Impact of arterial system alterations due to amputation on arterial stiffness and hemodynamics: a numerical study

doi:10.21203/rs.3.rs-4685424/v1

Download PDF

Article

Impact of arterial system alterations due to amputation on arterial stiffness and hemodynamics: a numerical study

https://doi.org/10.21203/rs.3.rs-4685424/v1

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

Subjects with amputation of the lower limbs are at increased risk of cardiovascular mortality and morbidity. We hypothesize that amputation-induced alterations in the arterial tree negatively impact arterial biomechanics, blood pressure and flow behavior. These changes may interact with other biological factors, potentially increasing cardiovascular risk. To evaluate this hypothesis regarding the purely mechanical impact of amputation on the arterial tree, we used a simulation computer model including a detailed one-dimensional (1D) arterial network model (143 arterial segments) coupled with a zero-dimensional (0D) model of the left ventricle. Our simulations included five settings of the arterial network: 1) 4-limbs control, 2) unilateral amputee (right lower limb), 3) bilateral amputee (both lower limbs), 4) trilateral amputee (lower-limbs and right upper-limb), and 5) quadrilateral amputee (lower and upper limbs). Analysis of regional stiffness, as calculated by pulse wave velocity (PWV) for large-, medium- and small-sized arteries, showed that, while aortic stiffness did not change with increasing degree of amputation, stiffness of medium and smaller-sized arteries increased with greater amputation severity. Despite a staged decrease in cardiac output, the systolic and diastolic blood pressure values increased, resulting in an increase in both central and peripheral pulse pressures but with an attenuation of pulse pressure amplification. The most significant increase in peak systolic pressure and decrease in peak systolic blood flow was observed at the site of the abdominal aorta. Wave separation analysis indicated no changes in the shape of the forward and backward wave components. However, the results from wave intensity analysis showed that with extended amputation, there was an increase in peak forward wave intensity and a rise in the inverse peak of the backward wave intensity, suggesting potential alterations in cardiac hemodynamic load. In conclusion, this simulation study showed that biomechanical and hemodynamic changes in the arterial network geometry could interact with additional risk factors to increase the cardiovascular risk in patients with amputations.

Physical sciences/Mathematics and computing/Computational science

Biological sciences/Computational biology and bioinformatics/Computational models

pulse wave velocity

1-D modelling

arterial tree

limb amputees

wave separation analysis

wave intensity analysis

Subjects with post-traumatic amputation of the lower limbs are at increased risk of cardiovascular mortality and morbidity (1, 2). Indeed, several studies have demonstrated that the relative risk of death due to causes is higher in bilateral than in unilateral lower limb amputees (3, 4). This increased cardiovascular risk may be related to an ensemble of psychological stressors, reduced physical activity, unhealthy lifestyle, and other neurometabolic dysregulations such as insulin resistance and altered sympathetic activity (5).

High blood pressure and increased arterial stiffness are prevalent in this population, but it is unclear whether this is related to the metabolic risk factors or purely biomechanical alterations in the arterial tree. Amputees have modified arterial trees due to limb loss, which could result in changes in blood flow, blood pressure, arterial diameter, and arterial wall structure, all potentially affecting arterial stiffness (6). Generally, increasing arterial stiffness leads to increased systolic and pulse pressures, increased cardiac workload, and reduced coronary perfusion pressure. Arterial stiffness, as measured by pulse wave velocity (PWV), is a well-established independent risk factor for cardiovascular disease (7, 8, 9, 10), but its impact on amputees remains poorly understood. Studies also suggest that lower limb amputation is associated with increased risk of abdominal aortic aneurysm (3). Investigating the intrinsic effect of biomechanical alterations caused by limb amputation on arterial stiffness, hemodynamics, and wave reflection is critical as it may provide insights into the pathophysiology of cardiovascular disease in this population (11).

While previous studies have examined the effect of lower limb amputation level on aortic hemodynamics (12) and wall shear stress (13), neither of these methods offer both temporal and quantitative insights into energy exchange between pulsatile blood flow and the arterial wall. A promising approach for gaining deeper understanding in this area is wave intensity analysis (WIA) (14). This method, grounded in a comprehensive treatment of fundamental fluid flow equations using the method of characteristics without assumptions of periodicity or linearity, centers on the concept that the cardiac cycle involves the propagation of minuscule wavefronts characterized by alterations in pressure (P) and velocity (U) (15). Through time domain analysis of P and U waveforms, it allows for the computation of the product of changes in P and U, referred to as "wave intensity," providing a snapshot of the instantaneous energy conveyed by the wavefront (16). By dissecting the individual components of forward and backward waves, it provides crucial insights into the hemodynamic properties and vascular function, aiding in the diagnosis and management of cardiovascular conditions.

To the best of our knowledge, no previous study has investigated PWV/hemodynamics in the setting of different levels of amputations. Thus, the aim of the present study was to use a numerical simulation model that examines the impact of amputation on blood pressure and flow waveforms, as well as arterial stiffness, without confounding metabolic, psychosocial, and behavioral determinants of cardiovascular health. We hypothesized that hemodynamic parameters are altered with increasing severity of amputation, leading to biomechanical alterations that influence the whole arterial system.

1D Arterial network model – topology of the control and amputation cases

We used a human 1D arterial tree model and adapted it to create settings that represent different stages of upper and lower limbs amputees.

