W.
November 1996, Wall strength and stiffness of aneurysmal and nonaneurysmal abdominal aorta. Annals of the New York Academy of Sciences, 18, Vol.800, pp.274-6
[13] José Augusto Tavares Monteir, Simãoda Silva, Madhavan L.Raghavan. Pedro Puech-Leão Maria
de Lourdes Higuchi, José Pinhata Otoch. May 2014, Histologic, histochemical, and biomechanical properties of fragments isolated from the anterior wall of abdominal aortic aneurysms. Journal of Vascular Surgery, Volume 59, Issue 5, Pages 1393-1401.
[14] M. M. J. Sweeting, S. G. Thompson, L. C. Brown, J. T. Powell. May 2012, Meta-analysis of
[15] Mark F. Fillinger, a, Steven P. Marra, PhDa,b, M.L. Raghavan, PhDa,b,c, Francis E. Kennedy,
PhDb. April 2003, Prediction of rupture risk in abdominal aortic aneurysm during observation: Wall stress versus diameter. Journal of Vascular Surgery, Volume 37, Issue 4, Pages 724–732
[16] Daniel G Hackam, Deva Thiruchelvam, Donald A Redelmeier. August 2006, Angiotensin-converting enzyme inhibitors and aortic rupture: a population-based case-control study. The lancet, Volume 368, Issue 9536, 19–25 Pages 659-665
[17] Clement Klein Streuer Zhonghua Li, 2006, Analysis and computer program for rupture-risk prediction of abdominal aortic aneurysms. Biomed Eng Online. issue 5, chapter 19
[18] Michalis Xenos, Suraj H. Rambhia, Yared Alemu, Shmuel Einav, Nicos Labropoulos, Apostolos
Tassiopoulos, John J. Ricotta, Danny Bluestein. November 2010, Patient-Based Abdominal Aortic Aneurysm Rupture Risk Prediction with Fluid Structure Interaction Modeling. Annals of Biomedical Engineering, Volume 38, Issue 11, pp 3323–3337
[19] Ruby C. Lo, Bing Lu, Margriet T.M. Fokkema, Mark Conrad, Virendra I. Patel, Mark Fillinger,
Robina Matyal, and Marc L. Schermerhorn. May 2014, Relative importance of aneurysm diameter and body size for predicting AAA rupture in men and women. Journal of Vascular Surgery. issue 59, pages 1209–1216.
[20] Katie A.Wilson, Amanda J.Lee, Amanda J.Lee, Peter R.Hoskins, F.Gerry R.Fowkes, C.Vaughan
Ruckley, Andrew W.Bradbury. January 2003, The relationship between aortic wall distensibility and rupture of infrarenal abdominal aneurysm. Journal of Vascular Surgery, Volume 37, Issue 1, Pages 112-117
[21] R.V.C. Buijsa, T.P. Willems, R.A.Tio, H.H. Boersmad, I.F.J.Tielliu, R.H.J.A. Slart, C.J.Zeebregts.
Calcification as a risk factor for rupture of abdominal aortic aneurysm. European Journal of Vascular and Endovascular Surgery. Volume 46, Issue 5, November 2013, Pages 542-548
[22] A. Maier, M. W. Gee, C. Reeps, J. Pongratz, H.-H. Eckstein, October 2010, Wall A Comparison of Diameter, Wall Stress, and Rupture Potential Index for Abdominal Aortic Aneurysm Rupture Risk Prediction. Annals of Biomedical Engineering, Volume 38, Issue 10, pp 3124–3134
[23] Jiang Xiong, Zhongyin Wu, Chen Chen, Wei Guo. 2016, Chronic obstructive pulmonary disease
effect on the prevalence and postoperative outcome of abdominal aortic aneurysms: A meta-analysis. Scientific reports, issue 6
[24] V.J.Gokani, D.Sidloff, M.F.Bath, M.J.Bown, R.D.Sayers, E.Choke. February–March 2015, A retrospective study: Factors associated with the risk of abdominal aortic aneurysm rupture, Vascular
Pharmacology, Volumes 65–66, Pages 13-16
[25] Louise C. Brown, and Janet T. Powell, 1999, Risk Factors for Aneurysm Rupture in Patients Kept
Under Ultrasound Surveillance. Annals of surgery, volume 230, issue 3,
[26] Samarth S. Raut, Santanu Chandra, Judy Shum, Ender A. Finol. T. 2013, he Role of Geometric and
Biomechanical Factors in Abdominal Aortic Aneurysm Rupture Risk Assessment, Annals of Biomedical Engineering. July, issue 41, pages1459–1477.
