Dynamic Multiscale Regulation of Perfusion Recovery in Experimental Peripheral Arterial Disease

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SUMMARY
In peripheral arterial disease (PAD), the degree of endogenous capacity to modulate revascularization of limb muscle is central to the management of leg ischemia. To characterize the multiscale and multicellular nature of revascularization in PAD, we have developed the first computational systems biology model that mechanistically incorporates intracellular, cellular, and tissue-level features critical for the dynamic reconstitution of perfusion after occlusion-induced ischemia. The computational model was specifically formulated for a preclinical animal model of PAD (mouse hindlimb ischemia [HLI]), and it has gone through multilevel model calibration and validation against a comprehensive set of experimental data so that it accurately captures the complex cellular signaling, cell-cell communication, and function during post-HLI perfusion recovery. As an example, our model simulations generated a highly detailed description of the time-dependent spectrum-like macrophage phenotypes in HLI, and through model sensitivity analysis we identified key cellular processes with potential therapeutic significance in the pathophysiology of PAD. Furthermore, we computationally  In severe PAD conditions (eg, critical limb ischemia), patients have rest pain and/or nonhealing ulcers or gangrene that can lead to amputation (2,3). Due to the significant occlusions in the major blood vessels that supply the legs, blood flow and perfusion to the lower limbs in patients with PAD become heavily dependent on the degree of vascular remodeling (from arteriogenesis and angiogenesis) in the ischemic limb muscle (4). Therapeutic agents and gene delivery aimed at stimulating vascular growth and remodeling in the ischemic limb by manipulating pro-angiogenic transcription factors (eg, hypoxiainducible factor-1 alpha) or growth factors (eg, vascular endothelial growth factor [VEGF]) have, to date, largely failed (3,5). However, novel targeted strategies (eg, antibodies, macrophage-and stem cell-based therapies) are being actively investigated in preclinical studies as well as in earlyphase clinical trials given the large unmet medical need (6)(7)(8)(9)(10).
In PAD, perfusion recovery in the ischemic muscle is a complex multiscale process involving a number of resident and mobilized cell types that dynamically participate in an orchestrated program of cellular signaling, communication, and tissue-level remodeling. For example, as a direct consequence of muscle ischemia, stressed and damaged skeletal myocytes and endothelial cells (ECs) can release massive amounts of high-mobility group box 1 (HMGB1), an early and endogenous danger signal that is suggested to broadly influence immune response, angiogenesis, and muscle regeneration (11,12). At the intracellular level, reduced blood supply is expected to lead to significant tissue ischemia and hypoxia that stabilize hypoxia-inducible factors within cells and activate the production of a number of strong pro-angiogenic factors (eg, VEGF, angiopoietins, matrix metalloproteinases) (13,14).
In addition to their direct pro-angiogenic effects on ECs, many of these factors regulate key processes in other cell types within the ischemic muscle. For example, VEGF has been shown to promote the survival and migration of myoblasts and their differentiation into skeletal myocytes, which are critical steps in postischemia skeletal muscle regeneration (15,16). Moreover, VEGF, by signaling through its receptor VEGFR1 on myeloid cells, can potently stimulate monocyte/macrophage recruitment, and this axis also contributes to the functional polarization of macrophages (eg, M1-like, M2-like) in the ischemic tissue microenvironment to modulate perfusion recovery (17)(18)(19). Macrophages, as shown by a number of studies, are quick responders following ischemic injury in PAD, and their infiltration and functional activities, such as their capacities to exacerbate or resolve inflammation and influence arteriogenesis and angiogenesis, are tightly controlled by the dynamic cytokine milieu and inflammatory status in the muscle (9,(20)(21)(22). Compared with other immune cells, macrophages are present in relatively high quantities in the lower limb skeletal muscle (23,24), and they produce an array of biochemical signals during ischemia to communicate with other cells and themselves in paracrine and autocrine manners, in addition to performing phagocytosis. For example, pro-inflammatory M1-like macrophages secrete high levels of cytotoxic cytokines such as interferon (IFN)-g and tumor necrosis factor (TNF)-a, which can potentially speed up apoptosis of ECs and skeletal myocytes (25)(26)(27). It was shown in the mouse model of PAD (hindlimb ischemia [HLI]) that M1-like macrophages dominate during the early phase of ischemic injury, whereas over time, this pro-inflammatory profile gradually diminishes as limb perfusion recovers, along with an increase in subjects' walking ability (28).
VEGF molecules, including the alternatively spliced isoform VEGF 165 b, are also produced by macrophages in HLI mice and can differentially affect pro-angiogenic signaling on ECs (7,19). Furthermore, the functional polarization of macrophages is rarely all or none and is heavily influenced by autocrine and paracrine signaling (29). In addition to skeletal myocytes, ECs, and macrophages, many other cell types are found with varying abundance in the leg muscle of human and mouse (23,24); however, their cell dy- MURINE MODEL OF HLI. We used a previously detailed HLI scheme (7,9,31). Before surgery, male mice, 10 to 12 weeks of age, were anesthetized with 1.5% to 2% isoflurane, and the lower limbs were shaved, depilated to remove excess hair, and prepped for aseptic surgery. On the day of surgery, mice were anesthetized (120 mg/kg ketamine and 10 mg/kg xylazine intraperitoneally). Ophthalmic ointment was applied to both eyes according to ointment instructions. With the animal in the supine position, a longitudinal incision approximately 1.5 cm long was made along the left medial thigh beginning at the inguinal ligament. The femoral artery was first ligated by using 8-0 Prolene sutures (Ethicon), then resected from just above the inguinal ligament to its bifurcation at the origin of the saphenous and popliteal arteries proximal to the saphenous artery bifurcation.
The surgical site was then closed with 5.0 Prolene sutures. A sham surgery, wherein the femoral artery was exposed but not ligated, was performed on the contralateral hindlimb (eg, right leg).
Animals received subcutaneous injections of buprenorphine for analgesia immediately after surgery and every 12 hours for the next 48 hours. In addition, all mice received prophylactic treatment with antibiotics (Baytril, Bayer Corporation) and analgesics (2 mg/mL acetaminophen) in their drinking water for 7 days after surgery. BALB/c mice were treated with either 1.6 mg/kg/d Nec-1s or vehicle control (0.05% dimethyl sulfoxide) intraperitoneally for 7 days after HLI surgery.
Only male mice were used in the current study.
There was no active process of selection of one sex or another. A short list of manuscripts from the Annex laboratory will show that either sex has been used in similar studies (31)(32)(33)(34)(35). Therefore, to avoid the need to stratify mice based on sex and to avoid the unnecessary use of animals, the required number of mice of one sex were used.   Relative normalized expression to HPRT was quantified by using the comparative 2 DDCt method and was tested for statistical significance by using Student's t-test.

