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REVIEW 2 major objections 4 minor 89 references

A spatially resolved and lipid-structured model for macrophage populations in early human atherosclerotic lesions

T0 review · 2 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Lipid-laden macrophages stall rather than die faster, and that stalling is what creates the internal lipid and macrophage peaks of early coronary lesions, according to a new spatial model.

desk verdict The qualitative peak-formation result is plausible and the negative proofs are solid, but a boundary-condition mismatch in the text means the central phase diagram needs verification before I'd trust the ψD>0.98 conclusion. read the letter →

arxiv 2502.05039 v1 pith:SNGJHO53 submitted 2025-02-07 q-bio.CB

Keith L. Chambers , Mary R. Myerscough , Michael G. Watson , Helen M. Byrne This is my paper · ORCID
classification q-bio.CB MSC 92C3792C5035Q92
keywords atherosclerosislipid-structuredpopulationmodelmacrophagefoamcellsLDLretentionHDLspatiallipid-dependentmobility
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper builds a one-dimensional, lipid-structured model of the artery-wall intima in which monocyte-derived macrophages (MDMs) are labelled by their lipid content as well as their position, and asks which biological mechanisms can produce the two hallmark features of early human coronary lesions seen in Nakashima's images: lipid that first collects deep in the intima, and later a lipid-plus-macrophage peak inside the wall rather than at either boundary. It finds the deep lipid accumulation is explained by a spatially non-uniform LDL retention capacity that rises toward the media. The central result is that the interior peaks appear only when MDM mobility falls steeply with lipid load (diffusivity sensitivity $\psi_D$ close to 1) while MDM lifespan depends only weakly on load ($\psi_\beta$ small); lipid-dependent death alone provably cannot produce an internal maximum. The authors conclude that what creates the lesion's characteristic peaks is that lipid-laden macrophages lose motility and become trapped, not that they die faster. They also find that mean MDM lipid content rises with depth for every blood LDL/HDL combination tested.

What carries the argument

The central object is the lipid-structured MDM density $m_\ell(x,t)$, where $\ell=0,\dots,\ell_{\max}$ indexes the discrete lipid content $a_0+\ell\Delta a$ and $x\in[0,1]$ is depth into the intima. The carrying mechanism is the lipid-content-dependent mobility coefficient $D_M(1-\psi_D \ell/\ell_{\max})$ in the diffusion term of the equation for $m_\ell$, which makes fully loaded cells immobile when $\psi_D=1$. The argument works because this term couples the total MDM density $M(x,t)$ to the second derivative of the ingested-lipid density $L_M-M$: at steady state $d^2M/dx^2 = (\psi_D/\kappa)\,d^2(L_M-M)/dx^2 + M/D_M$, so an internal peak requires $\kappa(L_M-M)$ to be sufficiently concave. A sigmoidal LDL retention capacity $K_r(x)$ supplies the initial deep-lipid gradient, and a fast-mediator quasi-steady reduction closes the recruitment loop by relating endothelial mediator density to a weighted integral of retained LDL.

What would settle it

Measure single-cell migration speed as a function of intracellular lipid content in monocyte-derived macrophages under controlled LDL/HDL conditions; if the speed-versus-load relationship is not approximately linear (for example, mobility drops sharply only beyond a threshold load, or saturates before zero), the model's necessity claim for $\psi_D>0.98$, $\psi_\beta<0.2$ is a linearity artefact. A second check: scan many early human lesions for the transient deep MDM infiltration that the model produces before the peak forms; never observing it would support the authors' own suspicion that this wave is an artefact of the linear assumption.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes a necessary condition on the biology: to match the spatial structure of early human atherosclerotic lesions, the effective diffusion coefficient of an MDM must decrease linearly from $D_M$ to $D_M(1-\psi_D)$ as its lipid index $\ell$ goes from 0 to $\ell_{\max}$, with $\psi_D$ so large that only a narrow neighbourhood of $(\psi_D,\psi_\beta)=(1,0)$ reproduces global internal maxima in both the MDM density $M(x)$ and total lipid density $L_{\rm tot}(x)$. The proof has two parts. With $\psi_D=\psi_\beta=0$, the steady-state MDM profile is exactly $M(x)=A\cosh((1-x)/\sqrt{D_M})+B\sinh((1-x)/\sqrt{D_M})$ with positive $A,B$, so $M'(x)<0$ everywhere. With $\psi_\beta>0=\psi_D$, the steady-state equation gives $d^2M/dx^2\ge 0$, so $M$ is concave-up and cannot have an interior maximum. Only for $\psi_D>0$ can the ingested-lipid density $\kappa(L_M-M)$ be sufficiently concave to make $d^2M/dx^2<0$ and produce the observed internal peak; the paper verifies numerically that this requires $\psi_D$ above roughly 0.92 and, for the peak to be the global maximum, $\psi_D>0.98$ and $\psi_\beta<0.2$ with blood LDL sufficiently high relative to HDL.

Load-bearing premise

The whole 'stall, not die' conclusion rests on the model's assumption that MDM mobility falls linearly with lipid content, so that a fully loaded cell is immobile when $\psi_D=1$; if the real mobility-versus-load curve is nonlinear or saturating, the narrow parameter window that reproduces the lesion peaks could shift or vanish.

