As a first line option in the treatment of acute ischemic stroke (AIS), direct aspiration is a fast and effective technique with promising outcomes. In silico models are widely used for design and preclinical assessment of new developed devices and therapeutic methods. Accurate modelling of the mechanical behaviour of blood clot is a key factor in the design and simulation of aspiration devices. In this study we develop a new constitutive model which incorporates the unrecoverable plastic deformation of clots. The model is developed based on the deformation-induced microstructural changes in fibrin network, including the formation and dissociation of the cross-links between fibrin fibres. The model is calibrated using previously reported experimentally measured permanent clot deformation following uniaxial stretching. The calibrated plasticity model is then used to simulate aspiration thrombectomy. Results reveal that inclusion of permanent plastic deformation results in ~15 % increase in clot aspiration length at an applied aspiration pressure of 100 mmHg. The constitutive law developed in this study provides a basis for improved design and evaluation of novel aspiration catheters leading to increased first-pass revascularization rate. 1. Introduction Acute Ischemic Stroke (AIS), mainly caused by intracranial large vessel occlusions, is the second leading cause of death worldwide (“WHO global health estimate,” 2020). Mechanical Thrombectomy (MT) is an established non-invasive treatment of large vessel occlusion. Despite significant improvement of MT method in recent years, the proportion of patients experiencing successful procedural revascularization (TICI >=2b) ranged from 76% (Maus et al., 2018) to 85.4% (Chueh et al., 2011) after all procedures. Although complete revascularization (TICI =3) is achieved in less than 61% of cases (Yoo and Andersson, 2017), and it often takes multiple attempts to remove the complete thrombus. First-pass revascularisation is associated with better clinical outcome. Revascularization in multiple passes leads to complications such as increased risk of distal embolization due to the clot fragmentation (Fereidoonnezhad et al., 2021a; Gralla et al., 2006; Kaesmacher et al., 2017; Po Sit, 2009). Moreover, a recent study shows that successful first pass recanalization in MT in US and EU reduces hospitalization and care costs in first year after stroke (Zaidat et al., 2020). In order to maximize the number of patients with first-pass revascularization, new AIS therapies have been developed. One such therapy that has attracted attentions in the recent years is A Direct Aspiration first Pass Technique (ADAPT) in which a large-bore catheter is used for clot aspiration. Clinical studies demonstrate that ADAPT is fast and effective for vessel recanalization as the first line option, results in quick and successful revascularization in more than 50% of patients (Kowoll et al., 2016). Boisseau et al., (2020) published a comprehensive review that compares ADAPT with other techniques such as thrombectomy with stent retriever. Based on this review paper direct aspiration is a fast, safe and efficient thrombectomy technique. However, further randomized trials are needed to better capture the true efficiency of direct aspiration