[27] Stephen C.Nicholls, Jon B.Gardner, Mark H.Meissner, Kaj H.Johansen. November 1998, Rupture
in small abdominal aortic aneurysms. Journal of Vascular Surgery, Volume 28, Issue 5, Pages 884-888 [28] H. Gharahi, B. A. Zambrano, C. Lim, J. Choi,W. Lee, S. Baek. Julöy 2015 On growth
measurements of abdominal aortic aneurysms using maximally inscribed spheres. Medical Engineering and Physics. issue 37, pages 683–691.
[29] Claude Kauffmann, Claude Kauffmann, An Tang, Éric Therasse, Marie-France Giroux, Stephane
Measurements and detection of abdominal aortic aneurysm growth: Accuracy and reproducibility of a segmentation software. European journal of radiology, Volume 81, Issue 8, Pages 1688–1694
[30] National heart, lung and blod institute, Calculate your Body Mass index, last updated 2017.
Available at: https://www.nhlbi.nih.gov/health/educational/lose_wt/BMI/bmicalc.htm [Accessed 2017-08-14]
[32] Giampaolo Martufi, Martin Auer, Joy Roy, Jesper Swedenborg. Natzi Sakalihasan, Giuseppe
Panuccio, T. Christian Gasser. September 2013, Multidimensional growth measurements of abdominal aortic aneurysms. Journal of Vascular Surgery, Volume 58, Issue 3, Pages 748-755
[33] Medcalc statistical software, ROC curve analysis. Last updated 24 of June 2017. Available at:
https://www.medcalc.org/manual/roc-curves.php . [Accessed 2017-08-14]
[34] Moritz Lindquist Liljeqvist, Rebecka Hultgren, T. Christian Gasser, Joy Roy. June 2016, Volume growth of abdominal aortic aneurysms correlates with baseline volume and increasing finite element analysis-derived rupture risk. Journal of Vascular Surgery, Volume 63, Issue 6, Pages 1434-1442.
[35] Stevens, R., Grytsan, A., Biasetti, J., Roy, J., Lindquist Liljeqvist, M., & Gasser, T. C. (2016).
Biomechanical changes during abdominal aortic aneurysm growth. Retrieved from
Appendix A
Literature study
Introduction
Contents
1.
Part I. Basic biomechanical definitions.
1.1.
Stress………..X2
1.2.
Tension………X2
1.3.
Strength………..X2
1.4.
Stiffness………..X2
1.5.
Finite element model……….X3
1.6.
Equilibrium equations………X3
2.
Part II.
Abdominal aortic aneurysm
2.1.
Clinical view………X4
2.2.
Biomechanical view………..X4
3.
Part III.
Biomechanical rupture risk assessment.
3.1.
Requirements for model………X5
3.2.
PWS and PWRI………..X5
3.3.
Workflow of BRRA……….X6
4.
Part IV.
Improvements of BRRA
4.1.
Risk factor studies……….X8
4.2.
Deficiencies of current BRRA…………..X9
4.3.
Summary……….X10
5.
References
Part I.
Basic biomechanical definitions.
Stress is defined as the force that is transmitted through an area and has a unit of newton per
square meter. When the force is acting in the normal direction of the area it is termed a normal stress, whilst when the force is acting in parallel with the area it is termed a shear stress, see Figure 1a and 1b. In three dimensions, there are three normal stresses and three shear stresses that constitute the stress tensor. In the blood circulatory system the shear stress is primarly caused by the blood flow whilst the normal stress is caused by the blood pressure.