Editorial extensions

If this is right

  • The early deep-intima lipid accumulation is set by the LDL retention profile $K_r(x)$ before macrophages arrive, matching Nakashima's observation that the deep intima is the first site of lipid deposition.
  • When $\psi_D>0.98$ and $\psi_\beta<0.2$, both $M(x)$ and $L_{\rm tot}(x)$ develop internal global maxima that approximately coincide, reproducing the Nakashima images; outside this region the profiles are monotone or have only a local maximum that is not global.
  • Increasing $\psi_\beta$ alone lowers MDM density, MDM lipid content, and infiltration depth while raising total lesion lipid, because dying cells deposit necrotic lipid; increasing $\psi_D$ alone does the opposite for MDM lipid content because trapped lipid-laden cells are retained.
  • Mean MDM lipid content increases with depth for all tested blood LDL and HDL levels, so deep cells are not just more numerous but also more lipid-laden.
  • HDL lipid capacity stays nearly uniform across the lesion at all times, so its spatial profile cannot explain spatial heterogeneity; only its time course changes, rising then falling as MDM efflux takes over.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the model's necessity result rests on the linear decrease of mobility with lipid load, a nonlinear mobility-loss curve (saturating or threshold-like) could broaden or shift the $\psi_D$ window; the authors themselves flag the linearity assumption as a possible source of the transient deep-infiltration artefact, so the 'stall, not die' conclusion should be tested against measured speed-vers
  • If maximal MDM infiltration depth really can retreat as the lesion matures, then depth-based staging of early lesions may be unreliable; a prospective counting of MDM positions across many Nakashima-stage lesions would tell whether the transient deep wave is real.
  • The model's prediction that high LDL relative to HDL is required for peak formation suggests that interventions raising HDL capacity might suppress the internal macrophage peak; this consequence is untested because the paper varies HDL only as a boundary condition, not as a therapy.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This paper develops a one-dimensional, spatially resolved PDE model in which monocyte-derived macrophages are structured by a discrete lipid-content index m_l(x,t), coupled to extracellular free LDL, retained LDL, apoptotic and necrotic lipid, HDL, and inflammatory mediators. The model is calibrated to the Nakashima et al. (2007) human coronary artery images through a sigmoidal LDL-retention capacity K_r(x) with steepness theta=10. The principal results are: (i) when MDM kinetics are lipid-independent (psi_D=psi_beta=0), the steady-state total MDM density M(x) is strictly decreasing, proved by a closed-form solution; (ii) when only lifespan depends on lipid content (psi_D=0, psi_beta>0), M satisfies M''>=0 and therefore cannot have an internal maximum; (iii) when only mobility depends on lipid content (psi_D>0, psi_beta=0), internal maxima are possible if the ingested-lipid density L_M-M is sufficiently concave (Eq. 71); and (iv) numerical sweeps over (psi_D,psi_beta) and (L*,H*) identify a small region near (psi_D,psi_beta)=(1,0) where both M and total lipid L_tot have internal global maxima at steady state, matching the images. The authors conclude that lipid-induced loss of MDM mobility, rather than lipid-induced apoptosis, is the mechanism responsible for the internal MDM and lipid peaks.

Significance. The paper's main strengths are the structured-population framework that combines spatial position and lipid content, and the two rigorous negative results: the closed-form monotonicity proof for psi_D=psi_beta=0 (Eqs. 63--66) and the convexity obstruction for psi_beta>0, psi_D=0 (Eq. 69). These are clean and checkable. The positive result, captured in the Fig. 12 phase diagram, is biologically plausible and useful, but it is established only by numerical sweeps with a qualitative shape classification. The boundary-condition inconsistency described below, together with the absence of code, means the numerical evidence for the central claim is not yet fully reproducible. The paper is transparent about several limitations, including the linear mobility assumption and the calibration of K_r(x), which is a distinct strength.

major comments (2)
  1. [§2.2, Eqs. (3) and (41)] The text following Eq. (3) states that MDMs at x=0 and x=X exit the lesion at a rate proportional to their mobility, gamma(1-psi_D l/l_max), but Eq. (3) and its dimensionless counterpart Eq. (41) impose the lipid-independent flux gamma m_l at both boundaries (with the R(t) delta_{l,0} term at x=0). The moment equations (26)--(27) are derived by summing Eq. (3) and therefore also contain gamma M and gamma L_M, not the mobility-weighted sums that the prose would imply. This is a load-bearing issue: if the simulations used Eq. (3), the stated egress--mobility coupling was not part of the model that produced Fig. 12; if the simulations used the text version, the governing equations in the manuscript do not match the numerics. Please reconcile the text and equations, state explicitly which boundary condition was implemented, and ideally provide the numerical code or the discretized form used.
  2. [§3.4, Fig. 12] The phase diagram in Fig. 12 is the primary evidence for the central conclusion that internal global maxima require psi_D>0.98 and psi_beta<0.2. However, the paper does not specify how the categories 'monotone', 'local maximum not equal to global maximum', and 'local maximum equal to global maximum' are computed from the numerical steady states. No threshold for identifying a local maximum, no statement of how many extrema are found, and no convergence check for the classification under the reported Delta x=0.02 discretization are given. Because the claimed region is a small neighbourhood of (psi_D,psi_beta)=(1,0), the classification procedure must be reproducible and robust; please provide the algorithm or the code used to generate Fig. 12.
minor comments (4)
  1. [Abstract and §4 Q1] The abstract says the model 'predicts' deep initial lipid accumulation and internal peak formation, but feature 1 is imposed through the calibrated retention profile K_r(x) (Eq. 7) and feature 2 is used to select the parameter region in Fig. 12; consider using language such as 'reproduces' or 'is consistent with' and explicitly distinguishing calibrated features from emergent ones.
  2. [Table 2] In Table 2, the row for the dimensionless lifespan sensitivity parameter lists '~psi_beta psi_D Sensitivity of MDM lifespan to lipid load'; the parameter name should be psi_beta, not psi_D.
  3. [§4 Q1] The Discussion already flags that the transient deep infiltration could be an artefact of the linear mobility decrease with lipid content; it would strengthen the paper to include a sensitivity test with a nonlinear or saturating mobility function, such as D(l)=D_M(1-psi_D(l/l_max)^p), to show that the Fig. 12 region is not an artefact of linearity.
  4. [§3.4] The text states that peak formation in both M and L_tot requires psi_D>0.98 and psi_beta<0.2, but Fig. 12 uses a grid resolution of only 0.1 for psi_D<0.9; it would be useful to state explicitly how the reported thresholds were derived from the grid and whether they are sensitive to the grid resolution.

Circularity Check

1 steps flagged · score 4.0 of 10

Deep-lipid 'prediction' is built into the fitted LDL-retention profile, but the central ψD–ψβ peak-formation result is an emergent model output.

  1. fitted input called prediction [Abstract; §2.2 Eq. (7); §4 Discussion, Q1]
    "We accounted for feature 1 by assuming a spatially non-uniform LDL retention capacity, Kr(x), which increases with x in a step-like manner. The steepness of the step is determined by a parameter, θ ≈ 10, which we approximate by comparison to Fig. 1(e, h)."