The in-silico 1-D cardiovascular model adopted in this study has been previously described by Reymond et al. (17). This model provides physiological, realistic pressure and flow waveforms by solving one-dimensional (1D) Navier-Stokes equations, while accounting for non-linearities (18). The arterial tree (103 segments) includes the main arteries of the systemic circulation, including a detailed network representation of the cerebral circulation and the coronary circulation. The arterial segments of the model are considered as long tapered tubes, and their compliance is defined by a nonlinear function of pressure and location (19). The arterial wall behavior is considered to be non-linear and viscoelastic (20). The governing equations of the model are acquired via integration of the longitudinal momentum and continuity of the Navier-Stokes equations over the arterial cross section. Given proper boundary conditions, flow and pressure waves are obtained at all locations of the systemic arterial tree, by solving the governing equations using an implicit finite-difference scheme. Local arterial compliance is computed by approximating pulse wave velocity as an inverse power function of arterial lumen diameter (17). The resistance of the distal vasculature is considered by coupling the terminal vessels with three-element Windkessel models (21, 22). More details on the 1D model can be found in the original publications (23, 24). This model has been thoroughly validated against in-vivo data and was found to be capable of providing accurate pressure and flow waves, particularly with respect to shape and wave details. The arterial topology of the initial model, as described above, was extended by Obeid et al. (25) to account for more distal arterial segments including hand and foot topologies (radial and tibial arteries), combined and terminated with three-element Windkessel models. The extended version consists of 143 segments (Fig. 1- i).

The previously validated human arterial tree model was adapted to mimic different stages of upper and lower limb amputation. Alterations in the arterial tree were performed in terms of anatomy, while all the systemic and heart model parameters of the in-silico model were kept unchanged and equal to their default values (17). Specifically, five model settings were simulated and illustrated in Fig. 1:

(i) 4-limbs control: all limbs are accurately positioned in their typical anatomical arrangements within the 1D model.

(ii) unilateral lower limb amputee: to simulate a single lower limb amputee, we created a setting characterized by removal of the right lower limb segments (52, 54, 55, 124-130) from the systemic circulation.

(iii) bilateral lower limbs amputee: to simulate a bilateral lower limbs amputee, we created a setting characterized by removal of the right and left lower limb segments (segments: 46, 38, 49, 52, 54, 55, 124-143) from the systemic circulation.

(iv) trilateral limbs amputee: to simulate a trilateral limbs amputee, we created a setting characterized by removal of the right and left lower limb segments (segments: 46, 48, 49, 52, 54, 55, 124-143) and the right upper limb segments (104-113) from the systemic circulation.

(v) quadrilateral limbs amputee: to simulate a quadrilateral limbs amputee, we created a setting characterized by removal of the right and left lower limb segments (segments: 46, 38, 49, 52, 54, 55, 124-143) and the right and left upper limb segments (104-123) from the systemic circulation.

Through the rest of the manuscript, the terms defined above will be used to refer to the different settings. The decision to remove the right lower and upper limbs before the left lower or upper limb was made arbitrarily.

Boundary conditions

At its proximal end, the arterial tree is coupled with a time-varying elastance model for the contractility of the left ventricle (26). Parameters were chosen such that a cardiac output value equal to 5 L/min was generated for the control case. The cardiac parameters (namely filling pressure, heart rate, end-systolic and end-diastolic elastance) were kept constant for the amputation cases, such that the dynamic interaction of the normal heart with the altered arterial tree would determine cardiac output and input into the model, rather than a hard prescribed inlet boundary condition. The default model's cardiovascular parameters are based on a representation of a healthy subject, where all limb segments are accounted for. This model assumes an aortic systolic blood pressure of 122 mmHg, a heart rate of 75 beats per minute, and an Aortic PWV_{Bramwell−Hill} of 5.9 m/s, with an in-silico aortic distensibility set at 27 \(\:{KPa}^{-1}\times\:{10}^{-3}.\)

Impact of amputation on arterial stiffness

Central stiffness was assessed via carotid-femoral PWV (cfPWV), aortic PWV (aPWV), aortic-carotid PWV (acPWV) and ileofemoral PWV (ifPWV), while peripheral stiffness was measured using the carotid-radial PWV (crPWV) (27), and radial-digital PWV (rdPWV) (28). It's noteworthy that peripheral PWV cannot be calculated for quadruple amputees. Inputting different settings into the in-silico model, we ran numerical simulations designed to mimic different stages of amputation and examined the variations in PWV, hemodynamics, wave reflections and impedance values at the different arterial regions. Considering that alterations in PWV affect the arterial pressure waveform, we employed wave separation and intensity analysis (forward and backward pressure waves) within a comprehensive examination of the arterial system, integrating measurements of central pressure and flow waveforms (29, 30). Finally, we performed a more in-depth analysis of abdominal aortic hemodynamics in relation to lower limb amputation, as these analysis could yield novel insight into the mechanisms of development of abdominal aortic aneurysm.

The cfPWV, aPWV, acPWV, ifPWV, crPWV, and rdPWV were determined by measuring the foot-to-foot pulse transit time (PTT) between the passage of the pressure signals at the carotid artery and the femoral artery (cfPTT), the ascending aorta and the abdominal aorta (aPTT), the ascending aorta and the carotid artery (acPTT), the abdominal aorta and the femoral artery (ifPTT), the carotid artery and the radial artery (crPTT), and the radial artery and proper palmar digital artery (rdPTT), respectively. The foot-to-foot PTT algorithm used the maximum second derivative, and was implemented in Matlab (Mathworks, Natick, Massachusetts, United States). This approach was chosen based on the consideration that, for numerical signals, the level of noise is negligible, thereby ensuring that the results remain independent of the algorithm employed. This method uses the time point where the maximum second derivative occurs to calculate the foot of the pressure wave. To ensure that the short-time delays between small arteries are captured, the sampling frequency for all the BP waveforms was set to 900 Hz, an order of magnitude significantly higher than the 100 Hz threshold value for temporal resolution suggested by (31). This specific sampling frequency was selected as a fair trade-off between computational time and high signal fidelity.