Von Mises equivalent stress 𝜎𝑀 is an example of how to obtain a single scalar stress value that
describes the multidimensional stresses. When performing a rupture risk assessment the Von Mises stress can be defined in terms of the principal stresses i.e. the stress components in the principal plane, where no shear stresses are acting. Assuming the aorta can be represented by a simplified cylindrical geometry characterised by a diameter of d and a wall thickness of h, the principal stresses act in the axial, circumferential and radial directions, see Figure 1c. Furthermore if the vessel is thought of as a thin walled pressure vessel, planar stress can be assumed and as such the stresses in the radial direction reduce to zero. The axial and circumferential stresses can thus be described by 𝜎𝑧 = 𝒑𝒅/𝟐𝒉 and 𝜎𝜃 = 𝒑𝒅/𝟒𝒉 respectively, where p is the inflation pressure. Based upon the aforementioned assumptions, the Von Mises equivalent stress reduces to 𝜎𝑀=
√𝜎𝜃2+ 𝜎
𝜃 𝜎𝑧 + 𝜎𝑧2.
Figure 1. Definition of normal, image a) and shear, image b) stress. Image c) defines axial and circumferential directions. Image modified from T. Christian Gasser [14].
Strain is a dimensionless measurement of the deformation of a material. As with stresses, there are
six independent strain components that populate the strain tensor, three for shear strain and three for normal strain.
Tension is a force normalized by the length where it is transmitted. This is independent of the
thickness of the object where the force is exerted. The unit of tension is newton per meter.
Strength is defined as the magnitude of stress that a tissue or material can withstand before failure.
Stiffness describes how the stress changes in relation to strain when dealing with specific tissues.
Vascular tissue does not have a linear relation between the stress and strain. It is therefore necessary to calculate tangents from the stress and strain curve to identify the specific stiffness values. The stiffness of vascular tissue is therefore dependant on the loading conditions of the vessel.
Figure 3. Stress strain curve used to evaluate stiffness. The specific strain to certain stress is defined as the tangent to stress strain curve. Image modified from T. Christian Gasser [14].
Finite element model (FEM) is used to numerically find the solution to equilibrium equations and
problems with boundary, initial and equilibrium conditions. This is done by discretizing the problem, in the BRRA the aortic tissue is divided into a large number of regular structural finite elements (FE’s). The equations are then solved for each element and summed to describe the whole body. The accuracy of the model depends on the number of elements representing the geometry; a larger number will increase the accuracy. The difference between the exact solution and the FEM solution is called the discretization error.
Equilibrium equations, there are multiple forces that are acting on the vessel wall and these need to
Part II.
Abdominal aortic aneurysm
Clinical view
The largest blood vessel in the body is the aorta, it fascilitates the transport of oxygenated and nutrient rich blood throughout the body. The segment of the aorta that stretches from behind the diaphragm and ends at the division into the femoral arteries is termed the abdominal aorta. An abdominal aortic aneurysm (AAA) is pathology characterised by the localised dilation of the abdominal aorta. Several risk factors have been identified as being associated with AAA development such as age, smoking and hypertension [2, 3]. They are also seen to greatly influence the continued expansion of the aneurysm, contributing to the further weakening the vessel wall [20]. The most severe outcome of an aneurysm is the case when it ruptures, resulting in a mortality rate of 75-90 % [1, 2, 5]. To prevent the rupture of an AAA, surgical intervention is often required, general practice is to repair a non-ruptured aneurysm through either open surgery or endovascular repair (EVAR). In order to provide a measurement for when an intervention is justified, clinical management utilizes the transverse diameter and growth of the aneurysm. If the aneurysm has a diameter that exceeds 5.5 cm or a growth rate of 1 cm per year, surgical intervention is considered [2, 4]. This indicator has low sensitivity and specificity since there are aneurysms with a diameter exceeding 5.5 cm that do not ruptures and those with a diameter less that do rupture [4, 6, 7]. The expansion criteria is a time consuming factor since there is a need for surveillance and regular ultrasound assessment [2]. The use of the diameter and expansion rate is also too general when assessing rupture risks, said criteria cannot apply for every patient. It is therefore necessary to individualize the assessment procedure and take into account patient specific characteristics.