    The abstract's claim that 'the model predicts that lipid initially accumulates deep in the intima due to a spatially non-uniform LDL retention capacity' restates the input: Kr(x) is defined as an increasing sigmoid of x (Eq. 7), with θ estimated directly from the Nakashima images, and §3.1 states that 'the spatial profile of rLDL is dominated by the non-uniform retention capacity, Kr(x)'. The deep lipid feature is therefore placed in the model by construction rather than derived from independent first principles. The central peak-formation claim (ψD > 0.98, ψβ < 0.2) is separate and does not reduce to this fit.

full rationale

Aside from the deep-lipid construction, I find no circularity in the load-bearing peak-formation argument. The ψD–ψβ phase diagram (Fig. 12) is obtained by sweeping two free parameters against steady-state solutions and comparing qualitatively with the Nakashima images; no parameter is fitted to the peak feature, and the conclusion that high lipid-sensitivity of mobility and low lipid-sensitivity of death are needed is an emergent property of the model. Citations to the authors' prior lipid-structured models ([41]–[44]) supply the uptake/efflux framework, but the spatial peak mechanism is analyzed and proven within this paper (e.g., Eqs. (70)-(71)), so self-citation is not load-bearing. The text/equation mismatch for MDM egress (stated γ(1−ψD ℓ/ℓmax) versus Eq. (3)/(41), which impose γmℓ) is an internal consistency problem that could affect which model was actually simulated, but it is not circularity. The authors' own Q1 caveat about the linear mobility assumption is a sensitivity limitation, not a circular step. Overall: one advertised prediction reduces to a fitted input, while the central claim retains independent content.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The model's conclusions rest on the assumed spatial profile of LDL retention and on the chosen linear forms for lipid-dependent mobility and lifespan. These are inputs calibrated to the same images against which the model is evaluated, which limits the independence of the 'predictions'. The quasi-steady mediator approximation and the fixed-domain, no-proliferation simplifications are standard and well-justified.

free parameters (4)
  • θ = 10
    LDL retention profile steepness, estimated by eye from Fig. 1(e,h) to make Kr(x) increase smoothly with depth; directly encodes feature 1.
  • ψD = explored over [0,1]; needed near 1
    Mobility sensitivity to lipid content, swept to find the region that reproduces the internal maxima; the central conclusion requires ψD ≈ 1.
  • ψβ = explored over [0,1]; needed near 0
    Lifespan sensitivity to lipid content, swept in parallel; the conclusion requires small ψβ.
  • X = 0.40 mm
    Intima width estimated from Fig. 1; sets the spatial scale of the model.
assumptions (7)
  • domain assumption MDM mobility decreases linearly with lipid content (Eq. 1 first term).
    Based on qualitative observation that foam cells are less mobile [14,15]; the linear form is chosen for simplicity and the paper notes the retreat behavior may be an artifact of this linearity (Discussion, Q1).
  • domain assumption MDM mean lifespan decreases linearly with lipid content (Eq. 1 second term).
    Based on free cholesterol cytotoxicity [13]; the linear form is a modeling choice.
  • ad hoc to paper LDL retention capacity Kr(x) is a fixed sigmoidal function of depth (Eq. 7) with θ=10.
    Chosen to reproduce the deep lipid accumulation seen in Fig. 1; this is the mechanism for feature 1.
  • domain assumption Egress rates at x=0 and x=X are equal.
    Stated in Sect. 2.2 because IEL egress rates have not been measured.
  • domain assumption No local proliferation of MDMs.
    Justified by [51] showing limited proliferation in aortic macrophages.
  • domain assumption Quasi-steady approximation for inflammatory mediators (Eqs. 49-53).
    Uses separation of timescales with ε = 1/δS = 6.25e-4; requires mediator dynamics to be fast relative to other processes, and enables the reduced model.
  • domain assumption Initial lesion is empty (Eq. 48).
    Standard initial condition corresponding to a healthy intima.

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Cite this review

Pith. "Pith review of A spatially resolved and lipid-structured model for macrophage populations in early human atherosclerotic lesions." pith.science (2026). https://pith.science/paper/SNGJHO53

@misc{pith2026250205039,
  author       = {Pith},
  title        = {Pith review of: A spatially resolved and lipid-structured model for macrophage populations in early human atherosclerotic lesions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SNGJHO53}},
  note         = {Machine review of arXiv:2502.05039}
}
read the original abstract

Atherosclerosis is a chronic inflammatory disease of the artery wall. The early stages of atherosclerosis are driven by interactions between lipids and monocyte-derived-macrophages (MDMs). The mechanisms that govern the spatial distribution of lipids and MDMs in the lesion remain poorly understood. In this paper, we develop a spatially-resolved and lipid-structured model for early atherosclerosis. The model development and analysis are guided by images of human coronary lesions by Nakashima et al. 2007. Consistent with their findings, the model predicts that lipid initially accumulates deep in the intima due to a spatially non-uniform LDL retention capacity. The model also qualitatively reproduces the global internal maxima in the Nakashima images only when the MDM mobility is sufficiently sensitive to lipid content, and MDM lifespan sufficiently insensitive. Introducing lipid content-dependence to MDM mobility and mean lifespan produced minimal impact on model behaviour at early times, but strongly impacted lesion composition at steady state. Increases to the sensitivity of MDM lifespan to lipid content yield lesions with fewer MDMs, less total lesion lipid content and reduced mean MDM infiltration depth. Increases to the sensitivity of MDM mobility to lipid content also reduces the MDM infiltration depth, but increases the proportion of lipid-laden MDMs. We find that MDM lipid content increases with spatial depth, regardless of blood LDL and HDL content. These results shed light on the mechanisms that drive spatial variation in the composition of early atherosclerotic lesions, and the role of macrophage lipid content in disease progression.

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Works this paper leans on

89 extracted references · 73 canonical work pages

  1. [1]

    Arteriosclerosis, throm- bosis, and vascular biology 27(5), 1159–1165 (2007)

    Nakashima, Y., Fujii, H., Sumiyoshi, S., Wight, T.N., Sueishi, K.: Early human atherosclerosis: accumulation of lipid and proteoglycans in intimal thickenings followed by macrophage infiltration. Arteriosclerosis, throm- bosis, and vascular biology 27(5), 1159–1165 (2007). https://doi.org/10. 1161/ATVBAHA.106.134080

    2007

  2. [2]

    Nature 407, 233–241 (2000)

    Lusis, A.: Atherosclerosis. Nature 407, 233–241 (2000). https://doi.org/ 10.1038/35025203

    work page doi:10.1038/35025203 2000

  3. [3]

    Current opinion in lipidology 27(5), 473–483 (2016)

    Bor´ en, J., Williams, K.J.: The central role of arterial retention of cholesterol-rich apolipoprotein-b-containing lipoproteins in the patho- genesis of atherosclerosis: a triumph of simplicity. Current opinion in lipidology 27(5), 473–483 (2016). https://doi.org/10.1097/MOL. 0000000000000330

    work page doi:10.1097/mol 2016

  4. [4]

    Jour- nal of lipid research 41(11), 1703–1714 (2000)

    ¨O¨ orni, K., Pentik¨ ainen, M.O., Ala-Korpela, M., Kovanen, P.T.: Aggre- gation, fusion, and vesicle formation of modified low density lipoprotein particles: molecular mechanisms and effects on matrix interactions. Jour- nal of lipid research 41(11), 1703–1714 (2000). https://doi.org/10.1016/ S0022-2275(20)31964-7