The carotid-femoral distance was determined as the distance from the common carotid artery to the femoral artery, resulting in Δx_cf = 66 cm (Fig. 2-i). Given that the precise length of every arterial segment of the 1D model was known, the distance between two arterial sites was computed by summing the individual arterial lengths of all segments within the carotid-femoral path. The carotid to abdominal aortic segment length was determined as the distance from the common carotid to the abdominal aorta, resulting in Δx_ca = 45 cm (Fig. 2-ii). The aortic-carotid length was determined as the distance from the common carotid to the ascending aorta, resulting in Δx_ac = 9 cm (Fig. 2-iii). The abdominal aorta to femoral length was determined as the distance from the abdominal aorta to femoral artery, resulting in Δx_af = 21cm (Fig. 2-iv). The carotid-radial and the radial-digital distances were determined by the summation of the lengths of the arterial segments that connected the two corresponding nodes and were found to be equal to Δx_cr = 55 cm (Fig. 2-v) and Δx_rd = 22 cm (Fig. 2-vi), respectively. Finally, the value of PWV was calculated by dividing the travel distance by the PTT.

Impact of amputation on wave reflection

Wave separation is acknowledged as the definitive technique for exploring wave phenomena, as it precisely quantifies details regarding both forward and backward waves by dissecting the pressure waveform into distinct signals using principles rooted in fluid dynamics within compliant tubes. The forward pressure component delineates the influence of systolic waves on the recorded pressure, whereas the backward pressure component characterizes the impact of early diastolic waves. Wave separation analysis (32) was performed in the frequency domain. The calculation of aortic characteristic impedance involved averaging the modulus of the input impedance within the frequency range between the 3rd and the10th harmonic. By employing the methodology described in Westerhof et al., we separated the total aortic pressure waveforms into their respective forward and backward components. We quantified the magnitude and timing of the forward and backward pressure waves and defined the reflection magnitude as the ratio between the amplitude of the backward wave and that of the forward wave.

Impact of amputation on wave intensity analysis

We also performed wave intensity analysis to explore the intricacies of cardiovascular dynamics. The concept of wave intensity analysis (WIA) was pioneered by Parker et al. in 1988 (33) as an intuitive approach within the time domain for both visualizing and quantifying arterial waves. WIA operates on the foundational principles of one-dimensional flow equations and utilizes the method of characteristics, a familiar tool within the realm of fluid dynamics, to unveil the concealed forward and backward-propagating 'information' that might not be readily evident when inspecting raw pressure and velocity signals (34). Wave intensity (dI) is succinctly defined as the product of incremental changes in pressure (dP) and velocity (dU) over a given sampling interval, namely dI = dP×dU.

While WIA readily identifies the propagation direction of waves at a single location, distinguishing the specific impact of a wave becomes evident: a forward wave presents as a positive value, and a backward wave as negative. However, the nature of a wave's effect on pressure—whether it triggers a pressure increase (termed a compression wave) or a decrease (a decompression wave, also known as an 'expansion' or 'succion' wave) remains ambiguous from the wave intensity signal alone. To ascertain the wave type, wave separation of the pressure waveform is necessary. A forward wave is labeled as a compression wave if it aligns with an increase in the forward pressure wave, while a backward wave is identified as a decompression wave if it aligns with a decrease in the backward pressure wave, and so forth.

With this analytical technique, we can unravel the complex interplay between arterial pressure and flow within the circulatory system under the different simulated conditions. Specifically, we first look at the frequency content of the waveforms using the fast Fourier transform which allows us to get useful information about the power spectrum. Wave intensity is then calculated as the product of the differences in pressure and flow velocity signals. Pressure and flow velocity data were then processed offline using custom-written Matlab code (Mathworks, Inc., Natick, MA, United States). More details on the model can be found in the original publication (35).

Wall shear stress

The determination of wall shear stress (WSS), as outlined by Nordgaard et al., 2010 (36) serves as a crucial metric for comprehending the dynamic forces exerted on vessel walls across diverse model settings. Essentially, heightened flow rates induce an escalation in WSS. Wall shear stress (denoted as τ) is elucidated through a composite of variables encompassing blood properties and vessel morphology, expressed by the formula τ=(v × µ)/d, where v represents flow velocity, µ denotes blood viscosity, and d signifies vessel diameter. This parameter is measured in Newton per m² (N/m²). Typically, in normal arterial conditions, wall shear stress ranges from 1 to 7 N/m². However, instances of elevated WSS > 7 N/m², have been documented, particularly in severe stenosis, cardiac valves, and stents (37).

Impact of amputation on cardiac output, systolic, and diastolic blood pressures

Variations in cardiac output and blood pressure for the setting healthy control and all the amputation scenarios are shown in Table 1. The unilateral and bilateral limb amputee settings reduced cardiac output by 2% and 5%, respectively. Further amputation with trilateral and quadrilateral settings reduced cardiac output by 6% and 7% as compared to the control setting. These findings are coherent with the reduction of blood supply to the respective limbs.

Despite a reduction in cardiac output, the systolic blood pressure (SBP) was increased across all arterial sites with increasing severity of amputations. A greater increase was reported between the control and unilateral settings. Meanwhile, diastolic blood pressure (DBP) was increased to a greater extent in simulations of more severe amputation. The concomitant changes in SBP and DBP led to an augmentation in pulse pressure (PP). Notably, aortic SBP was increased by 23% between control and quadrilateral settings, while aortic DBP increased by 17%, leading to a 31% increase in aortic PP. At the brachial artery, the magnitude of change was smaller, namely SBP was reported to be 143 mmHg for control, 145 mmHg for unilateral, 148 mmHg for bilateral, 152 mmHg for trilateral, and 156 mmHg for quadrilateral, respectively. Meanwhile, brachial DBP remained almost constant around 81 ± 0.9 mmHg across the different simulated scenarios. Overall, this resulted in the attenuation of SBP amplification from aorta to the brachial artery in cases of lower limb amputation.