Biomechanical view
Through the Implementation of biomechanical concepts it is possible to evaluate the mechanical stress of a localized segment of the aorta and compare it to the strength of that segment. In the event that the stress exceeds the local strength of the degenerated arterial wall, the aneurysm will rupture. It has been shown that peak wall stress is a better predictor of aneurysm rupture on an individual basis compared to current statistical based criteria [8], a rupture risk index derived from wall strength and wall stress is therefore thought to be better suited to evaluating the need for surgical intervention [9].
What also must be taken into account when performing a biomechanical assessment of the abdominal aortic aneurysm is the presence of an intraluminal thrombus (ILT). Clinical studies have shown that an ILT has a structural impact upon the aortic wall strength and stress [10, 11, 12]; a factor that undoubtedly influences the occurrence of aneurysm rupture.
cylinder with a constant radius. Therefore in order to perform more accurate calculations, the finite element method (FEM) is a more viable method [13, 15, 17].
Part III. Biomechanical rupture risk assessment.
Requirements for model
In recent years a biomechanical approach has been developed that improves the predictability of AAA rupture. The biomechanical rupture risk assessment (BRRA) takes patient characteristics into consideration and calculates the rupture risk using the FE-method [14]. In order to perform the FE- based prediction, there are a number of elements that are required [14]:
Three-dimensional geometry of the ILT and the vessel wall Mechanical characteristics of the ILT and wall tissue.
Assumptions on how the AAA interacts with the surroundings. The blood pressure at which wall stress is predicted.
As with all models there will be a slight difference when compared to the real world. In order to be able to effectively model something, one needs to make a series of assumptions and simplifications. The question is then how accurate the model will be and how can we verify it? This depends upon the intended application of the model in question. The model is meant as a medical tool and must then implement the measurements provided by the clinicians. The result must then be in terms that the clinicians require to provide a proper diagnosis or treatment [16]. If the model is able to provide results that comply with real life values, the model can be used. What also needs to be considered is the amount of variables that are used within the model. AAA’s are very complex structures and as discussed previously, several factors can influence them. However the implementation of all known factors may not result in the best model considering the usage area. Just because the model is more complex does not mean that it will provide better clinical information [14]. Therefore, once again, the intended purpose must be regarded.
The BRRA model focuses on the aortic wall strength and stresses when assessing the rupture risk. In order to obtain the strength values, the mechanical properties of the vascular tissue must be known. There is however an inherent difficulty in determining patient specific mechanical properties because of the requirement for tissue samples, which is clearly not feasible. The mechanical properties of aortic tissue used in the BRRA are thus based on mean population data obtained from biaxial and uniaxial destructive mechanical testing [14].
PWS and PWRI
obtained by using individual parameters such as smoking, gender and ILT thickness. The FEM divides the aneurysm sack into a large number of volume segments and each segment will have a strength value related to it. The volume segment where the wall rupture index has its maximum value is called the peak wall rupture index (PWRI), this corresponds to the location where the aneurysm will most likely rupture. The PWRI can have a value of between 0 and infinity, a PWRI equal to 1 means a ruptured aneurysm in an average specimen. By using the PWRI it is possible to individualize the rupture risk assessment. Instead of using general criteria such as the diameter and expansion rate, multiple individual characteristics and demographics are used to provide patient specific evaluations. [14,18].
Figure 4. Flow chart of work using the biomechanical rupture risk assessment and specifically A4CLINICS. Image modified from T. Christian Gasser [14].