    2000

  5. [5]

    Jour- nal of clinical medicine 10(8), 1769 (2021)

    ¨O¨ orni, K., Kovanen, P.T.: Aggregation susceptibility of low-density lipoproteins—a novel modifiable biomarker of cardiovascular risk. Jour- nal of clinical medicine 10(8), 1769 (2021). https://doi.org/10.3390/ jcm10081769 Springer Nature 2021 LATEX template A spatially resolved and lipid-structured model for early atherosclerosis39

    2021

  6. [6]

    The Journal of Pathology 250(5), 705–714 (2020)

    Willemsen, L., de Winther, M.P.: Macrophage subsets in atherosclerosis as defined by single-cell technologies. The Journal of Pathology 250(5), 705–714 (2020). https://doi.org/10.1002/path.5392

    work page doi:10.1002/path.5392 2020

  7. [7]

    International Journal of Molecular Sciences 22(1), 216 (2020)

    Kloc, M., Uosef, A., Kubiak, J.Z., Ghobrial, R.M.: Role of macrophages and rhoa pathway in atherosclerosis. International Journal of Molecular Sciences 22(1), 216 (2020). https://doi.org/10.3390/ijms22010216

    work page doi:10.3390/ijms22010216 2020

  8. [8]

    Arteriosclerosis, thrombosis, and vascular biology 16(1), 4–11 (1996)

    Guyton, J.R., Klemp, K.F.: Development of the lipid-rich core in human atherosclerosis. Arteriosclerosis, thrombosis, and vascular biology 16(1), 4–11 (1996). https://doi.org/10.1161/01.atv.16.1.4

    work page doi:10.1161/01.atv.16.1.4 1996

Show all 89 references
  1. [9]

    Canadian Journal of Cardiology 33(3), 303–312 (2017)

    Gonzalez, L., Trigatti, B.L.: Macrophage apoptosis and necrotic core development in atherosclerosis: a rapidly advancing field with clinical rel- evance to imaging and therapy. Canadian Journal of Cardiology 33(3), 303–312 (2017). https://doi.org/10.1016/j.cjca.2016.12.010

    2017 doi

  2. [10]

    JACC: Cardiovascular Imaging 10(12), 1472–1483 (2017)

    Costopoulos, C., Huang, Y., Brown, A.J., Calvert, P.A., Hoole, S.P., West, N.E., Gillard, J.H., Teng, Z., Bennett, M.R.: Plaque rupture in coronary atherosclerosis is associated with increased plaque structural stress. JACC: Cardiovascular Imaging 10(12), 1472–1483 (2017). htt...

    2017 doi

  3. [11]

    British Medical Journal Publishing Group (2007)

    Rothwell, P.: Atherothrombosis and ischaemic stroke. British Medical Journal Publishing Group (2007). https://doi.org/10.1136/bmj.38964. 489051.80

    2007 doi

  4. [13]

    Journal of Biological Chemistry 276(45), 42468–42476 (2001)

    Yao, P.M., Tabas, I.: Free cholesterol loading of macrophages is associated with widespread mitochondrial dysfunction and activation of the mito- chondrial apoptosis pathway. Journal of Biological Chemistry 276(45), 42468–42476 (2001). https://doi.org/10.1074/jbc.M101419200

    2001 doi

  5. [14]

    a mechanism for atherosclerosis regression? Arteriosclerosis and Thrombosis: A Journal of Vascular Biology 12(8), 936–944 (1992)

    Pataki, M., Lusztig, G., Robenek, H.: Endocytosis of oxidized ldl and reversibility of migration inhibition in macrophage-derived foam cells in vitro. a mechanism for atherosclerosis regression? Arteriosclerosis and Thrombosis: A Journal of Vascular Biology 12(8), 936–944 (199...

    1992 doi

  6. [15]

    Atherosclerosis 290, 19–30 (2019)

    Chen, L., Zhang, J., Yang, X., Liu, Y., Deng, X., Yu, C.: Lysophosphatidic Springer Nature 2021 LATEX template 40 A spatially resolved and lipid-structured model for early atherosclerosis acid decreased macrophage foam cell migration correlated with down- regulation of fucosyl...

    2019 doi

  7. [16]

    Briefings in bioinformatics 17(4), 562–575 (2016)

    Parton, A., McGilligan, V., O’Kane, M., Baldrick, F.R., Watterson, S.: Computational modelling of atherosclerosis. Briefings in bioinformatics 17(4), 562–575 (2016). https://doi.org/10.1093/bib/bbv081

    2016 doi

  8. [17]

    Annals of Biomedical Engineering 47, 1764–1785 (2019)

    Avgerinos, N.A., Neofytou, P.: Mathematical modelling and simula- tion of atherosclerosis formation and progress: a review. Annals of Biomedical Engineering 47, 1764–1785 (2019). https://doi.org/10.1007/ s10439-019-02268-3

    2019

  9. [18]

    https://doi.org/10.1016/j.cmpb.2021.106435

    Cai, Y., Li, Z.: Mathematical modeling of plaque progression and associ- ated microenvironment: How far from predicting the fate of atherosclero- sis? Computer Methods and Programs in Biomedicine211, 106435 (2021). https://doi.org/10.1016/j.cmpb.2021.106435

    2021

  10. [19]

    WIREs Mechanisms of Disease 14(3), 1546 (2022)

    Mc Auley, M.T.: Modeling cholesterol metabolism and atherosclerosis. WIREs Mechanisms of Disease 14(3), 1546 (2022). https://doi.org/10. 1002/wsbm.1546

    2022

  11. [20]

    Journal of biomechanics 38(4), 903–917 (2005)

    Prosi, M., Zunino, P., Perktold, K., Quarteroni, A.: Mathematical and numerical models for transfer of low-density lipoproteins through the arte- rial walls: a new methodology for the model set up with applications to the study of disturbed lumenal flow. Journal of biomechanic...