Impact of amputation on arterial stiffness

The changes in PWV of the different arterial segments under the five simulation settings are presented in Table 2.

In the unilateral setting, there was an asymmetrical increase of cfPWVs (15% on the right and 8% on the left). This increase is related to higher PWV values along the iliofemoral path (5% on the right and 2% on the left), as the aPWV and acPWVs did not change. There were also asymmetrical increases in both crPWVs (13% on the right and 8% on the left) and rdPWVs (7% on the right and 5% on the left) as shown in Table 2.

In the case of bilateral leg amputation, there was a further, but symmetrical increase of cfPWV of 25%. This increase was related to a symmetrical increase along the iliofemoral path (10% increase). Symmetrical increases in crPWV and rdPWV by 24% and 9%, respectively, were observed.

The inclusion of the right arm amputation (unilateral) to the bilateral leg amputation resulted in an asymmetrical increase in cfPWV when compared to the control model (37% on the right and 32% on the left) and the bilateral leg amputation (9% on the right and 5% on the left). Table 2 shows that the aortic-carotid PWV increased by 3% on the right side but was unchanged on the left. Iliofemoral PWV increased by a further 3% on the right side compared to bilateral leg amputations. As with the previous scenarios, aortic PWV did not change. There were increases in the left crPWV by 32% compared to the control setting and 6% compared to the bilateral leg amputee setting. The left rdPWV increased by 12% compared to the control setting and 3% compared to the bilateral leg amputee setting.

The four-limb amputation (quadrilateral) setting resulted in a symmetrical increase of cfPWV, aortic-carotid PWV and iliofemoral PWV respectively by 50%, 3% and 15%, as compared to the control condition, but no changes were observed for aortic PWV.

Impact of amputation on pressure and flow waveforms

Figure 3 illustrates the pressure and flow waveforms observed at distinct arterial sites. Within the brachial and carotid arteries (depicted in Fig. 3A and 3B, respectively), a notable trend emerges: systolic pressure exhibits a gradual and symmetrical augmentation corresponding to the ascending level of amputation, with a notable increase in early diastolic pressure, but only minimal changes in flow velocity at the respective arterial sites. In the ascending aorta, there was also a successive increase in blood pressure waveform during systole (Fig. 3C), and a slight upshift of early DBP, without any major differences in end-diastolic BP. This was accompanied by a reduction in peak systolic flow velocity without any changes in the diastolic blood flow wave. A similar pattern of BP was observed in the thoracic aorta (Fig. 3D), however, there were successive decreases in flow velocity early in diastole, with a more pronounced increase in flow later in diastole. In the abdominal aorta, the amplitude of increase in systolic pressure was more pronounced in the bilateral amputation model, compared to more proximal sections of the aorta (Fig. 3E). However, the blood flow velocity decreased successively with unilateral and bilateral leg amputations, with only slight changes in flow velocity in the trilateral amputation setting (Fig. 3E). The shape of the flow waveform was similar in the diastolic phase of the abdominal aorta. In the femoral artery, an ipsilateral amputation resulted in a significant increase in the amplitude of systolic BP, and significant change in the shape of BP waveform (Fig. 3F), with a significant and expected decline in the femoral artery blood flow velocity. There was an additional upward shift in systolic BP waveform in the bilateral lower limb amputation model. Further addition of the upper limb amputations increased BP only slightly, without any further changes in blood flow velocity.

Impact of amputation on wave separation and intensity analysis

Results from the WSA and the WIA applied to the aortic pressure and flow waves are presented in Fig. 4 for all five model settings. With respect to WSA, no changes in the shape of the forward or backward wave components were observed. In WIA, we observed an increase in the peak value of the forward wave intensity across settings of increased amputation severity, namely 2.5, 3, 3.3, 3.6, 4×10⁹ Wm^− 2s^− 2. In a similar way, the absolute value of the peak of the backward wave intensity component was increased from 1.8×10⁹ Wm^− 2s^− 2 in control condition to 2.7×10⁹ Wm^− 2s^− 2 in the quadrilateral amputee model. In all cases, the forward compression wave (peak intensity) was followed by a smaller decompression forward wave and then a second forward compression wave. Notably, the peak of the second forward compression wave was increased while transitioning from control to quadrilateral amputation settings. A nearly-mirror effect was noticed between the forward and backward wave intensity components.

Impact of asymmetrical and symmetrical leg amputation on abdominal aorta and femoral pressure-flow

Figure 5 shows a more detailed analysis of the impact of unilateral and bilateral leg amputations on the changes of the amplitude, shape and timing of abdominal aorta, right and left femoral arteries. Figures 5A and 5B show the symmetrical pressure and flow waves in both femoral arteries (healthy control setting). After right leg amputation, Fig. 5C shows an asymmetrical increase in pressure of the ipsilateral femoral artery with a corresponding reduction in flow (Fig. 5D). It is interesting to notice that in the contralateral femoral artery systolic BP increased only slightly, while the blood flow velocity decreased. This resulted not only in a reduction in shear stress of the right femoral artery (2.1 to 1.0 N/m²), but also a reduction in the shear stress of the left femoral artery (i.e. contralateral to the amputation) from 2.2 to 1.5 N/m². The shear stress in the abdominal aorta declined from 4.1 N/m² in healthy control condition to 3.8 N/m²in the unilateral amputation model.