Workflow of BRRA
The first step in the work flow is Image segmentation, where computed tomography angiography scans are used to segment the luminal and exterior surfaces of the aneurysm and thus generate an accurate 3D geometry. To be able to perform the FE analysis, the geometry must be subsequently discretised into a large number of FEs with a predefined wall thickness of the aneurysm, this stage is often referred to as mesh generation. In the FE analysis step the patients individual mean arterial pressure and characteristics are taken into consideration when calculating the stresses acting upon the aneurysm wall. The resulting values provide the magnitude of the wall stress that is needed in order to carry the acting blood pressure for the patient specific aneurysm and ILT geometry. As previously mentioned there are a multitude of factors related to the stress of the aneurysm wall. Therefore, the calculations in the FE analysis are based upon mean values from large population studies concerning the material properties of the abdominal aortic wall. The data analysis step then interprets the localised stress values that were determined and in conjunction with the localized calculations of the aneurysm strength, yields the wall rupture indexes over the entirety of the aneurysm. Key measurements and resulting values are then extracted and compiled into an analysis report [14,18]. The resulting PWRI value can then be evaluated by the operating clinician. To easier understand these values a ruptured risk equivalent diameter (RRED) is introduced, which makes it possible to evaluate the aneurysm based upon the diameter and expansion rate criteria and compare it to the average diameter AAA [2,4]. For example, if a patient has a PWRI of 0.5, this would result in a RRED of 580 mm. This means that the patient has the same risk of rupturing as that of a patient with an aneurysm with diameter 580 mm. [14,18]
Figure 5. Definition of rupture risk equivalent diameter for individual patients. The RRED is the diameter of a
average patient that experiences the same peak wall rupture index. Image from [14] with the permission to use by T. Christian Gasser.
Part IV. Improvements of BRRA
Risk factor studies
Currently the characteristics implemented into the equation used in clinical BRRA are the mean arterial pressure, intraluminal thrombus thickness (ILT), family history of aneurysm (HIST), gender (SEX) and diameter of aneurysm (NORD). Women have a higher risk of rupture compared to men, higher blood pressure increases the stress effecting the wall, ILT decreases the wall strength and the diameter has been an indicator used in the clinical practice for a long time [2, 3]. The effect on the wall strength is described by Equation 1.
Wall strength =
𝟕𝟏𝟗 − 𝟑𝟕𝟗 (√𝑰𝑳𝑻 − 𝟎. 𝟖𝟏) − 𝟏𝟓𝟔(𝑵𝑶𝑹𝑫 − 𝟐. 𝟒𝟔) − 𝟐𝟏𝟑𝑯𝑰𝑺𝑻 +
𝟏𝟗𝟑𝑺𝑬𝑿 [𝒌𝑷𝒂] [𝟐𝟏] (1)
Louise C. Brown, and Janet T. Powel [22] performed an evaluation using the ultrasound surveillance data from a large group of patients over a 7 year period. All participants had aneurysms with an initial diameter of 3-6 cm and rupture risks were assessed using regression analysis. Factors that were identified were age, sex, initial AAA diameter, smoking status, BMI, mean blood pressure, ankle-brachial blood pressure index, forced expiratory volume and cholesterol. For each factor the hazard ratio and statistical significance was derived. The factors that were statistically significant were age, female sex, AAA diameter, current smoking, blood pressure and forced expiratory volume. The specific hazard ratios are shown in table 1. The factors not statistically significant had either no correlation to the rupture risk or there were insufficient data to draw any conclusions.
Risk factors Hazard ratio
Sweeting et al. [3]
Age 1.04 (per year)
Smoking 2.02
female sex 3.76
BMI 0.93 (per kg/m2)
MAP 1.32 (per 10 mmHg)
PP 1.11 (per 10mmHg)
Louise C. Brown, and Janet T. Powel [22]
Age 1.02 (per year)
Female sex 4.50
AAA diameter 2.51 (per cm)
Current smoking 2.11
MAP 1.04 (per mmHg)
FEV (L) 0.62 (per L)
Table 1. Statistically significant risk factors (Abbrevations - FEV: forced expiratory volume, MAP: mean arterial pressure).
Hatakeyama et al. [23] summarized multiple data acquisitions from patients under regular aneurysm surveillance. Several factors were then evaluated based on their impact on rupturing and expansion rate for both diameter and volume of the aneurysms. The evaluation utilises correlation coefficients to express the relation between risks factor and either rupturing or expansion rates. The most efficient predictors were then incorporated into equations of a similar form to Equation 1. For the diameter expansion rate the cross sectional diameter, tobacco usage and tortuosity were the most efficient predictors. This equation was then combined with blood pressure and intra luminal thrombus thickness to describe the rupture risk. Compared to Equation 1, Hatakeyama used smoking, blood pressure and tortuosity to express the rupture risk. Both of these studies show that it is possible to combine several different risk factors and calculate rupture risk. It should then be possible to further improve already existing equations.