compared with stent retriever (Luraghi et al., 2021a, 2021b) with rates of near complete recanalization and first pass effect as the new standard definitions for technical success in these future trials. Development of improved design and simulation of aspiration thrombectomy devices is highly dependent on accurate modelling of the mechanical behaviour of blood clots. The authors recently developed hyperelastic constitutive model which have been shown to replicate the isochoric and volumetric deformation of thrombi during compression and tension tests (Fereidoonnezhad et al., 2021b, 2021a). The main objective of the current paper is to incorporate permanent (unrecoverable) deformation, as reported in recent experimental investigations (Sugerman et al., 2020). A physically-based thermodynamically-consistent model based on inelastic deformation of the fibrin network is developed, including the stretch- dependent formation and dissociation of cross-links between fibrin fibers. The model is developed withing the framework of finite deformation plasticity theory employing a multiplicative decomposition of the deformation gradient into an elastic and plastic part. The framework is calibrated using reported experimental data (Sugerman et al., 2020) and is used to simulate the aspiration of a clot into an aspiration catheter. Results reveal that permanent deformation leads to a significant (15%) increase in clot aspiration length in comparison to predictions that assume a hyperplastic clot without inclusion of plasticity mechanisms. 2. Continuum modelling Blood clots exhibit complex mechanical behaviour (Boodt et al., 2021; Johnson et al., 2020, 2019; Rausch et al., 2021). In our previous studies (Fereidoonnezhad et al., 2021b, 2021a), we have characterised the nonlinear hyperelastic behaviour of clots, including elastic deformation and reorientation of the fibrin network. In the current study we extend our previous hyperelastic modelling framework to incorporate permanent inelastic deformation of clots based on formation and dissociation of the cross-links between fibrin fibres. 2.1 Kinematics A multiplicative decomposition of deformation gradient tensor is employed, such that:𝐅 𝐅=𝐅𝑒𝐅𝑝 (1) where and are elastic and plastic deformation gradient tensors, respectively. The 𝐅𝑒 𝐅𝑝 spatial velocity gradient is then given as: 𝒍 𝒍=𝐅𝐅―1=𝐅𝑒𝐅―1𝑒+𝐅𝑒(𝐅𝑝𝐅―1𝑝)𝐅―1𝑒 (2) A pull-back of the spatial velocity gradient to the intermediate configuration leads to 𝐋=𝐅―1𝑒𝒍 𝐅𝑒=𝐋𝑒+𝐋𝑝, 𝐋𝑒=𝐅―1𝑒𝐅𝑒, 𝐋𝑝=𝐅𝑝𝐅―1𝑝 (3) 𝐂𝑒=𝐅𝑇𝑒𝐅𝑒=𝐅―𝑇𝑝𝐂𝐅―1𝑝, 𝐂=𝐅𝑻𝐅 (4) where and are the elastic right Cauchy–Green tensor and right Cauchy–Green tensor, 𝐂𝑒 𝐂 respectively. Moreover, following from (Fereidoonnezhad et al., 2021b) a further multiplicative decomposition of deformation gradient and elastic deformation gradient 𝐅=𝐽1/3𝐅 𝐅𝑒=𝐽1/3𝑒𝐅𝑒 is considered, where are volume ratio, elastic volume ratio, modified isochoric 𝐽, 𝐽𝑒, 𝐅, 𝐅𝑒 deformation gradient, and modified isochoric elastic deformation gradient, respectively. The isochoric elastic right Cauchy–Green tensor is given as . The principal stretches , 𝐂𝑒=𝐅𝑇 𝑒𝐅𝑒 (𝜆𝑖) modified principal stretches ( , elastic principal stretches ( , and isochoric elastic principal 𝜆𝑖) 𝜆𝑖𝑒) stretches ( are principal values of , , , and , respectively. 