    2005 doi

  12. [22]

    International Journal of Heat and Mass Transfer 51(3-4), 497–505 (2008)

    Yang, N., Vafai, K.: Low-density lipoprotein (ldl) transport in an artery–a simplified analytical solution. International Journal of Heat and Mass Transfer 51(3-4), 497–505 (2008). https://doi.org/10.1016/j. ijheatmasstransfer.2007.05.023

    2008 doi

  13. [23]

    Journal of theoretical biology 314, 23–33 (2012)

    Fok, P.-W.: Mathematical model of intimal thickening in atherosclerosis: vessel stenosis as a free boundary problem. Journal of theoretical biology 314, 23–33 (2012). https://doi.org/10.1016/j.jtbi.2012.07.029

    2012 doi

  14. [24]

    Journal of Mathematical Biology 81(2), 725–767 (2020)

    Watson, M.G., Byrne, H.M., Macaskill, C., Myerscough, M.R.: A mul- tiphase model of growth factor-regulated atherosclerotic cap formation. Journal of Mathematical Biology 81(2), 725–767 (2020). https://doi.org/ 10.1007/s00285-020-01526-6 Springer Nature 2021 LATEX template A s...

    2020 doi

  15. [25]

    Computers in biology and medicine 118, 103623 (2020)

    Corti, A., Chiastra, C., Colombo, M., Garbey, M., Migliavacca, F., Casarin, S.: A fully coupled computational fluid dynamics–agent-based model of atherosclerotic plaque development: multiscale modeling frame- work and parameter sensitivity analysis. Computers in biology and me...

    2020

  16. [26]

    PLoS Computa- tional Biology 16(11), 1008413 (2020)

    Bayani, A., Dunster, J.L., Crofts, J.J., Nelson, M.R.: Spatial considera- tions in the resolution of inflammation: elucidating leukocyte interactions via an experimentally-calibrated agent-based model. PLoS Computa- tional Biology 16(11), 1008413 (2020). https://doi.org/10.137...

    2020 doi

  17. [27]

    Journal of theoretical biology 297, 1–10 (2012)

    Bulelzai, M.A., Dubbeldam, J.L.: Long time evolution of atherosclerotic plaques. Journal of theoretical biology 297, 1–10 (2012). https://doi.org/ 10.1016/j.jtbi.2011.11.023

    2012 doi

  18. [28]

    Bulletin of mathematical biology 76, 1117–1142 (2014)

    Cohen, A., Myerscough, M.R., Thompson, R.S.: Athero-protective effects of high density lipoproteins (hdl): an ode model of the early stages of atherosclerosis. Bulletin of mathematical biology 76, 1117–1142 (2014). https://doi.org/10.1007/s11538-014-9948-4

    2014 doi

  19. [29]

    ANZIAM Journal 57, 320–345 (2015)

    Islam, M.H., Johnston, P.: A mathematical model for atherosclerotic plaque formation and arterial wall remodelling. ANZIAM Journal 57, 320–345 (2015). https://doi.org/10.21914/anziamj.v57i0.10386

    2015 doi

  20. [30]

    Bulletin of mathematical biology 80, 175–214 (2018)

    Thon, M.P., Ford, H.Z., Gee, M.W., Myerscough, M.R.: A quantita- tive model of early atherosclerotic plaques parameterized using in vitro experiments. Bulletin of mathematical biology 80, 175–214 (2018). https: //doi.org/10.1007/s11538-017-0367-1

    2018 doi

  21. [31]

    Bulletin of Mathematical Biology 83(9), 96 (2021)

    Lui, G., Myerscough, M.R.: Modelling preferential phagocytosis in atherosclerosis: delineating timescales in plaque development. Bulletin of Mathematical Biology 83(9), 96 (2021). https://doi.org/10.1007/ s11538-021-00926-z

    2021

  22. [32]

    Journal of mathematical analysis and applications 505(2), 125606 (2022)

    Xie, X.: Well-posedness of a mathematical model of diabetic atheroscle- rosis. Journal of mathematical analysis and applications 505(2), 125606 (2022). https://doi.org/10.1016/j.jmaa.2021.125606

    2022

  23. [33]

    In: ESAIM: Proceedings, vol

    Calvez, V., Ebde, A., Meunier, N., Raoult, A.: Mathematical modelling of the atherosclerotic plaque formation. In: ESAIM: Proceedings, vol. 28, pp. 1–12 (2009). https://doi.org/10.1051/proc/2009036. EDP Sciences

    2009

  24. [34]

    Mathemat- ical medicine and biology: a journal of the IMA 29(4), 301–327 (2012)

    Fok, P.-W.: Growth of necrotic cores in atherosclerotic plaque. Mathemat- ical medicine and biology: a journal of the IMA 29(4), 301–327 (2012). https://doi.org/10.1093/imammb/dqr012 Springer Nature 2021 LATEX template 42 A spatially resolved and lipid-structured model for ear...

    2012 doi

  25. [35]

    PloS one 9(3), 90497 (2014)

    Hao, W., Friedman, A.: The ldl-hdl profile determines the risk of atherosclerosis: a mathematical model. PloS one 9(3), 90497 (2014). https://doi.org/10.1371/journal.pone.0090497

    2014 doi

  26. [36]

    Journal of mathematical biology 71, 1451–1480 (2015)

    Chalmers, A.D., Cohen, A., Bursill, C.A., Myerscough, M.R.: Bifurcation and dynamics in a mathematical model of early atherosclerosis: How acute inflammation drives lesion development. Journal of mathematical biology 71, 1451–1480 (2015). https://doi.org/10.1007/s00285-015-0864-5

    2015 doi

  27. [37]

    Modeling Earth Sys- tems and Environment 5, 1853–1865 (2019)

    Mukherjee, D., Guin, L.N., Chakravarty, S.: A reaction–diffusion mathematical model on mild atherosclerosis. Modeling Earth Sys- tems and Environment 5, 1853–1865 (2019). https://doi.org/10.1007/ s40808-019-00643-6

    2019

  28. [38]

    American Journal of Physiology-Heart and Circulatory Physiology 319(4), 835–846 (2020)

    Mohammad Mirzaei, N., Weintraub, W.S., Fok, P.-W.: An integrated approach to simulating the vulnerable atherosclerotic plaque. American Journal of Physiology-Heart and Circulatory Physiology 319(4), 835–846 (2020). https://doi.org/10.1152/ajpheart.00174.2020

    2020

  29. [39]

    Bulletin of Mathematical Biology 85(5), 37 (2023)

    Ahmed, I.U., Byrne, H.M., Myerscough, M.R.: Macrophage anti- inflammatory behaviour in a multiphase model of atherosclerotic plaque development. Bulletin of Mathematical Biology 85(5), 37 (2023). https: //doi.org/10.1007/s11538-023-01142-7

    2023 doi

  30. [40]

    Proceedings of the Royal Society B 286(1904), 20190730 (2019)

    Ford, H.Z., Zeboudj, L., Purvis, G.S., Ten Bokum, A., Zarebski, A.E., Bull, J.A., Byrne, H.M., Myerscough, M.R., Greaves, D.R.: Efferocyto- sis perpetuates substance accumulation inside macrophage populations. Proceedings of the Royal Society B 286(1904), 20190730 (2019). http...