Deficiencies of current BRRA
The current model that utilises Equation 1 has a risk of generalizing some patients. All patients may not follow the same conditions that the model is setting up. As discussed previously, it has been statistically shown that a person that smokes will have twice the risk of rupture compared to one that doesn’t smoke, whilst a patient that has been treated with angiotensin-converting-enzyme (ACE) inhibitors will have a decreased risk of rupture [3, 22]. If the current model were to be used on the patient that is a current smoker, it may lead to the conclusion that there is no need for surgery, however as the risk is doubled for smokers, it may in fact be the case that surgery is required. Conversely, a patient with ACE inhibitors treatment could be recommended surgery but due to the lowered risk of rupture arising from there treatment, it could be the case that they do not require surgical intervention. These are but a few of the risk factors that exists for AAA; Since there are multiple factors that can affect the outcome of the AAA it would be beneficial if these factors can be implemented into the model. This would make it possible to individualise the model further to better predict the rupture of individual aneurysms [23, 24].
Summary
References
[1]. T.C.Gasser, M. Auer, F.Labruto, J. Swedenborg, J.Roy. Biomechanical Rupture Risk Assessment of
Abdominal Aortic Aneurysms: Model Complexity versus Predictability of Finite Element Simulations. European Journal of Vascular and Endovascular Surgery. Volume 40, Issue 2, August 2010, Pages 176–185
[2] E.M.J. van Disseldorp, N.J. Petterson, M.C.M. Rutten, F.N. van de Vosse, M.R.H.M. van Sambeek, R.G.P.
Lopata. Patient Specific Wall Stress Analysis and Mechanical Characterization of Abdominal Aortic Aneurysms Using 4D Ultrasound.
European Journal of Vascular and Endovascular Surgery, Volume 52, Issue 5, November 2016, Pages 635–642
[3] M. J. Sweeting, S. G. Thompson, L. C. Brown, J. T. Powell. Meta-analysis of individual patient data to
examine factors affecting growth and rupture of small abdominal aortic aneurysms. British Journal of surgery Volume 99, Issue 5, May 2012, Pages 655–665
[4] M.L. Raghavan, David A. Vorp. Toward a biomechanical tool to evaluate rupture potential of abdominal
aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. Journal of Biomechanics Volume 33, Issue 4, April 2000, Pages 475–482.
[5] J.J. Reimerink, M.J. van der Laan, M.J. Koelemay, R. Balm, D.A. Legemate
Systematic review and meta-analysis of population-based mortality from ruptured abdominal aortic aneurysm. British journal of surgery, 100 (11) (2013), pp. 1405–1413
[6] Stephen C. Nicholls, MD, Jon B. Gardner, MD, Mark H. Meissner, MD, Kaj H. Johansen, MD, PhD.
Rupture in small abdominal aortic aneurysms. Journal of Vascular Surgery Volume 28, Issue 5, November 1998, Pages 884–888
[7] K.P. Conway, MB, BCha, J. Byrne, MCh, FRCSIa, M. Townsend, BSc, MScb, I.F. Lane, DM, FRCSa.
Prognosis of patients turned down for conventional abdominal aortic aneurysm repair in the endovascular and sonographic era: Szilagyi revisited? Journal of Vascular Surgery, Volume 33, Issue 4, April 2001, Pages 752– 757
[8]. A. Venkatasubramaniam, M. Fagan, T. Mehta, K. Mylankal, B. Ray, G. Kuhan, et al.
A comparative study of aortic wall stress using finite element analysis for ruptured and non-ruptured abdominal aortic aneurysms. Eur J Vasc Endovasc Surg, 28 (2) (2004), pp. 168–176
[9] J.P. Vande Geest, E.S. Di Martino, A. Bohra, M.S. Makaroun, D.A.A. Vorp.
Biomechanics-based rupture potential index for abdominal aortic aneurysm risk assessment: demonstrative application.
Annals of the New York Academy of Sciences, Volume 1085, The Abdominal Aortic Aneurysm: Genetics, Pathophysiology, and Molecular Biology, Pages 11–21
[10]. M. Kazi, J. Thyberg, P. Religa, J. Roy, P. Eriksson, U. Hedin, et al.