𝜆𝑖𝑒) 𝐅𝐅𝐅𝑒 𝐅𝑒 In (Fereidoonnezhad et al., 2021a) we propose a framework for the elastic deformation and rotation of the fibrin network in the development of anisotropic hyperelastic behaviour of blood clots. In the current study we extend this framework to incorporate the permanent plastic deformation of clots due to formation and dissociation of cross-links in the fibrin network. Considering a fibrin fibre characterised by a direction vector , we define a structural tensor 𝐚0𝑖 as 𝐀0𝑖 𝐀0𝑖=𝐚0𝑖⊗𝐚0𝑖 (5) [Figure 1 goes here] An schematic representation of the multiplicative decomposition of deformation gradient is 𝐅 shown in Figure 1. 2.2 Free energy and thermodynamic consistency The Clausius–Duhem inequality for a system with constant mass and an isothermal process is given as 𝒟=1 2𝐒:𝐂―𝜓≥0(6) where represents the internal energy dissipation, is the second Piola-Kirchhoff stress 𝒟 𝐒 tensor, is the Helmholtz free energy per unit volume and the first derivative of with respect 𝜓 𝜓 to time is denoted by . Motivated by previous works on the modelling of inelastic deformations 𝜓 in shape memory alloys (Arghavani et al., 2011) and fibrous soft biological tissues (Gasser and Holzapfel, 2002), we propose the following form for the Helmholtz free energy per unit volume of blood clot 𝜓=𝜓𝑒 (𝐂𝑒, 𝐀0𝑖)+𝜓𝑝 (𝐅𝑝) (7) where is the hyperelastic energy and is the energy dissipation due to the frictional 𝜓𝑒 𝜓𝑝 (𝐅𝑝) contact between RBCs during volumetric contraction. We then define in the following form: 𝜓𝑝 𝜓𝑝 (𝐅𝑝)=1 2𝑓〈1―𝐽𝑝〉2 (8) in which denotes McCauley bracket and is a material parameter. The time derivative of 〈∎〉 𝑓 the free energy is then calculated as: 𝜓=∂𝜓𝑒 ∂𝐂𝑒:∂𝐂𝑒 ∂𝐂: 𝐂+∂𝜓𝑒 ∂𝐂𝑒:∂𝐂𝑒 ∂𝐅𝑝: 𝐅𝑝+∂𝜓𝑒 ∂𝐀0,𝑖: 𝐀0𝑖+∂𝜓𝑝 ∂𝐅𝑝: 𝐅𝑝(9) The structural tensors change only through and , and no additional evolution law is 𝐀0𝑖 𝐅𝑒 𝐅𝑝 required for fibre reorientation, such that 𝐀0𝑖=𝟎. Substituting (9) into (6) then results in 𝒟=(1 2𝐒―∂𝜓𝑒 ∂𝐂𝑒:∂𝐂𝑒 ∂𝐂): 𝐂―∂𝜓𝑒 ∂𝐂𝑒:∂𝐂𝑒 ∂𝐅𝑝: 𝐅𝑝―∂𝜓𝑝 ∂𝐅𝑝: 𝐅𝑝≥0(10) Thus, with the standard arguments of continuum thermodynamics we obtain the following expression for the second Piola–Kirchhoff stress tensor, i.e. 𝐒=2∂𝜓𝑒 ∂𝐂𝑒:∂𝐂𝑒 ∂𝐂 (11) The dissipation inequality (10) then reduced to 𝒟=―∂𝜓𝑒 ∂𝐂𝑒:∂𝐂𝑒 ∂𝐅𝑝: 𝐅𝑝―∂𝜓𝑝 ∂𝐅𝑝: 𝐅𝑝≥0 (12) After some mathematical elaboration (Fereidoonnezhad et al., 2017) equation (12) is re- written as 𝒟=(𝐌𝑒―𝐗): 𝐋𝑝≥0, (13) in which is the elastic Mandel stress defined as, 𝐌𝑒 𝐌𝑒=𝐂𝑒𝐒𝑒, 𝐒𝑒=2∂𝜓𝑒 ∂𝐂𝑒,(14) and 𝐗=𝑓 〈1―𝐽𝑝〉𝐽𝑝𝐈 (15) The internal dissipated energy is calculated in Appendix A. 𝒟 2.3 Evolution law for plastic deformation To satisfy the inequality (13), we propose the following form for the plastic velocity tensor 𝐋𝑝 𝐋𝑝=𝜉𝐌𝐷𝑒 ‖𝐌𝐷𝑒‖―𝜌𝑐𝐈 (16) where stands for the deviatoric of a tensor defined as: . It is noted (∎)𝐷(∎)𝐷=(∎)―1 3tr(∎)𝐈 that is a diagonal matrix and . 𝐗 𝐗𝐷=𝟎 The variables and are internal variables. The internal variable 𝜉 is a measure of 𝜉 𝜌𝑐 deformation-induced anisotropy in the fibrin network, whereby isochoric deformations will results in preferential alignment of fibrin fibres with associate change in cross-link positions without a change in the density of cross-links. The internal variable is the density of cross- 𝜌𝑐 links in the fibrin networks which can be changed during volumetric expansion or contraction. We assume that volumetric deformation of the clot cause