Figures 5E and 5F show the respective changes in pressure and flow in the abdominal aorta and femoral arteries after bilateral leg amputation. The pressure waves within both femoral arteries were symmetrical but with a higher systolic peak that occurred later during the cardiac cycle. Flow waves became relatively symmetrical with a lower peak flow velocity, this resulted in a further reduction in the shear stress of the abdominal aorta to 3.4 N/m² in the bilateral leg amputation model.

Impact of asymmetrical right arm amputation on the carotid pressure-flow

Due to an asymmetry observed in aortic-carotid PWV following the imposition of right arm amputation alongside bilateral leg amputation, we further explored the effects of this asymmetry on carotid pressure and flow. However, our investigation found no discernible asymmetrical changes in blood pressure and flow wave patterns upon the imposition of right arm amputation on the bilateral leg amputations.

In this study, we employed a numerical model of the arterial tree to assess pulse wave velocity (PWV) in individuals with limb amputations. Our findings demonstrate a proportional increase in PWV corresponding to the number of amputated limbs, despite the absence of inherent alterations in aortic stiffness.

Limb amputations can result in several physiological and biomechanical changes (38), including alterations in blood flow and in the biomechanical properties of the cardiovascular system which, can potentially modify arterial stiffness and hemodynamics. To examine this hypothesis, we used a validated model of the human arterial tree and ran numerical simulations and determined PWV, arterial pressure and flow waves at different locations in various configurations that mimic different degrees of amputation. This provided us with unique opportunities to distinguish between mechanical and biological events, which could increase the risk of cardiovascular disease in patients with amputation. As such, the study shows an increase in the functional arterial stiffness of medium-sized to small-sized arteries with increasing degree of amputations, without changes in the aortic stiffness per se. Nevertheless, despite a proportional reduction in the cardiac output, blood pressure increased, and the pulse pressure amplification decreased. In addition, the lower limb amputations resulted in more pronounced changes in the pressure and flow in the abdominal aorta, decreasing shear rate in both the aorta and iliac arteries.

Limb amputations in the context of critically ischemic limbs or diabetic foot complications are associated with increased medium to long-term risk of cardiovascular events and mortality, and decreased overall survival (39, 40). However, it is difficult in these conditions to distinguish whether the act of amputation increases the cardiovascular risk or whether critical limb ischemia is merely a proxy for more severe vascular disease. As such, traumatic limb amputations or limb removal for other clinical condition (cancer, infection, etc.) may help to distinguish between these two possible explanations. Several studies have clearly shown that victims of traumatic limb amputations are at increased risk of aortic aneurysm, cardiovascular morbidity and mortality(1–4). Nevertheless, other risk factors such as inactivity, substance abuse, psychosocial stress, obesity, insulin resistance, diabetes and lipid disorders are among other cardiovascular risk factors that are frequently encountered in patients with traumatic limb amputation (1, 2, 41–45). Therefore, the use of a numerical simulation model of the arterial tree provides an opportunity to dissect between mechanical and biological risk factors.

Arterial stiffness is an important determinant of isolated systolic hypertension (46), since physiologically, it is the aortic stiffness that has the greatest impact in increasing cardiac workload and increasing central pulse pressure. Indeed, epidemiological studies have clearly shown that aortic stiffness, as measured by cfPWV, is associated with increased cardiovascular risk. In the present study, we report an increase in cfPWV by 0.9 m/s and 0.5 m/s on the right and left side per amputated limb, respectively. This is in agreement with the higher cfPWV of 0.9 m/s on the right side in unilateral lower limb amputees in humans reported by Magalhães and colleagues (47). This degree of increase in cfPWV is clinically significant. As a 1 m/s increase in cfPWV translates to a risk factor-adjusted risk increase of 14% and 15% in total cardiovascular events, cardiovascular mortality, and all-cause mortality, respectively (48). Interestingly, our findings suggest that this increase is mostly related to an increase in ileo-femoral PWV rather than PWV over the aorta itself. Thus, the present study suggests that the increased cfPWV observed in the amputee population may not solely be related to aortic stiffness but at least partially explained by a hemodynamically induced ileo-femoral stiffness.

In this numerical study, brachial SBP increased by 2–3 mmHg in unilateral lower limb amputation, and up to 13–14 mmHg in the quadrilateral amputation model. In case-control studies, Magalhães and colleagues have reported that the brachial SBP was increased by 9 mmHg in unilateral leg amputees when compared to age-matched nonamputees (47). Similar findings were observed by Paula-Ribeiro and colleagues with 8 mmHg higher brachial SBP in amputees (49). In our simulation model, the increase in aortic SBP was more significant with an increase of 9 mm Hg in the unilateral leg amputation and it further increased to 28 mm Hg in the model of the most severe amputation. Mechanistically, higher aortic SBP has more crucial implications for the heart and target organs such as the brain and the kidneys than brachial blood pressure (50). Given the reports indicating heightened arterial stiffness and blood pressure, we can infer that the rise in PWVs following amputation is likely due to the pressure and area-dependent nature of stiffness. Specifically, increased blood pressure contributes to an overall stiffness elevation (pressure-dependent effect) in both central and peripheral arteries. This effect is accentuated in lower limb amputations due to heightened resistance. Additionally, considering the pressure-area relationship, larger (central) arteries exhibit a comparatively smaller stiffness increase, while smaller (peripheral) arteries experience a more significant rise (area-dependent effect). These combined effects result in a greater increase in peripheral stiffness indices compared to markers of central stiffness.

