Aortic Root

Plasma samples and associated clinical study data were identified in patients referred for cardiac evaluation at a tertiary care center. All subjects gave written informed consent and the Institutional Review Board of the Cleveland Clinic approved all study protocols. Unbiased metabolic profiling was performed using liquid chromatography coupled to electrospray ionization mass spectrometry (LC/MS). Target analyte structural identification was achieved using a combination of LC/MS/MS, LC-MSⁿ, multinuclear NMR, gas chromatography-mass spectrometry, and choline isotope tracer feeding studies in mice as outlined in Methods. Statstical analyses were performed using R (version 2.10.1)36 . Intestinal microflora was suppressed by supplementation of drinking water with a cocktail of broad spectrum antibiotics37 (link). Germ-free mice were purchased from Taconic SWGF. QTL analyses to identify atherosclerosis related genes were performed on F2 mice generated by crossing atherosclerosis prone C57BL/6J.apoe−/− mice and atherosclerosis resistant C3H/HeJ.apoe−/− mice38 (link). mRNA expression was assayed by Microarray Analysis and Real Time PCR. Aortic root lesion area in mice was quantified by microscopy after staining39 (link). Mouse peritoneal macrophages were collected by lavage for foam cell quantification and cholesterol accumulation assay. Surface protein levels of scavenger receptors, CD36, SR-A1, were determined by flow cytometry.

The parameters of the three-element Windkessel outflow models were calculated as described below. Given a target diastolic (P_d) and systolic (P_s) pressure, and flow rate at the inlet (Q_in(t)), the initial estimate for the net peripheral resistance (R_T) was calculated as [50 (link)]
$$R_{\mathrm{T}}=\frac{P_{\mathrm{m}}-P_{\text{out}}}{{\overline{Q}}_{\text{in}}},P_{\mathrm{m}}=P_{\mathrm{d}}+\frac{1}{3}(P_{\mathrm{s}}-P_{\mathrm{d}}),$$ where Q̄_in is the mean flow rate and P_m is the mean blood pressure, assumed uniform throughout the arterial network. We then calculated the resistance R₁ + R₂ at the outlet of each terminal vessel that yields the desired flow distribution and satisfies
$$\frac{1}{R_{\mathrm{T}}}=\sum _{j=2}^M\frac{1}{R_1^j+R_2^j},$$ where M is the number of terminal branches and j = 1 corresponds to the aortic root. For each individual outlet, the proximal resistance (R₁) is assumed to be equal to the characteristic impedance of the upstream 1-D domain; i.e.
$$R_1=\frac{{\rho }_{\mathrm{f}}{c}_{\mathrm{d}}}{A_{\mathrm{d}}},$$ where c_d and A_d are, respectively, the wave speed and area at diastolic pressure (P_d). This choice of R₁ minimizes the magnitude of the waves reflected at the outlet of the 1-D domain [38 ].
The total compliance (C_T) was calculated from either (i) the time constant τ = 1.79 s of the exponential fall-off of pressure during diastole given in [51 ] or (ii) using an approximation to
$C_{\mathrm{T}}=\frac{\mathrm{d}V}{\mathrm{d}P}$ , where V(t) is the total blood volume contained in the systemic arteries. According to [50 (link)],
$$C_{\mathrm{T}}=\frac{\tau }{R_{\mathrm{T}}},$$ which can be calculated once R_T is determined using Eq. (13). Alternatively,
$C_{\mathrm{T}}=\frac{\mathrm{d}V}{\mathrm{d}P}$ can be approximated by [50 (link)]
$$C_{\mathrm{T}}=\frac{Q_{max}-Q_{min}}{P_{\mathrm{s}}-P_{\mathrm{d}}}\mathrm{\Delta }t,$$ where Q_max and Q_min are the maximum and minimum flow rates at the inlet and Δt is the difference between the time at Q_max and the time at Q_min. We use both Eqs. ( 16) and (17) depending on the available input data.
According to [52 (link)] we have
$$C_{\mathrm{T}}=C_{\mathrm{c}}+C_{\mathrm{p}},C_{\mathrm{c}}=\sum _{i=1}^N{C}_{0\mathrm{D}}^i,C_{\mathrm{p}}=\sum _{j=2}^M\frac{R_2^j{C}^j}{R_2^j+R_1^j},$$ where C_c is the total arterial conduit compliance, C_p is the total arterial peripheral compliance, N is the total number of vessels in the 1-D domain, M < N is the number of terminal branches (j = 1 denotes the inlet and is not included in the sum), R₁, R₂, and C are parameters of the three-element Windkessel model (Fig. 1) and C_0D is the compliance of each vessel, which is calculated as
$$C_{0\mathrm{D}}=\frac{A_{\mathrm{d}}L}{{\rho }_{\mathrm{f}}{(c_{\mathrm{d}})}^2},$$ where L is the length of the vessel. We calculated C_p = C_T − C_c and distributed it following the methodology described by Alastruey et al. [52 (link)] More specifically, we have
$${\stackrel{\sim }{C}}^j=C_p\frac{R_{\mathrm{T}}}{R_2^j+R_1^j},$$ where C̃^j is the terminal compliance of each branch distributed in proportion to flow as described by Stergiopulos et al. [2 (link)]. We then introduced a correction factor to arrive at the final value of C^j:
$$C^j={\stackrel{\sim }{C}}^j\frac{R_2^j+R_1^j}{R_2^j}=C_{\mathrm{p}}\frac{R_{\mathrm{T}}}{R_2^j}.$$
This expression follows from a linear analysis of the 1-D equations in a given arterial network in which each terminal branch is coupled to a three-element Windkessel model [52 (link)].
For all of the simulations, the Windkessel compliances and resistances (C^j, j = 2, …, M), (
$R_1^j$ and
$R_2^j$ , j = 2, …, M) were iteratively calculated to achieve physiologically realistic pressure ranges. To reach a desired pulse pressure (P_pulse = P_s − P_d) and diastolic pressure (P_d) at a particular vessel, we calculated
$R_{\mathrm{T}}^0$ and
$C_{\mathrm{T}}^0$ given by Eqs. (13) and (16) or (17) using the iterative formulae
$$R_{\mathrm{T}}^{n+1}=R_{\mathrm{T}}^n+\frac{\mathrm{\Delta }{P}_{\mathrm{m}}^n}{{\overline{Q}}_{\text{in}}},\mathrm{\Delta }{P}_{\mathrm{m}}^n=P_{\mathrm{d}}-P_{\mathrm{d}}^n,$$
$$C_{\mathrm{T}}^{n+1}=C_{\mathrm{T}}^n-\frac{Q_{max}-Q_{min}}{{(P_{\text{pulse}}^n)}^2}\mathrm{\Delta }t\mathrm{\Delta }{P}_{\text{pulse}}^n,\mathrm{\Delta }{P}_{\text{pulse}}^n=P_{\text{pulse}}-P_{\text{pulse}}^n,$$ where the superscript n is the iteration number of the windkessel parameter estimation process performed using the 1-D formulation, and
$P_{\mathrm{d}}^n$ and
$P_{\text{pulse}}^n$ are the diastolic and pulse pressure, respectively, at a specific target location in the 1-D model, typically the inlet, at each iteration. Equations (22) and (23) follow from a first-order Taylor expansion of Eqs. (13) and (17) around the current mean and pulse pressures
$P_{\mathrm{m}}^n$ and
$P_{\text{pulse}}^n$ , respectively, with
$\mathrm{\Delta }{P}_{\mathrm{m}}^n$ approximated using the change in diastolic pressure. The total compliance was adjusted by altering the total peripheral compliance C_p, since the total conduit compliance C_c is a function of the vessel geometry and wall stiffness. This process was iterated using the 1-D model until
$P_{\mathrm{d}}^n$ and
$P_{\text{pulse}}^n$ were smaller than 1% of the target P_d and P_pulse, respectively. Fig. 2 shows the evolution of the systolic, mean and diastolic pressure, net peripheral resistance and total compliance calculated using the 1-D formulation to match the target systolic and diastolic pressures for the baseline aorta model. The final values of the Windkessel compliances and resistances were used in the 3-D counterparts of the 1-D models.
Other methods have been proposed in the literature to estimate the parameters of the outflow boundary conditions. A root-finding method is described by Spilker and Taylor [53 (link)] in the context of 3-D models with compliant arterial walls. Devault et al. proposed a Kalman-filter based methodology in a 1-D model of the circle of Willis [54 (link)].

