EXAMINATION OF THE ASSOCIATION BETWEEN ARTERIAL BLOOD PRESSURE BELOW THE LOWER LIMIT OF AUTOREGULATION AND ACUTE KIDNEY INJURY AFTER CARDIAC SURGERY

Acute kidney injury (AKI) is common among cardiac surgery patients. Although there are many causes of AKI, an important contributor is a reduction in arterial blood pressure (ABP). However, there are no clear guidelines on the minimum ABP required during surgery, and this value may vary between patients. Researchers have hypothesized that cerebral autoregulation monitoring could provide useful information to address this problem, with the assumption that maintaining ABP above the minimum value required for perfusion to the brain (the lower limit of autoregulation (LLA)) would also ensure perfusion to the kidneys. In support of this hypothesis, a previous study found an association between ABP below the LLA and AKI. Unfortunately, there are limitations to this body of research, including poor scalability of methods, few clinical studies, and assumptions in choosing parameters to quantify ABP below the LLA. This thesis addresses the limitations of prior autoregulation research. The initial steps were to develop an algorithm for automated LLA selection and to test its accuracy. This algorithm was used to analyze the strength of association between ABP below the LLA and AKI in a recent patient population. Finally, sensitivity analyses were performed to examine assumptions in quantifying ABP below the LLA. The algorithm’s primary method of LLA selection (threshold crossing) was accurate compared to expert adjudication. A secondary method (parabola fit) appeared to be useful in identifying an LLA in additional patients but could not be validated. Using the primary method, prior findings of an association between AKI and area of the ABP curve below the LLA (AUC)
 were reproduced in a new cohort. Sensitivity analyses demonstrated that time below LLA had a comparable strength of association with AKI, the optimal COx threshold appeared to be 0.325, and an association between AUC and AKI was absent in patients with reduced kidney function but was strong in patients with normal kidney function. These results support an association between ABP below the LLA and AKI and suggest that further studies to determine whether maintaining ABP above the LLA can reduce the risk of AKI are warranted, particularly in patients with normal kidney function. Primary Reader: Charles Brown Secondary Readers: Archana Venkataraman, Brian Bush

Universal energy transport law for dissipative and diffusive phase transitions

We present a scaling law for the energy and speed of transition waves in dissipative and diffusive media. By considering uniform discrete lattices and continuous solids, we show that—for arbitrary highly nonlinear many-body interactions and multistable on-site potentials—the kinetic energy per density transported by a planar transition wave front always exhibits linear scaling with wave speed and the ratio of energy difference to interface mobility between the two phases. We confirm that the resulting linear superposition applies to highly nonlinear examples from particle to continuum mechanics

Determining Thresholds for Three Indices of Autoregulation to Identify the Lower Limit of Autoregulation During Cardiac Surgery.

OBJECTIVES: Monitoring cerebral autoregulation may help identify the lower limit of autoregulation in individual patients. Mean arterial blood pressure below lower limit of autoregulation appears to be a risk factor for postoperative acute kidney injury. Cerebral autoregulation can be monitored in real time using correlation approaches. However, the precise thresholds for different cerebral autoregulation indexes that identify the lower limit of autoregulation are unknown. We identified thresholds for intact autoregulation in patients during cardiopulmonary bypass surgery and examined the relevance of these thresholds to postoperative acute kidney injury. DESIGN: A single-center retrospective analysis. SETTING: Tertiary academic medical center. PATIENTS: Data from 59 patients was used to determine precise cerebral autoregulation thresholds for identification of the lower limit of autoregulation. These thresholds were validated in a larger cohort of 226 patients. METHODS AND MAIN RESULTS: Invasive mean arterial blood pressure, cerebral blood flow velocities, regional cortical oxygen saturation, and total hemoglobin were recorded simultaneously. Three cerebral autoregulation indices were calculated, including mean flow index, cerebral oximetry index, and hemoglobin volume index. Cerebral autoregulation curves for the three indices were plotted, and thresholds for each index were used to generate threshold- and index-specific lower limit of autoregulations. A reference lower limit of autoregulation could be identified in 59 patients by plotting cerebral blood flow velocity against mean arterial blood pressure to generate gold-standard Lassen curves. The lower limit of autoregulations defined at each threshold were compared with the gold-standard lower limit of autoregulation determined from Lassen curves. The results identified the following thresholds: mean flow index (0.45), cerebral oximetry index (0.35), and hemoglobin volume index (0.3). We then calculated the product of magnitude and duration of mean arterial blood pressure less than lower limit of autoregulation in a larger cohort of 226 patients. When using the lower limit of autoregulations identified by the optimal thresholds above, mean arterial blood pressure less than lower limit of autoregulation was greater in patients with acute kidney injury than in those without acute kidney injury. CONCLUSIONS: This study identified thresholds of intact and impaired cerebral autoregulation for three indices and showed that mean arterial blood pressure below lower limit of autoregulation is a risk factor for acute kidney injury after cardiac surgery

A comparison of methods to measure the magnetic moment of magnetotactic bacteria through analysis of their trajectories in external magnetic fields.