Pressure and flow wave patterns in the present study provide additional information on the impact of changes in the arterial network. In general, the waveforms of the ascending aorta, thoracic aorta, carotid and brachial arteries showed a similar pattern of change with increasing degree of amputations of the lower and upper limbs from the arterial network, with a marked increase in early diastolic BP. However, the abdominal aorta was the site where there was a most significant increase in systolic blood pressure and the most significant decrease in peak systolic flow, especially in case of lower limb amputation models. These patterns of pressure waves along the aorta are relatively similar to those observed in humans with acute bilateral femoral artery occlusion reported by Latham and colleagues (51). In our simulation models, these collective changes result in a reduction in shear stress in the abdominal aorta which is a site for atherosclerosis and abdominal aortic aneurysm. A similar finding was observed in the iliac blood flow and pressure, which translated into a reduction in shear stress. Indeed, lower wall shear stress interacts with other atherogenic biological risk factors which may initiate the onset of plaque and promote atherosclerosis (52). This is in line with the reported increased risk of abdominal aortic aneurysm in patients with amputations (3). As such, our findings provide insight into the potential mechanisms that may originate from alterations of the arterial network.

The findings derived from the Wave Separation Analysis (WSA) and Wave Intensity Analysis (WIA) concerning aortic pressure and flow waves yield further elucidation regarding the impacts of amputations on arterial hemodynamics. While WSA delineated no discernible alterations in the configuration of forward and backward wave components, WIA unveiled a notable escalation in peak forward wave intensity correlated with heightened severity of amputation. This observation suggests an augmentation in arterial stiffness, particularly within medium- to small-sized arteries. Such heightened intensity may indicate a more robust contraction during the systolic phase among individuals with more extensive amputations. Simultaneously, there was an elevation in the absolute value of the inverse peak of backward wave intensity, implying modifications in the heart's diastolic phase among those experiencing significant limb loss.

A consistent pattern emerged, commencing with a forward compression wave succeeded by a minor decompression forward wave, succeeded again by a second forward compression wave. The peak of this secondary wave intensified from control to multilateral amputation scenarios, signifying an adaptive cardiovascular response. The nearly symmetrical alterations observed between forward and backward wave intensity components underscore the equilibrium between the heart's contraction and relaxation mechanisms. These revelations advance our comprehension of the biomechanical transformations occurring within the arterial network post-amputation and shed light on the potential contribution of these changes to heightened cardiovascular risk in this population.

The strength of the present study resides in its ability to show the impact of acute alterations in the arterial system and its hemodynamic behavior following limb amputation. However, there are some limitations that need to be acknowledged. The findings of this study rely on a 1-D numerical model of the arterial tree, in which anatomical modifications were performed to simulate different degrees of severity of amputation and the biomechanical effects were quantified using solely changes in the tree’s geometry. In addition, there are some limitations that need to be considered when we aim to transpose these findings to human subjects. First, in vivo acute changes in the arterial system are likely to be associated with compensatory mechanisms that might limit the effects otherwise observed in in-silico models. Second, reduction of blood flow in the artery proximal to the limb amputation results in reduction in the diameter of the artery and possibly secondary changes in arterial wall characteristics, which were not inputted in this study. Third, the remaining arteries might also behave differently through outward remodeling, with better ability to accommodate additional blood volume that is diverted following amputation. For example, it has been shown that 8.5 years after a unilateral above knee amputation, the external iliac artery diameter was smaller on the amputated side (7.25 mm versus 9.35 mm). Also, angiographic studies have confirmed a narrowing of both common and external iliac arteries on the amputated side, whereas there was an adaptive dilatation of pelvic and leg arteries on the non-amputated side (41). Others studies have shown that the blood flow of the brachial artery was not different in lower limb amputees but that there was an increase in the vascular resistance in the upper limb (49). However, these changes observed in response to amputation may not fully compensate for the alterations of the arterial system and might perhaps in some ways have long-term maladaptive or negative effect that contribute to the increased cardiovascular risk seen in this population. A promising avenue for future research could be the simulation of physical exercise, given that blood flow to limbs is particularly significant during such activity.

In conclusion, this study employed a previously validated human 1-D arterial tree model coupled with a 0-D model of the left ventricle to examine the influence of successive amputation of lower and upper limbs on arterial stiffness and hemodynamics. These findings provide novel insight into the potential interaction between alterations in arterial stiffness, and blood pressure and flow patterns following amputation, which may interact with other psychosocial and biological risk factors to increase cardiovascular risk in subjects with limb amputations.

Disclosures: All authors have reported that they have no relationships relevant to the contents of this paper to disclose.

Data availability: The datasets used and analysed during the current study available from the corresponding author on reasonable request.

Author Contribution

H.O. and B.V. wrote the main manuscript textP.S. and P.B. revised the manuscriptM.P. and N.S. prepared figuresM.A. and H.O. did the simulation and analyzed the results