dissociation of the current cross- links, when the volume increases, or formation of new cross-links, when the volume decreases. Such microstructural changes in cross-link distributions can be experimentally observed using confocal microscopy (Weisel and Litvinov, 2013). We assume that redistribution of cross-links and changes in the density of cross-links cause unrecoverable deformation in the fibrin network. The proposed plasticity mechanism is motivated by the qualitative experimental observations that stress-induced irrecoverable strain in blood clot is associated with a structural rearrangement (Nelb et al., 1981) and also the observation that crosslinking makes fibres more susceptible to plastic deformation (Liu et al., 2010). The proposed plasticity mechanisms are schematically demonstrated in Figure 2. The undeformed fibrin network (Figure 2A) deformed by an isochoric shear deformation (Figure 2B) leads to the redistribution of cross-links, i.e., dissociation of some bonds and formation of some new bonds. The formation of new cross-links in the fibrin network depends on the reduction of the distance between fibres, which can be related to the minimum isochoric principal stretch . The possibility of cross-link formation is higher in compact fibre network 𝜆𝑚𝑖𝑛 compared to a spare network. On the other hand, cross-link dissociation depends on the maximum stretch in the fibrin network, . In addition, as shown in Figure 2C, D, pure 𝜆𝑚𝑎𝑥 volumetric deformation can also cause fibrin networks compaction ( ) or expansion ( ) 𝐽<1 𝐽>1 which results in the change in the density of cross-links. [Figure 2 goes here] These changes in the microstructure of blood clot form a new fibrin network with different constraints and deformability. This new network of fibres is not able to fully recover its original shape after removal of the applied load. Based on the aforementioned explanations, we propose the following evolution law for the internal variable in equation (16): 𝜉 𝜉=𝑘1exp(〈𝜆―1〉 𝑎1)〈𝜉𝑠𝑎𝑡―𝜉〉𝑚1〈𝜆 |𝜆|〉(17) where and are material parameters, is the saturation value of , and 𝑘1, 𝑎1 𝑚1 𝜉𝑠𝑎𝑡𝜉 𝜆=𝜆𝑚𝑎𝑥 𝜆𝑚𝑖𝑛 is introduced. Also, denotes McCauley bracket and ensures that when 〈∎〉 〈𝜆 |𝜆|〉 𝜉=0 𝜆<0 which implies an elastic unloading. Moreover, we propose the following form for the evolution of : 𝜌𝑐 𝜌𝑐={𝑘2(1―𝐽)2𝑛1〈𝜌𝑠𝑎𝑡𝑐―𝜌𝑐〉𝑚2〈―𝐽 |𝐽|〉𝐽<1 ―𝑘3(𝐽―1)2𝑛2〈𝜌𝑐 𝜌0𝑐〉𝑚3 〈𝐽 |𝐽|〉𝐽≥1(18) where and are material parameters, and and are the saturation and 𝑘2,𝑘3,𝑚2,𝑚3,𝑛1 𝑛2 𝜌𝑠𝑎𝑡𝑐 𝜌0𝑐 initial values of , respectively. In a volumetric contraction deformation ( ), the density of 𝜌𝑐 𝐽<1 cross-links is increased, reaching to a saturation value ( ). Volumetric contraction results in 𝜌𝑠𝑎𝑡𝑐 a more compact fibrin network which increases the possibility of cross-link formation. Therefore, the time variation of is considered to be a function of . On the other hand, 𝜌𝑐 (1―𝐽) during a volumetric expansion deformation, is considered to be proportional to the current 𝜌𝑐 value of , because, by decreasing there are less cross-links available to be dissociated. 𝜌𝑐 𝜌𝑐 In addition, we highlight that during a volumetric contraction deformation, implies 𝐽<0 volumetric loading and implies volumetric unloading. Therefore, the term in 𝐽>0 〈―𝐽 |𝐽|〉 equation (18) 1 ensures an elastic unloading. In a similar way, the term in equation (18) 2 〈𝐽 |𝐽|〉 ensures an elastic unloading during a volumetric expansion deformation. 