Magnetotactic bacteria possess organelles called magnetosomes that confer a magnetic moment on the cells, resulting in their partial alignment with external magnetic fields. Here we show that analysis of the trajectories of cells exposed to an external magnetic field can be used to measure the average magnetic dipole moment of a cell population in at least five different ways. We apply this analysis to movies of Magnetospirillum magneticum AMB-1 cells, and compare the values of the magnetic moment obtained in this way to that obtained by direct measurements of magnetosome dimension from electron micrographs. We find that methods relying on the viscous relaxation of the cell orientation give results comparable to that obtained by magnetosome measurements, whereas methods relying on statistical mechanics assumptions give systematically lower values of the magnetic moment. Since the observed distribution of magnetic moments in the population is not sufficient to explain this discrepancy, our results suggest that non-thermal random noise is present in the system, implying that a magnetotactic bacterial population should not be considered as similar to a paramagnetic material

Dimensions of <i>M. magneticum</i> cells and magnetosomes.

<p>A) Distribution of cell lengths as measured from 118 cells observed under the light microscope. The reported length of each cell is an average of five measurements done in different movie frames. B) Transmission electron micrograph of a typical cell. Magnetosome dimension estimate from the image returns a value of the magnetic moment <i>μ</i> = 4.3×10⁻¹⁶ A⋅m² for this cell.</p

Average magnetic moment of <i>M. magneticum</i> AMB-1 cells measured by six different methods.

<p>± s.e.m for measurements on multiple cells.^a Mean </p><p>^b Value and error returned by least-square fitting of data.</p><p>± standard deviation from alternate forms of the same general method (e.g. assuming either two-dimensional or three-dimensional trajectories).^c Value returned by least-square fitting of the data assuming two-dimensional trajectories </p

Cell trajectories in constant magnetic fields.

<p>A) Trajectories of 25 cells in a zero (left) and non-zero (right, <i>B = </i>3.3 mT) magnetic field. B) Displacement of the cells after <i>t</i> = 46 ms (upper panels) and <i>t</i> = 139 ms (lower panels). Only regular trajectories used in subsequent analyses are presented here, with data for <i>B</i> = 0 mT (left panels, 10 cells) and <i>B = </i>3.3 mT (right panels, 51 cells). Each different colour represents a different cell, with the displacement of each cell measured over multiple time intervals.</p

Cell orientation distributions in constant magnetic fields.

<p>A) Mean orientation of the cells evaluated as the mean sine of the angle between the observed direction of movement in the focal plane and that of the magnetic field, <θ>>. B) Variance of θ>. Lines correspond to the expectation of the paramagnetic model: The solid line is a fit assuming 2D trajectories (Eq. 7, yielding <i>μ</i> = 1.9×10⁻¹⁶ A⋅m²), while the dashed line is a fit assuming 3D trajectories (Eq. 5, yielding <i>μ</i> = 2.1×10⁻¹⁶ A⋅m²). C) Distribution of cell orientations for three different values of the magnetic field. Fits are Boltzmann distributions for a monodisperse cell population according to the paramagnetic model for 2D trajectories (Eq. 6). D) Ratio of magnetic energy to thermal energy of the cells obtained from the fit of orientation distributions such as those shown in panel C, assuming either 2D trajectories (black symbols), or 3D trajectories (grey symbols, not visible on the graph as they overlap with the previous ones). Linear fit of the data measured at magnetic fields <i>B</i><2 mT yields a magnetic moment <i>μ</i> = 0.90±0.05×10⁻¹⁶ A⋅m² assuming 2D trajectories (continuous line) and <i>μ</i> = 0.92±0.05×10⁻¹⁶ A⋅m² assuming 3D trajectories (dashed line).</p

Cell trajectories in periodically reversing magnetic fields.

<p>A) Trajectories of four cells moving in response to a periodically reversing magnetic field of frequency 700 mHz and amplitude indicated by trace colour. Subsequent analysis of trajectory 1 is presented in panels B, C & D. B) Position of the cell in the direction perpendicular to that of the magnetic field. C) Sine of the angle between the direction of movement of the cell and the magnetic field. D) Square of the sine of the angle plotted in panel C. Fit to Eq. 12 yields a magnetic moment <i>μ</i> = 3.2×10⁻¹⁶ A⋅m² for this cell, as explained in the text.</p

Rotational bias of cells placed in constant magnetic fields.

<p>A) Average angular velocity of cells as a function of their initial orientation, plotted for magnetic fields with different magnitudes (mean ± standard error). Fit was performed according to the rotational bias model (Eq. 9). B) Ratio of magnetic torque to rotational drag coefficient for cells placed in magnetic fields of various magnitudes. Plotted values are obtained from fit of data such as those shown in panel A. Linear fit to the data measured at magnetic fields <i>B</i><2 mT yields a magnetic moment <i>μ</i> = 5.7±0.2×10⁻¹⁶ A⋅m², as explained in the text.</p