Hrubec Z, Ryder RA. Traumatic limb amputations and subsequent mortality from cardiovascular disease and other causes. J Chronic Dis. 1980;33(4):239–50.
Modan M, Peles E, Halkin H, Nitzan H, Azaria M, Gitel S, et al. Increased cardiovascular disease mortality rates in traumatic lower limb amputees. Am J Cardiol. 1998;82(10):1242–7.
Vollmar JF, Paes E, Pauschinger P, Henze E, Friesch A. Aortic aneurysms as late sequelae of above-knee amputation. Lancet Lond Engl. 1989;2(8667):834–5.
Yekutiel M, Brooks ME, Ohry A, Yarom J, Carel R. The prevalence of hypertension, ischaemic heart disease and diabetes in traumatic spinal cord injured patients and amputees. Paraplegia. 1989;27(1):58–62.
Nystoriak MA, Bhatnagar A. Cardiovascular Effects and Benefits of Exercise. Front Cardiovasc Med. 2018;5:135.
Naschitz JE, Lenger R. Why traumatic leg amputees are at increased risk for cardiovascular diseases. QJM Mon J Assoc Physicians. 2008;101(4):251–9.
Laurent S, Boutouyrie P, Asmar R, Gautier I, Laloux B, Guize L, et al. Aortic Stiffness Is an Independent Predictor of All-Cause and Cardiovascular Mortality in Hypertensive Patients. Hypertension. 2001;37(5):1236–41.
Ben-Shlomo Y, Spears M, Boustred C, May M, Anderson SG, Benjamin EJ, et al. Aortic pulse wave velocity improves cardiovascular event prediction: an individual participant meta-analysis of prospective observational data from 17,635 subjects. J Am Coll Cardiol. 2014;63(7):636–46.
Zoungas S, Asmar RP. Arterial stiffness and cardiovascular outcome. Clin Exp Pharmacol Physiol. 2007;34(7):647–51.
Vlachopoulos C, Aznaouridis K, Stefanadis C. Prediction of cardiovascular events and all-cause mortality with arterial stiffness: a systematic review and meta-analysis. J Am Coll Cardiol. 2010;55(13):1318–27.
Mendes-Pinto D, Rodrigues-Machado M da G, Avelar GL, Navarro TP, Dardik A. Arterial stiffness predicts amputation and death in patients with chronic limb-threatening ischemia. J Vasc Surg. 2021;74(6):2014–2022.e4.
Wei J, Li Z, Diao J, Li X, Min L, Jiang W, et al. [Effect of lower limb amputation level on aortic hemodynamics: a numerical study]. Sheng Wu Yi Xue Gong Cheng Xue Za Zhi J Biomed Eng Shengwu Yixue Gongchengxue Zazhi. 2022;39(1):67–74.
Li X, Li Z, Jiang W, Wei J, Xu K, Bai T. Effect of lower extremity amputation on cardiovascular hemodynamic environment: An in vitro study. J Biomech. 2022;145:111368.
Bleasdale RA, Parker KH, Jones CJH. Chasing the wave. Unfashionable but important new concepts in arterial wave travel. Am J Physiol-Heart Circ Physiol. 2003;284(6):H1879–85.
Parker KH, Jones CJ. Forward and backward running waves in the arteries: analysis using the method of characteristics. J Biomech Eng. 1990;112(3):322–6.
Khir AW, O’Brien A, Gibbs JS, Parker KH. Determination of wave speed and wave separation in the arteries. J Biomech. 2001;34(9):1145–55.
Reymond P, Merenda F, Perren F, Rüfenacht D, Stergiopulos N. Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol. 2009;297(1):H208-222.
Segers P, Stergiopulos N, Verdonck P, Verhoeven R. Assessment of distributed arterial network models. Med Biol Eng Comput. 1997;35(6):729–36.
Langewouters GJ, Wesseling KH, Goedhard WJ. The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J Biomech. 1984;17(6):425–35.
Holenstein R, Niederer P, Anliker M. A viscoelastic model for use in predicting arterial pulse waves. J Biomech Eng. 1980;102(4):318–25.
Stergiopulos N, Young DF, Rogge TR. Computer simulation of arterial flow with applications to arterial and aortic stenoses. J Biomech. 1992;25(12):1477–88.
Guan D, Liang F, Gremaud PA. Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model. J Biomech. 2016;49(9):1583–92.
Reymond P, Merenda F, Perren F, Rüfenacht D, Stergiopulos N. Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol. 2009;297(1):H208-222.
Reymond P, Bohraus Y, Perren F, Lazeyras F, Stergiopulos N. Validation of a patient-specific one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol. 2011;301(3):H1173-1182.
Obeid H, Soulat G, Mousseaux E, Laurent S, Stergiopulos N, Boutouyrie P, et al. Numerical assessment and comparison of pulse wave velocity methods aiming at measuring aortic stiffness. Physiol Meas. 2017;38(11):1953–67.
Sagawa K, Suga H, Shoukas AA, Bakalar KM. End-systolic pressure/volume ratio: a new index of ventricular contractility. Am J Cardiol. 1977;40(5):748–53.
Fortier C, Agharazii M. Arterial Stiffness Gradient. Pulse Basel Switz. 2016;3(3–4):159–66.
Obeid H, Fortier C, Garneau CA, Paré M, Boutouyrie P, Bruno RM, et al. Radial-Digital pulse wave velocity: a non-invasive method for assessing stiffness of small conduit arteries. Am J Physiol Heart Circ Physiol. 2021;
Westerhof N, Stergiopulos N, Noble MIM. Snapshots of Hemodynamics: An Aid for Clinical Research and Graduate Education. 2nd ed. Springer; 2010. XIV, 272.
Nichols WW, O’Rourke MF, Vlachopoulos C. McDonald’s blood flow In arteries. Sixth. London: Arnold; 2011.
Gaddum NR, Alastruey J, Beerbaum P, Chowienczyk P, Schaeffter T. A technical assessment of pulse wave velocity algorithms applied to non-invasive arterial waveforms. Ann Biomed Eng. 2013;41(12):2617–29.
Westerhof N, Sipkema P, van den Bos GC, Elzinga G. Forward and backward waves in the arterial system. Cardiovasc Res. 1972;6(6):648–56.
Parker KH, Jones CJ, Dawson JR, Gibson DG. What stops the flow of blood from the heart? Heart Vessels. 1988;4(4):241–5.
Wang JJ, Shrive NG, Parker KH, Tyberg JV. “Wave” as defined by wave intensity analysis. Med Biol Eng Comput. 2009;47(2):189–95.
Parker KH. An introduction to wave intensity analysis. Med Biol Eng Comput. 2009;47(2):175–88.
Nordgaard H, Swillens A, Nordhaug D, Kirkeby-Garstad I, Van Loo D, Vitale N, et al. Impact of competitive flow on wall shear stress in coronary surgery: computational fluid dynamics of a LIMA–LAD model. Cardiovasc Res. 2010;88(3):512–9.
Malek AM, Alper SL, Izumo S. Hemodynamic Shear Stress and Its Role in Atherosclerosis. JAMA. 1999;282(21):2035–42.
Murray AM, Gaffney BM, Davidson BS, Christiansen CL. Biomechanical Compensations of the Trunk and Lower Extremities during Stepping Tasks after Unilateral Transtibial Amputation. Clin Biomech Bristol Avon. 2017;49:64–71.
Abola MTB, Bhatt DL, Duval S, Cacoub PP, Baumgartner I, Keo H, et al. Fate of individuals with ischemic amputations in the REACH Registry: Three-year cardiovascular and limb-related outcomes. Atherosclerosis. 2012;221(2):527–35.
Fortington LV, Geertzen JHB, van Netten JJ, Postema K, Rommers GM, Dijkstra PU. Short and Long Term Mortality Rates after a Lower Limb Amputation. Eur J Vasc Endovasc Surg. 2013;46(1):124–31.
Paes E, Vollmar JF, Pauschinger P, Mutschler W, Wanjura W, Laboranovic E. Hemodynamic and Pathomorphologic Changes of the Aorto-Iliac Arteries Following Unilateral Above Knee Amputation. In: Liepsch DW, editor. Biofluid Mechanics. Berlin, Heidelberg: Springer; 1990. p. 159–65.
Rosengren A, Hawken S, Ounpuu S, Sliwa K, Zubaid M, Almahmeed WA, et al. Association of psychosocial risk factors with risk of acute myocardial infarction in 11119 cases and 13648 controls from 52 countries (the INTERHEART study): case-control study. Lancet Lond Engl. 2004;364(9438):953–62.
Boscarino JA. Posttraumatic stress disorder and mortality among U.S. Army veterans 30 years after military service. Ann Epidemiol. 2006;16(4):248–56.
Kang HK, Bullman TA, Taylor JW. Risk of selected cardiovascular diseases and posttraumatic stress disorder among former World War II prisoners of war. Ann Epidemiol. 2006;16(5):381–6.
Ephraim PL, MacKenzie EJ, Wegener ST, Dillingham TR, Pezzin LE. Environmental barriers experienced by amputees: the Craig Hospital Inventory of Environmental Factors-Short Form. Arch Phys Med Rehabil. 2006;87(3):328–33.
Boutouyrie P, Chowienczyk P, Humphrey JD, Mitchell GF. Arterial Stiffness and Cardiovascular Risk in Hypertension. Circ Res. 2021;128(7):864–86.
Magalhães P, Capingana DP, Silva ABT, Capunge IR, Gonçalves MAA. Arterial Stiffness in Lower Limb Amputees. Clin Med Insights Circ Respir Pulm Med. 2011;5:49–56.
Vlachopoulos C, Aznaouridis K, Stefanadis C. Prediction of cardiovascular events and all-cause mortality with arterial stiffness: a systematic review and meta-analysis. J Am Coll Cardiol. 2010;55(13):1318–27.
Paula-Ribeiro M, Garcia MMN, Martinez DG, Lima JRP, Laterza MC. Increased peripheral vascular resistance in male patients with traumatic lower limb amputation: one piece of the cardiovascular risk puzzle. Blood Press Monit. 2015;20(6):341–5.
McEniery CM, Cockcroft JR, Roman MJ, Franklin SS, Wilkinson IB. Central blood pressure: current evidence and clinical importance. Eur Heart J. 2014;35(26):1719–25.
Latham RD, Westerhof N, Sipkema P, Rubal BJ, Reuderink P, Murgo JP. Regional wave travel and reflections along the human aorta: a study with six simultaneous micromanometric pressures. Circulation. 1985;72(6):1257–69.
Zhou M, Yu Y, Chen R, Liu X, Hu Y, Ma Z, et al. Wall shear stress and its role in atherosclerosis. Front Cardiovasc Med. 2023;10:1083547.