2.4 Specific form of free energy To complete the formulation of the proposed constitutive framework, we need to specify the general form of elastic free energy function in equation (7). To this end, the elastic free energy is additively decomposed as 𝜓𝑒(𝐂𝑒, 𝐀𝑖0)=𝜓𝑣𝑜𝑙 (𝐽𝑒)+𝜓𝑖𝑠𝑜 (𝜆1𝑒,𝜆2𝑒,𝜆3𝑒)+𝑁 ∑ 𝑖=1𝜓𝑓,𝑖 (𝜆𝑓𝑒, 𝑖)(19) where, is the volumetric strain energy, is the isochoric strain energy corresponding 𝜓𝑣𝑜𝑙 𝜓𝑖𝑠𝑜 to the non-fibrous matrix, are the principal values of , and = is the 𝜆𝑖𝑒 (𝑖=1,2,3 ) 𝐂𝑒 𝐽𝑒𝜆1𝑒𝜆2𝑒𝜆3𝑒 elastic Jacobian. In addition, are the contribution of fibrin fibres in free energy, 𝜓𝑓,𝑖 (𝑖=1,…,𝑁 ) and are elastic fibre stretches. We then employ the following 𝜆𝑓𝑒, 𝑖=𝐚0𝑖.𝐂𝑒𝐚0𝑖 (𝑖=1,…,𝑁 ) models for each part of the strain energy as proposed in our previous works (Fereidoonnezhad et al., 2021b): 𝜓𝑖𝑠𝑜(𝜆1𝑒,𝜆2𝑒,𝜆3𝑒)=3 ∑ 𝑖=1𝜓(𝜆𝑖𝑒), 𝜓(𝜆𝑖𝑒)={𝐸1m(𝜆𝑖𝑒―ln𝜆𝑖𝑒―1) |𝜆𝑖𝑒―1|≤𝐷1𝑚 𝑝𝑚(𝜆𝑖𝑒2 2―2𝜆 𝑖𝑒+ln𝜆𝑖𝑒)+𝑞𝑚(𝜆𝑖𝑒―ln𝜆𝑖𝑒)+𝑟𝑚ln𝜆𝑖𝑒+𝜓01𝑚 𝐷1𝑚<|𝜆𝑖𝑒―1|<𝐷2𝑚 𝐸2𝑚(𝜆𝑖𝑒―(1+𝐷2𝑚)ln𝜆𝑖𝑒)+(𝑝𝑚𝐷22𝑚+𝑞𝑚𝐷2𝑚+𝑟𝑚)ln𝜆𝑖𝑒+𝜓02𝑚 |𝜆𝑖𝑒―1|≥𝐷2𝑚(20) where are material parameters, and and are two constants 𝐷1𝑚, 𝐷2𝑚, 𝐸1𝑚, and 𝐸2𝑚 𝜓01𝑚 𝜓02𝑚 which ensure the continuity of strain energy. Moreover and are not independent 𝑝𝑚, 𝑞𝑚, 𝑟𝑚 parameters; in order to maintain C0 and C1 continuity the following relations must be enforced: 𝑝𝑚=𝐸1𝑚―𝐸2𝑚 2(𝐷1𝑚―𝐷2𝑚), 𝑞𝑚=𝐸1𝑚―2𝐷1𝑚𝑝𝑚, 𝑟𝑚=(𝐸1𝑚―𝑞𝑚)𝐷1𝑚―𝑝𝑚𝐷21𝑚(21) The non-linear volumetric behaviour of clot is also represented as 𝜓𝑣𝑜𝑙(𝐽)={𝜅1(𝐽―ln𝐽𝑒―1) |𝐽𝑒―1|≤𝐷1𝑣 𝑝𝑣(𝐽𝑒2 2―2𝐽𝑒+ln𝐽𝑒)+𝑞𝑣(𝐽𝑒―ln𝐽𝑒)+𝑟𝑣ln𝐽𝑒+𝜓01𝑣 𝐷1𝑣<|𝐽𝑒―1|<𝐷2𝑣 𝜅2(𝐽𝑒―(1+𝐷2𝑣)ln𝐽𝑒)+(𝑝𝑣𝐷22𝑣+𝑞𝑣𝐷2𝑣+𝑟𝑣)ln𝐽𝑒+𝜓02𝑣 |𝐽𝑒―1|≥𝐷2𝑣(22) in which and are the initial small-strain and large-strain bulk modulus, respectively, the 𝜅1 𝜅2 parameters and control the transition volumetric strains, and and are obtained 𝐷1𝑣 𝐷2𝑣 𝑝𝑣, 𝑞𝑣, 𝑟𝑣 in a similar manner as equation (21) by using the corresponding volumetric parameters. The strain energy density function for fibrin fibres is also represented as (Fereidoonnezhad et al., 2020) 𝜓𝑓,𝑖={ 𝐸1𝑓(2 3𝜆3𝑓𝑒,𝑖―𝜆2𝑓𝑖+1 3), 𝜆𝑓𝑖―1≤𝐷1𝑓 2 3𝜆3𝑓𝑒,𝑖(𝑞𝑓―2𝑝𝑓)+𝑝𝑓 2𝜆4𝑓𝑒,𝑖+𝜆2𝑓𝑒,𝑖(𝑝𝑓―𝑞𝑓+𝑟𝑓)+𝜓01𝑓, 𝐷1𝑓<𝜆𝑓𝑖―1<𝐷2𝑓 2𝐸2𝑓 3𝜆3𝑓𝑒,𝑖+𝜆2𝑓𝑒,𝑖(𝑝𝑓𝐷22𝑓+𝑞𝑓𝐷2𝑓+𝑟𝑓―𝐸2𝑓―𝐸2𝑓𝐷2𝑓)+𝜓02𝑓 , 𝜆𝑓𝑖―1≥𝐷2𝑓(23 ) where and are transition strains of the fibres, and are material parameters, 𝐷1𝑓 𝐷2𝑓 𝐸1𝑓 𝐸2𝑓 and are two constants which ensure the continuity of strain energy and and 𝜓01𝑓 𝜓02𝑓 𝑝𝑓, 𝑞𝑓, are obtained in a similar manner as equation (21) by using the corresponding parameters 𝑟𝑓 for fibres. Equations (18)-(23) represent components of the elastic free energy, , which 𝜓𝑒 should be added to equation (8) to form the total free energy. 2.5Numerical implementation To solve the governing equations numerically, we implement the proposed constitutive equations into the FE framework via the user subroutine material UMAT in Abaqus (“Abaqus 2017. Analysis User’s Guide, Dassault Systèmes Simulia Corp.,” 2017). Calculation of stress and stiffness matrix are described in Appendix B. 3. Numerical Examples 3.1Material parameters identification In Figure 3A we demonstrate that the proposed model accurately reproduces experimentally observed nominal stress-strain behaviour of whole blood clot subjected to load-unload uniaxial tension with strain rate of 0.1 sec-1 (Sugerman et al., 2020). The model was calibrated to the experimental data, by using the optimization toolbox MATLAB (R2017b, The MathWorks, Inc.), and the optimised parameters are provided in Table 1. First, the uniaxial tension test is simulated in Abaqus, by using the proposed constitutive formulations implemented in a UMAT subroutine, as described in Section 2.5. Parameter identification was then performed using the nonlinear least-squares trust region algorithm to minimize the objective function χ=𝑛 ∑ 𝑖=1(𝜎exp𝑖―𝜎mod𝑖)2(24) where is the number of considered data points, are the nominal stresses determined 𝑛 𝜎exp𝑖 experimentally and are the corresponding values predicted by the proposed model. 𝜎mod𝑖 In section 3.3, we use the calibrated parameters to highlight the importance of considering the permanent deformation of clot in predicting the outcomes of aspiration thrombectomy. The computed evolution of the internal variables and for the blood clot subjected to load-unload 𝜉 𝜌𝑐 uniaxial tension is shown in Figure 3B, C. We highlight that the unloading is purely elastic and 𝜉=𝜌𝑐=0. In the current paper we assume an isotropic distribution of cross-links ( 𝜉0=0) with a corresponding isotropic distribution of fibrin network in the undeformed configuration. The initial value of cross-links density, and the evolution of and 𝜉, are calibrated based on 𝜌0𝑐 𝜌𝑐 the experimentally observed plasticity in uniaxial tests (Sugerman et al., 2020). [Figure 3 goes here] [Table 1 goes here] 3.2Sensitivity analysis of the model To demonstrate the main features of the developed model, a parameter sensitivity study is presented in Figure 4 where the clot is subjected to uniaxial loading-unloading boundary conditions described in Section 3.1, as well as the uniaxial loading-unloading compression, loading-unloading volumetric expansion, and loading-unloading volumetric compaction. The calibrated material parameters for the whole blood clot (Table 1) have been used as the baseline parameters. Figure 4 (A, B) demonstrate that, for the given material parameters, 𝑘1, and have significant influence on the stress-strain results in uniaxial tension and 𝑎1, 𝑚1 𝜉𝑠𝑎𝑡 compression tests. These parameters are associated with the role of isochoric deformation on the permanent deformation. Moreover, parameters and which represent the role of volumetric 𝑘2, 𝑘3,𝑛1, 𝑛2,𝑚2, 𝑚3, 𝜌0𝑐 𝜌𝑠𝑎𝑡𝑐 deformation on the induced plasticity, are investigated in volumetric expansion and volumetric compaction deformations in Figure 4 (C, D). Based on equation (18), is dependent on the 𝜌𝑐 volume change (compressibility) of blood clots. In our previous work (Fereidoonnezhad et al., 2021b), we have shown that volumetric change of blood clots is dependent on clot composition and the level of deformation and are not negligible. The experimental data of the uniaxial tensile test, which has been used for calibration of material parameters in this paper, is not sufficient to distinguish between volumetric and isochoric contributions of permanent deformation. Future experimental studies should investigate the contribution of volumetric and isochoric plasticity mechanisms to permanent deformation of clots. [Figure 4 goes here] The proposed plasticity mechanisms are also dependent on the rate of loading and unloading. In a quasi-static deformation (low strain-rate) blood clot has enough time for cross-link association/dissociation while in a very fast deformation (high strain-rate), there is less chance of such changes in clot microstructure. Sensitivity of the proposed model to the rate of deformation ( ) is shown in Figure 5. 