Mice aged 4–5 weeks old were i.p. injected with 250 μg of LCWE (total rhamnose amount as determined above) or PBS. Mice were sacrificed and hearts were removed at day 7 or 14 and embedded in OCT compound for histological examination. Following a cut through the aortic root, coronary artery lesions, aortic root vasculitic lesions (aortitis) and myocardial inflammation were identified in serial sections (7 μm) stained with hematoxylin and eosin or elastin/collagen staining. Only sections that showed the 2^nd coronary artery branch separating from aorta were analyzed. Histopathological examination and inflammation severity scoring of the coronary arteritis, aortic root vasculitis and myocarditis was performed by a coronary pathologist who was blinded to the genotypes or experimental groups (MF). KD lesions were assessed using the following scoring system: Score 0 = no inflammation, 1 = rare inflammatory cells, 2 = scattered inflammatory cells, 3 = diffuse infiltrate of inflammatory cells, 4 = dense clusters of inflammatory cells. Multi-nuclear cells were indicative of acute inflammation while mono-nuclear cells reflected chronic inflammation. Aortic root was evaluated for severity of aortitis, and cross sections of coronary artery for severity of coronary artery inflammation and combined the two scores to generate a severity score that we called “vessel inflammation score”. Myocardial inflammation score was described as follows; score 0 = no myocardial fibrosis, 1 = very minimal focal subepicardial interstitial fibrosis just infiltrating beneath epicardial fat, 2 = mild subepicardial interstitial fibrosis infiltrating deeper into subepicardial myocardium, 3 = multifocal subepicardial interstitial fibrosis, 4 = replacement fibrosis.Incidence rate was evaluated by the presence of any coronary, aortic or myocardial inflammation score of equal or greater to 1.