    1904

  31. [41]

    Bulletin of Mathematical Biology 85(9), 85 (2023)

    Watson, M.G., Chambers, K.L., Myerscough, M.R.: A lipid-structured model of atherosclerotic plaque macrophages with lipid-dependent kinet- ics. Bulletin of Mathematical Biology 85(9), 85 (2023). https://doi.org/ 10.1007/s11538-023-01193-w

    2023 doi

  32. [42]

    Bulletin of Mathematical Biology 86(8), 104 (2024)

    Chambers, K.L., Watson, M.G., Myerscough, M.R.: A lipid-structured model of atherosclerosis with macrophage proliferation. Bulletin of Mathematical Biology 86(8), 104 (2024). https://doi.org/10.1007/ s11538-024-01333-w

    2024

  33. [43]

    arXiv preprint arXiv:2404.07051 (2024)

    Chambers, K.L., Myerscough, M.R., Watson, M.G., Byrne, H.M.: Blood lipoproteins shape the phenotype and lipid content of early atheroscle- rotic lesion macrophages: a dual-structured mathematical model. arXiv preprint arXiv:2404.07051 (2024). https://doi.org/10.48550/arXiv.2404. 07051

    2024 doi arXiv

  34. [44]

    Mathematical Biosciences, 108971 (2023)

    Chambers, K.L., Myerscough, M.R., Byrne, H.M.: A new lipid-structured Springer Nature 2021 LATEX template A spatially resolved and lipid-structured model for early atherosclerosis43 model to investigate the opposing effects of ldl and hdl on atherosclerotic plaque macrophages....

    2023

  35. [45]

    Journal of Theoretical Biology 556, 111248 (2023)

    Celora, G.L., Byrne, H.M., Kevrekidis, P.: Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radio- therapy treatment. Journal of Theoretical Biology 556, 111248 (2023). https://doi.org/10.1016/j.jtbi.2022.111248

    2023

  36. [46]

    Journal of Theoretical Biology 535, 110980 (2022)

    Fiandaca, G., Bernardi, S., Scianna, M., Delitala, M.E.: A phenotype- structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment. Journal of Theoretical Biology 535, 110980 (2022). https://doi.org/10.1016/j.jtbi.2021.110980

    2022

  37. [47]

    Journal of Mathematical Biology 84(3), 19 (2022)

    Pan, Y.: Propagation dynamics for an age-structured population model in time-space periodic habitat. Journal of Mathematical Biology 84(3), 19 (2022). https://doi.org/10.1007/s00285-022-01721-7

    2022 doi

  38. [48]

    Discrete & Continuous Dynamical Systems- Series B 27(12) (2022)

    Boulouz, A.: A spatially and size-structured population model with unbounded birth process. Discrete & Continuous Dynamical Systems- Series B 27(12) (2022). https://doi.org/10.3934/dcdsb.2022038

    2022 doi

  39. [49]

    Computers & Mathematics with Appli- cations 78(1), 123–135 (2019)

    Hu, W.: Spatial–temporal patterns of a two age structured population model with spatial non-locality. Computers & Mathematics with Appli- cations 78(1), 123–135 (2019). https://doi.org/10.1016/j.camwa.2019.02. 030

    2019 doi

  40. [50]

    Liu, Z., Tang, H., Magal, P.: Hopf bifurcation for a spatially and age structured population dynamics model. Discr. Cont. Dyn. Syst. B 20, 1735–1757 (2015). https://doi.org/10.3934/dcdsb.2015.20.1735

    2015 doi

  41. [51]

    Nature immunology 21(10), 1194–1204 (2020)

    Williams, J.W., Zaitsev, K., Kim, K.-W., Ivanov, S., Saunders, B.T., Schrank, P.R., Kim, K., Elvington, A., Kim, S.H., Tucker, C.G., et al.: Limited proliferation capacity of aortic intima resident macrophages requires monocyte recruitment for atherosclerotic plaque progressio...

    2020

  42. [52]

    Nature medicine 19(9), 1166–1172 (2013)

    Robbins, C.S., Hilgendorf, I., Weber, G.F., Theurl, I., Iwamoto, Y., Figueiredo, J.-L., Gorbatov, R., Sukhova, G.K., Gerhardt, L., Smyth, D., et al.: Local proliferation dominates lesional macrophage accumulation in atherosclerosis. Nature medicine 19(9), 1166–1172 (2013)

    2013

  43. [53]

    Cellular immunology 330, 27–42 (2018)

    Remmerie, A., Scott, C.L.: Macrophages and lipid metabolism. Cellular immunology 330, 27–42 (2018). https://doi.org/10.1016/j.cellimm.2018. 01.020 Springer Nature 2021 LATEX template 44 A spatially resolved and lipid-structured model for early atherosclerosis

    2018 doi

  44. [54]

    Proceedings of the Royal Society of London

    Smith, E.B., Staples, E.M.: Plasma protein concentrations in interstitial fluid from human aortas. Proceedings of the Royal Society of London. Series B. Biological Sciences 217(1206), 59–75 (1982). https://doi.org/10. 1098/rspb.1982.0094

    1982

  45. [55]

    Am Heart Assoc (2005)

    Williams, K.J., Tabas, I.: Lipoprotein retention—and clues for atheroma regression. Am Heart Assoc (2005). https://doi.org/10.1161/01.ATV. 0000174795.62387.d3

    2005

  46. [56]

    The Korean jour- nal of internal medicine 27(3), 317 (2012)

    Lee, J.-G., Koh, S.J., Yoo, S.Y., Yu, J.R., Lee, S.A., Koh, G., Lee, D.: Characteristics of subjects with very low serum low-density lipoprotein cholesterol and the risk for intracerebral hemorrhage. The Korean jour- nal of internal medicine 27(3), 317 (2012). https://doi.org/...