𝜀 [Figure 5 goes here] 3.3Simulation of Aspiration thrombectomy Model construction: The objective of this section is to demonstrate the influence of permanent deformation on aspiration thrombectomy by performing finite element simulations of the interaction between a clot and an aspiration catheter (Figure 6A). Three aspiration catheter designs with diameters of 1.5 mm, 1.8 mm, 2 mm are considered, with a cylindrical clot of 3 mm diameter and 10 mm length. A suction pressure, linearly increasing from 0 mmHg to 100 mmHg over 5 seconds, is applied to the portion of the clot which is inside the catheter. The developed constitutive model, with the calibrated material parameters in Table 1, has been used to model the blood clot and the catheter is assumed as a rigid body. The aspiration length, u, is defined as the distance that the top surface of the clot moves into the catheter. In order to demonstrate the contribution of plasticity to clot deformation, simulations are also performed for a purely hyperelastic clot (equations (19)-(23)) by using the material parameters in Table 1. A mesh sensitivity study reveals that a converged solution is obtained using 24000 axisymmetric quadrilateral elements of type CAX4. It is noted that aspiration of a cylindrical- shape homogeneous clot with a cylindrical catheter is an axisymmetric problem. Results: The computed aspiration length, u, for three catheter diameters and for the proposed plasticity clot model is shown in Figure 6B. Moreover, the results of the proposed plasticity model and the purely hyperelastic model for a catheter of 1.5 mm diameter are compared in Figure 6C. As expected, an increase in catheter diameter results in an increase in aspiration length, u. Importantly, simulations suggest that permanent plastic deformation results in a 15% increase in aspiration length at an applied pressure of 100 mmHg. In other words, if plasticity is omitted from the model the aspiration length is significantly under-predicted (Figure 6C). Distribution of the maximum principal stress in clot at the point of maximum applied pressure for a catheter with 1.5 mm diameter, predicted by the proposed plastic model, and by the purely hyperelastic model, are shown in Figure 6D. The results suggest that the hyperelastic model overpredicts the maximum stress in the clot by 10%. The computed values of maximum principal stress for both models are lower than the critical values of crack initiation for different clot compositions (10-45 kPa), as reported in our previous study (Fereidoonnezhad et al., 2021a). Finally, the computed distributions of the maximum and minimum principal unrecoverable plastic stretch in the clot for a catheter with 1.5 mm diameter are shown in Figure 6E. (𝜆𝑝) Very high plastic strains (~12%) are computed near the opening of the aspiration catheter, highlighting the significant level of induced permanent deformation during aspiration. Good et al., (2020a, 2020b) investigated static and cyclic