MULTISCALE MODEL SCOPE AND FORMULATION.
In our multiscale computational model, as shown in Figure 1, we explicitly included 3 cell types (skeletal myocytes, ECs, and macrophages) to describe limb tissue ischemia (eg, HLI), and each cell type is assumed to have one coarse-grained production (eg, recruitment, differentiation, and proliferation steps are merged accordingly depending on the specific cell type) and one constitutive removal rate (eg, apoptosis, emigration), both of which can be dependent on tissue oxygen and cytokine levels. In addition, we assumed that skeletal myocytes and ECs will undergo necrotic cell death during severe tissue ischemia at a rate proportional to the level of perfusion deficit (30,38  were executed by using MATLAB scripts, and the ode15s solver in MATLAB was used.   Table 3. Methodologic details of other model analyses pre-   Table 2) in the 8-pathway macrophage signaling model (see Figure 1B).
(B to C) Relative time-course activation of phosphoinositide 3-kinase (PI3K) and extracellular receptor kinase (ERK) in response to HMGB1 stimulation in macrophages: model simulation results and corresponding experimental data (49). (D-E) Relative time-course production of macrophage phenotype markers, TNF-a, IL-12, and IL-10, in response to HMGB1 stimulation: model simulation results and corresponding experimental data (50). (B to F) All expression profiles are for protein levels and are normalized to their respective maximum values (y-axes are relative expression levels). D ¼ experimental data; MAPK ¼ mitogen-activated protein kinase; NF-kB ¼ nuclear factor kB; p ¼ phosphorylated; S ¼ simulation; TRAF6 ¼ tumor necrosis factor receptor-associated factor 6; other abbreviations as in Figure 1. with pre-HLI ( Figure 3G). The rate of muscle necrosis is also significantly lower in the later days compared with that in the early days after HLI ( Figure 3H).
Overall, these uncalibrated model predictions of celland tissue-level features in acute HLI have achieved good quantitative and qualitative agreements with experimentally observed trends (28,59).
We further tested the model, which was originally calibrated using only data from acute HLI settings, in    in Figure 6A suggest that the parameters that control EC and macrophage growth and death are among the most influential ones that regulate tissue perfusion recovery, and very intuitively the parameters that control myocyte growth and death ranked very high in terms of their influence on time-course muscle regeneration ( Figure 6B). Furthermore, to evaluate how macrophage-based perturbations can alter perfusion recovery, the results from the tissue-level analyses were summarized into one outcome measure to be optimized; the goal is to promote macrophage infiltration while decreasing its proinflammatory potential. We then performed sensitivity analysis at the macrophage single-cell level to determine the macrophage-specific parameters that can most significantly influence this outcome. The cell-level analysis results ( Figure 6C) revealed that a number of parameters relating to macrophage intracellular signaling and polarization can potentially drive this outcome, and these parameters were categorized into 4 functional modules.
Next, we wanted to simulate and analyze how targeted model perturbations, based on results of the sensitivity analyses, will regulate perfusion recovery and muscle regeneration in acute HLI animal models More technical details of the sensitivity analyses are available in Supplemental Protocol 1. The parameters listed in A (labels from bottom to top: k8, nonleakiness, k13, perfusion_IC, k9, kb9, kc9, k14, k10, k3, kb8, k15, k7, kb2, and ke8) and B (labels from bottom to top: perfusion_IC, k8, k1, k13, nonleakiness, k2, k12, k9, kd1, kb9, kc9, k10, k14, ka10, and k15) correspond to parameters in Supplemental Table 1. Details of the parameters listed in C can be found in Supplemental Table 2. PRCC ¼ partial rank correlation coefficient; SOCS ¼ suppressor of cytokine signaling; STAT ¼ signal transducer and activator of transcription; other abbreviations as in Figure 1.

CONCLUSIONS
To the best of our knowledge, this study presents the first computational model that characterizes the complex PAD pathophysiology in a preclinical setting at multiple scales. Our findings demonstrate its potential for extracting dynamic cell-and tissue-level features, identifying and assessing novel therapeutic interventions, and guiding experimental designs for future animal studies.