    2012 doi

  47. [57]

    Proceedings of the National Academy of Sciences 96(15), 8420–8425 (1999)

    Orlova, E.V., Sherman, M.B., Chiu, W., Mowri, H., Smith, L.C., Gotto Jr, A.M.: Three-dimensional structure of low density lipoproteins by electron cryomicroscopy. Proceedings of the National Academy of Sciences 96(15), 8420–8425 (1999). https://doi.org/10.1073/pnas.96.15.8420

    1999 doi

  48. [58]

    European heart journal 38(32), 2478–2486 (2017)

    Madsen, C.M., Varbo, A., Nordestgaard, B.G.: Extreme high high-density lipoprotein cholesterol is paradoxically associated with high mortality in men and women: two prospective cohort studies. European heart journal 38(32), 2478–2486 (2017). https://doi.org/10.1093/eurheartj/ehx163

    2017 doi

  49. [59]

    Atherosclerosis 123(1-2), 1–15 (1996)

    Nielsen, L.B.: Transfer of low density lipoprotein into the arterial wall and risk of atherosclerosis. Atherosclerosis 123(1-2), 1–15 (1996). https: //doi.org/10.1016/0021-9150(96)05802-9

    1996 doi

  50. [60]

    American Journal of Physiology-Heart and Circulatory Physiology 289(5), 2048–2058 (2005)

    Holzapfel, G.A., Sommer, G., Gasser, C.T., Regitnig, P.: Determina- tion of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive mod- eling. American Journal of Physiology-Heart and Circulatory Phys...

    2005

  51. [61]

    molecular size as a determinant of plasma lipoprotein influx

    Stender, S., Zilversmit, D.: Transfer of plasma lipoprotein components and of plasma proteins into aortas of cholesterol-fed rabbits. molecular size as a determinant of plasma lipoprotein influx. Arteriosclerosis: An Official Journal of the American Heart Association, Inc. 1(1...

    1981 doi

  52. [62]

    Circulation research 74(1), 74–82 (1994)

    Penn, M.S., Saidel, G.M., Chisolm, G.M.: Relative significance of endothe- lium and internal elastic lamina in regulating the entry of macromolecules into arteries in vivo. Circulation research 74(1), 74–82 (1994). https: //doi.org/10.1161/01.res.74.1.74

    1994 doi

  53. [63]

    Annals of biomedical engineering 38, 1463–1472 (2010)

    Yuan, W., Li, G., Fu, B.M.: Effect of surface charge of immortalized mouse Springer Nature 2021 LATEX template A spatially resolved and lipid-structured model for early atherosclerosis45 cerebral endothelial cell monolayer on transport of charged solutes. Annals of biomedical ...

    2010

  54. [64]

    Matrix Biology 71, 396–420 (2018)

    Wight, T.N.: A role for proteoglycans in vascular disease. Matrix Biology 71, 396–420 (2018). https://doi.org/10.1016/j.matbio.2018.02.019

    2018 doi

  55. [65]

    PloS one 18(1), 0280385 (2023)

    Liu, M., Samant, S., Vasa, C.H., Pedrigi, R.M., Oguz, U.M., Ryu, S., Wei, T., Anderson, D.R., Agrawal, D.K., Chatzizisis, Y.S.: Co-culture models of endothelial cells, macrophages, and vascular smooth muscle cells for the study of the natural history of atherosclerosis. PloS o...

    2023 doi

  56. [66]

    Journal of lipid research 50(3), 446–455 (2009)

    Bancells, C., Ben ´ ıtez, S., Jauhiainen, M., Ord´ o˜ nez-Llanos, J., Kovanen, P.T., Villegas, S., S´ anchez-Quesada, J.L., Katariina, O.,et al.: High bind- ing affinity of electronegative ldl to human aortic proteoglycans depends on its aggregation level. Journal of lipid res...

    2009 doi

  57. [67]

    Journal of leukocyte biology 86(6), 1331–1343 (2009)

    Williams, M.R., Sakurai, Y., Zughaier, S.M., Eskin, S.G., McIntire, L.V.: Transmigration across activated endothelium induces transcrip- tional changes, inhibits apoptosis, and decreases antimicrobial protein expression in human monocytes. Journal of leukocyte biology 86(6), 1...

    2009 doi

  58. [68]

    Experimental & Molecular Medicine 51(4), 1–12 (2019)

    Lee, S.J., Baek, S.E., Jang, M.A., Kim, C.D.: Sirt1 inhibits monocyte adhesion to the vascular endothelium by suppressing mac-1 expression on monocytes. Experimental & Molecular Medicine 51(4), 1–12 (2019). https://doi.org/10.1038/s12276-019-0239-x

    2019 doi

  59. [69]

    : Fate mapping reveals origins and dynamics of monocytes and tissue macrophages under homeostasis

    Yona, S., Kim, K.-W., Wolf, Y., Mildner, A., Varol, D., Breker, M., Strauss-Ayali, D., Viukov, S., Guilliams, M., Misharin, A., et al. : Fate mapping reveals origins and dynamics of monocytes and tissue macrophages under homeostasis. Immunity 38(1), 79–91 (2013). https: //doi....

    2013 doi

  60. [70]

    Arte- riosclerosis, thrombosis, and vascular biology 38(8), 1702–1710 (2018)

    Williams, J.W., Martel, C., Potteaux, S., Esaulova, E., Ingersoll, M.A., Elvington, A., Saunders, B.T., Huang, L.-H., Habenicht, A.J., Zin- selmeyer, B.H., et al.: Limited macrophage positional dynamics in pro- gressing or regressing murine atherosclerotic plaques—brief report...

    2018 doi

  61. [71]

    Cardiovascular research 45(3), 528–537 (2000)

    Saraste, A., Pulkki, K.: Morphologic and biochemical hallmarks of apop- tosis. Cardiovascular research 45(3), 528–537 (2000). https://doi.org/10. 1016/S0008-6363(99)00384-3 Springer Nature 2021 LATEX template 46 A spatially resolved and lipid-structured model for early atherosclerosis

    2000

  62. [72]

    Cells Tissues Organs 142(3), 246–248 (1991)

    Sokol, R., Wales, J., Hudson, G., Goldstein, D., James, N.: Changes in cellular dry mass during macrophage development. Cells Tissues Organs 142(3), 246–248 (1991). https://doi.org/10.1159/000147197

    1991 doi

  63. [73]

    Oxford Univer- sity Press, ??? (2022)

    Cooper, G., Adams, K.: The Cell: a Molecular Approach. Oxford Univer- sity Press, ??? (2022)

    2022

  64. [74]

    Plos one 16(1), 0245797 (2021)

    Sanda, G.M., Stancu, C.S., Deleanu, M., Toma, L., Niculescu, L.S., Sima, A.V.: Aggregated ldl turn human macrophages into foam cells and induce mitochondrial dysfunction without triggering oxidative or endoplasmic reticulum stress. Plos one 16(1), 0245797 (2021). https://doi.o...