Tables 1 and 2 are available in the Supplementary Files section.

No competing interests reported.

tables.docx

Download PDF

Editorial decision: Revision requested
05 Aug, 2024
Reviews received at journal
28 Jul, 2024
Reviews received at journal
23 Jul, 2024
Reviewers agreed at journal
15 Jul, 2024
Reviewers agreed at journal
13 Jul, 2024
Reviewers invited by journal
13 Jul, 2024
Editor assigned by journal
12 Jul, 2024
Editor invited by journal
12 Jul, 2024
Submission checks completed at journal
09 Jul, 2024
First submitted to journal
04 Jul, 2024

You are reading this latest preprint version

Impact of arterial system alterations due to amputation on arterial stiffness and hemodynamics: a numerical study

Status:

Version 1

Abstract

Figures

INTRODUCTION

MATERIALS & METHODS

1D Arterial network model – topology of the control and amputation cases

Boundary conditions

Impact of amputation on arterial stiffness

Impact of amputation on wave reflection

Impact of amputation on wave intensity analysis

Wall shear stress

RESULTS

Impact of amputation on cardiac output, systolic, and diastolic blood pressures

Impact of amputation on arterial stiffness

Impact of amputation on pressure and flow waveforms

Impact of amputation on wave separation and intensity analysis

Impact of asymmetrical and symmetrical leg amputation on abdominal aorta and femoral pressure-flow

Impact of asymmetrical right arm amputation on the carotid pressure-flow

DISCUSSION

Conclusion

Declarations

Author Contribution

References

Tables

Additional Declarations

Supplementary Files

Status:

Version 1