Influence of intraluminal thrombus on structural and cellular composition of abdominal aortic aneurysm wall. Journal of Vascular Surgery, volume 38, issue 6 (2003 Dec), pages. 1283–1292
[11]. D.A. Vorp, P.C. Lee, D.H. Wang, M.S. Makaroun, E.M. Nemoto, S. Ogawa, et al.
Association of intraluminal thrombus in abdominal aortic aneurysm with local hypoxia and wall weakening Journal of Vascular Surgery, volume 34 issue 2, (2001 Aug), pp. 291–299
[12]. S.S. Hans, O. Jareunpoon, M. Balasubramaniam, G.B. Zelenock
[13]. M.L. Raghavan, David A. Vorp, Toward a biomechanical tool to evaluate rupture potential of abdominal
aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. Journal of Biomechanics, Volume 33, Issue 4, April 2000, Pages 475–482
[14]. T.Christian Gasser, Biomechanical Rupture Risk Assessment, A Consistent and Objective Decision-Making
Tool for Abdominal Aortic Aneurysm Patients. AORTA, April 2016, volume 4, issue 2, pages 42-60.
[15]. David A. Vorp, PhD, Biomechanics of abdominal aortic aneurysm,
Journal of Biomechanics, Volume 40, Issue 9, Jan 2007, Pages 1887-1902
[16]. Robert G. Sargent, Verification and validation of simulation models,
Proceedings of the 2011 Winter Simulation Conference S. Jain, R.R. Creasey, J. Himmelspach, K.P. White, and M. Fu, eds.
[17]. William R. Mower. M.D, Larry J. Baraff. M.D, James Sneyd. Ph.D. Stress Distributions in Vascular
Aneurysms: Factors Affecting Risk of Aneurysm Rupture, Journal of Surgical Research, Volume 55, Issue 2, August 1993, Pages 155-161
[18]. P. Erhart, A. Hyhlik-Dürr,P. Geisbüsch, D. Kotelis, M. Müller-Eschner, T.C. Gasser,
H. von Tengg-Kobligk, D. Böckler. Finite Element Analysis in Asymptomatic, Symptomatic, and Ruptured Abdominal Aortic Aneurysms: In Search of New Rupture Risk Predictors.
European Journal of Vascular and Endovascular Surgery, Volume 49, Issue 3, March 2015, Pages 239–245
[19]. Mark F. Fillinger, MDa, Steven P. Marra, PhDa,b, M.L. Raghavan, PhDa,b,c, Francis E. Kennedy, PhDb.
Prediction of rupture risk in abdominal aortic aneurysm during observation: Wall stress versus diameter. Journal of Vascular Surgery, Volume 37, Issue 4, April 2003, Pages 724–732
[20]. S. Khosla, D. R. Morris, J. V. Moxon, P. J. Walker, T. C. Gasser, J. Golledge.
Meta-analysis of peak wall stress in ruptured, symptomatic and intact abdominal aortic aneurysms, British journal of surgery, volume 101, issue 11 (2013), pp. 1350-1357
[21]. A. Maier, M. W. Gee, C. Reeps, J. Pongratz, H.-H. Eckstein, W. A. Wall
A Comparison of Diameter, Wall Stress, and Rupture Potential Index for Abdominal Aortic Aneurysm Rupture Risk Prediction. Annals of Biomedical Engineering, October 2010, Volume 38, Issue 10, pp 3124–3134
[22]. Louise C. Brown, and Janet T. Powell, Risk Factors for Aneurysm Rupture in Patients Kept Under
Ultrasound Surveillance. Annals of surgery, volume 230, issue 3, 1999
Appendix B
Simulation plots
Figure 1. Control patient without any risk factors affecting the wall stress or strength. colour red indicates high
Figure 3. Patient with single risk factor diastolic pressure increase 10%.
Figure 5. Patient with single risk factor Cholesterol.
Figure 6. Patient with single risk factor body mass index (BMI). Bar A represent an increased BMI value of 5
Figure 7. Patient with single risk factor female gender
Figure 9. Patient with single risk factor mean arterial pressure increase 10%.