    2021

  65. [75]

    JoVE (Journal of Visualized Experiments) (138), 58149 (2018)

    Taruc, K., Yin, C., Wootton, D.G., Heit, B.: Quantification of efferocy- tosis by single-cell fluorescence microscopy. JoVE (Journal of Visualized Experiments) (138), 58149 (2018). https://doi.org/10.3791/58149

    2018 doi

  66. [76]

    Arteriosclerosis, thrombosis, and vascular biology 25(6), 1256–1261 (2005)

    Schrijvers, D.M., De Meyer, G.R., Kockx, M.M., Herman, A.G., Mar- tinet, W.: Phagocytosis of apoptotic cells by macrophages is impaired in atherosclerosis. Arteriosclerosis, thrombosis, and vascular biology 25(6), 1256–1261 (2005). https://doi.org/10.1161/01.ATV.0000166517.18801.a7

    2005

  67. [77]

    Molecular biology of the cell 15(3), 1089–1100 (2004)

    Brouckaert, G., Kalai, M., Krysko, D.V., Saelens, X., Vercammen, D., Ndlovu, M., Haegeman, G., D’Herde, K., Vandenabeele, P.: Phagocytosis of necrotic cells by macrophages is phosphatidylserine dependent and does not induce inflammatory cytokine production. Molecular biology o...

    2004

  68. [78]

    Arte- riosclerosis, thrombosis, and vascular biology 18(10), 1589–1599 (1998)

    Kritharides, L., Christian, A., Stoudt, G., Morel, D., Rothblat, G.H.: Cholesterol metabolism and efflux in human thp-1 macrophages. Arte- riosclerosis, thrombosis, and vascular biology 18(10), 1589–1599 (1998). https://doi.org/10.1161/01.ATV.18.10.1589

    1998 doi

  69. [79]

    https: //doi.org/10.3389/fphar.2017.00989

    Woudberg, N.J., Pedretti, S., Lecour, S., Schulz, R., Vuilleumier, N., James, R.W., Frias, M.A.: Pharmacological intervention to modulate hdl: what do we target? Frontiers in pharmacology 8, 989 (2018). https: //doi.org/10.3389/fphar.2017.00989

    2018

  70. [80]

    Journal of neuroinflammation 12, 1–18 (2015)

    O’Carroll, S.J., Kho, D.T., Wiltshire, R., Nelson, V., Rotimi, O., John- son, R., Angel, C.E., Graham, E.S.: Pro-inflammatory tnf α and il-1 β differentially regulate the inflammatory phenotype of brain microvas- cular endothelial cells. Journal of neuroinflammation 12, 1–18 (...

    2015 doi

  71. [81]

    Proceedings of the National Academy of Sciences 90(7), 2744–2748 (1993)

    Pugin, J., Sch¨ urer-Maly, C., Leturcq, D., Moriarty, A., Ulevitch, R.J., Tobias, P.S.: Lipopolysaccharide activation of human endothelial and epithelial cells is mediated by lipopolysaccharide-binding protein and Springer Nature 2021 LATEX template A spatially resolved and li...

    1993 doi

  72. [82]

    Advanced Science 8(15), 2004433 (2021)

    Liu, C., Chu, D., Kalantar-Zadeh, K., George, J., Young, H.A., Liu, G.: Cytokines: From clinical significance to quantification. Advanced Science 8(15), 2004433 (2021). https://doi.org/10.1002/advs.202004433

    2021 doi

  73. [83]

    Arteriosclerosis, thrombosis, and vascular biology 27(8), 1843– 1849 (2007)

    Kontush, A., Therond, P., Zerrad, A., Couturier, M., N´ egre-Salvayre, A., de Souza, J.A., Chantepie, S., Chapman, M.J.: Preferential sphingosine- 1-phosphate enrichment and sphingomyelin depletion are key features of small dense hdl3 particles: relevance to antiapoptotic and ...

    2007 doi

  74. [84]

    https://doi.org/10.14670/HH-18-252

    Taefehshokr, N., Yin, C., Heit, B.: Rab gtpases in the differential process- ing of phagocytosed pathogens versus efferocytosed apoptotic cells (2021). https://doi.org/10.14670/HH-18-252

    2021 doi

  75. [85]

    Euro- pean Biophysics Journal 45, 301–309 (2016)

    Adlerz, K.M., Aranda-Espinoza, H., Hayenga, H.N.: Substrate elasticity regulates the behavior of human monocyte-derived macrophages. Euro- pean Biophysics Journal 45, 301–309 (2016). https://doi.org/10.1007/ s00249-015-1096-8

    2016

  76. [86]

    Bulletin of math- ematical biology 81(10), 4022–4068 (2019)

    Thon, M.P., Myerscough, M.R., Gee, M.W.: A spatially resolved and quantitative model of early atherosclerosis. Bulletin of math- ematical biology 81(10), 4022–4068 (2019). https://doi.org/10.1007/ s11538-019-00646-5

    2019

  77. [87]

    Analytica chimica acta 1000, 205–213 (2018)

    Ross, A., Pompano, R.: Diffusion of cytokines in live lymph node tis- sue using microfluidic integrated optical imaging. Analytica chimica acta 1000, 205–213 (2018). https://doi.org/10.1016/j.aca.2017.11.048

    2018 doi

  78. [88]

    Nature Reviews Cardiology 16(7), 389–406 (2019)

    B¨ ack, M., Yurdagul Jr, A., Tabas, I., ¨O¨ orni, K., Kovanen, P.T.: Inflam- mation and its resolution in atherosclerosis: mediators and therapeutic opportunities. Nature Reviews Cardiology 16(7), 389–406 (2019). https: //doi.org/10.1038/s41569-019-0169-2

    2019 doi

  79. [89]

    New England Journal of Medicine 316(22), 1371–1375 (1987)

    Glagov, S., Weisenberg, E., Zarins, C.K., Stankunavicius, R., Kolet- tis, G.J.: Compensatory enlargement of human atherosclerotic coronary arteries. New England Journal of Medicine 316(22), 1371–1375 (1987). https://doi.org/10.1056/NEJM198705283162204

    1987 doi

  80. [90]

    Computer Methods in Applied Mechanics and Engineering 363, 112860 (2020)

    Fok, P.-W., Gou, K.: Finite element simulation of intimal thickening in 2d multi-layered arterial cross sections by morphoelasticity. Computer Methods in Applied Mechanics and Engineering 363, 112860 (2020). https://doi.org/10.1016/j.cma.2020.112860 Springer Nature 2021 LATEX ...

    2020

  81. [91]

    Mathematical Biosciences 373, 109208 (2024)

    Ahmed, I.U., Myerscough, M.R.: Hdl and plaque regression in a mul- tiphase model of early atherosclerosis. Mathematical Biosciences 373, 109208 (2024). https://doi.org/10.1016/j.mbs.2024.109208

    2024

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