pressure aspiration through computational modelling and in-vitro experiments where they have shown that cyclic aspiration outperforms static aspiration in removal speed and overall clearance. In the current study, we have shown that permanent deformation of thrombus affects the performance of aspiration thrombectomy in static aspiration. Influence of thrombus permanent deformation on the performance of cyclic pressure aspiration should be investigated in future studies. [Figure 6 goes here] 4. Conclusions In this study we have proposed a new material model for the permanent plastic deformation of thrombus material. This new formulation is incorporated into our recently developed anisotropic hyperelastic model that describes elastic deformation and rotation of the fibrin network. The model is developed based on the deformation-induced microstructural changes in fibrin network, including the formation and dissociation of the cross-links between fibrin fibres. Although, establishment of a relationship between plastic deformation and cross-link formation/dissociation in blood clots is proposed in this paper for the first time, it has been previously done for other soft tissues such as collagen networks (Ban et al., 2018). We demonstrate that the addition of our new plasticity formulation to the purely hyperelastic model allows for the accurate simulation of recent experiment measurements of permanent thrombus deformation following uniaxial stretching (Sugerman et al., 2020). We then present simulations of aspiration of a clot into a catheter, demonstrating the importance of our plasticity mechanism in the deformation of the clot. This model provides a basis for design and assessment of novel aspiration catheter design to improve the first-pass revascularization rate in aspiration thrombectomy. Future studies should aim to perform benchtop tests to measure the permanent deformation during aspiration thrombectomy for a specific catheter and clot type to further validate the developed model. Future works should also investigate the influence of catheter design and loading profile (e.g. cyclic versus static pressure) on the performance of aspiration thrombectomy of a clot, incorporating the plastic and hyperelastic mechanisms developed in the current study. Large- bore aspiration catheters demonstrate improved recanalization rates compared to smaller lumen devices in aspiration thrombectomy (Long et al., 2019). On the other hand, smaller catheters have the advantage of better navigability and allow easier access to the occlusion site. The current study suggests that higher levels of plastic deformation will occur for small diameter catheters. The future works should also consider the risk of clot fragmentation while it is sucked into the aspiration catheter as it may result in distal embolization. Future experimental data are required to calibrate/validate the developed model for volumetric plasticity during compaction, and permanent fibre alignment due to the plastic deformation of thrombus. Influence of clot composition (fibrin content) on permanent deformation and influence of plasticity on fracture resistance of thrombus should also be investigated in future studies. 5. Acknowledgment This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 777072. 6.