Response of expanding hydrogel to step changes in stiffness.

<p>(a) The AFM stiffness clamp was applied to a rehydrated hydrogel that deflected an AFM cantilever as it expanded. Cantilever position is precisely measured using an optical lever system. Feedback was implemented by moving a piezo-controlled substrate. (b) A typical trace of how force and gel height () changed over time as the cantilever deflected in response to the expansion of the hydrogel against apparent stiffnesses of 1, 10, and 100 nN/µm. Separate experiments conducted on 5 different gels all exhibited the same stiffness-dependent behavior shown above. Note that the slope of the force trace clearly changes when the apparent stiffness changes, while the slope of the height trace remains basically constant over this range of stiffness. (c) Categorical plot of the force rate and velocity of gel expansion under three different apparent stiffnesses from the trace depicted in (b). The rates are determined from a linear regression fit where the 95% confidence interval for each slope is within 0.25 nN/min and 5 nm/min for the force and height, respectively. Force rate changes with stiffness while expansion rate does not over this range of stiffness. (d) Plot of force versus gel height as the gel expanded under a wide range of apparent stiffnesses. Each trace represents a different apparent stiffness listed in the table and applied using the stiffness clamp algorithm. The traces were translated to begin at the origin for comparison. The horizontal and vertical traces represent desired stiffnesses approaching 0 and , corresponding to a force and position clamp with standard deviations of 15 pN and 0.34 nm. Inset depicts the discrete but highly linear nature of the data. The * marks the trace without any feedback loop and whose slope is the spring constant of the cantilever, 42 nN/µm.</p

Comparison of mobile phone microscopes.

<p>A) <i>Left panel:</i> Cartoon schematic of a ball lens mobile phone microscope. Red brackets indicate microscope attachment optics outside of the phone (a ball lens), and blue brackets indicate mobile phone camera optics inside the phone (a lens group and CMOS sensor). <i>Middle panel:</i> Image of stained cheek epithelial cells taken with a 6 mm ball lens. <i>Right panel:</i> Enlargement of the area indicated within the dashed line in the middle panel. B) <i>Left panel</i>: Cartoon schematic of a standard finite objective microscope attachment to a mobile phone, consisting of an objective and an eyepiece. <i>Middle panel:</i> Image of stained cheek epithelial cells taken with a 4X/0.10 NA objective and a 20X eyepiece. <i>Right panel:</i> Enlargement of the area indicated within the dashed line in the middle panel. Note that despite the image being in-focus at the center of the field of view, some image degradation due to field curvature is detectable at the edge of the field. C) <i>Left panel:</i> Cartoon schematic of the reversed lens microscope presented in this paper, with opposing identical lens groups outside the phone (red brackets) and inside the phone (blue brackets). <i>Middle panel:</i> Image of stained cheek epithelial cells taken with the opposed lens group setup. <i>Right panel:</i> Enlarged area of the area indicated within the dashed line in the middle panel. Note that despite the image being focused at the center of the field, no field curvature is detectable in the reversed lens microscope image, in contrast to the ball lens A) and standard finite objective B) microscope images.</p

Cell contraction rapidly responds to stiffness changes.

<p>(a) An AFM was used to expose a single fibroblast cell to dynamically changeable apparent stiffness values with the AFM stiffness clamp. The piezo-controlled substrate was moved in response to deflections of the cantilever, which were precisely measured with an optical lever system. (b) Force and cell height as the cell contracts under different apparent stiffnesses from a typical experiment. A total of 30 cells were tested, all exhibiting the same stiffness-dependent behavior shown above. Each interval is under an apparent stiffness of 3.6, 18, or 90 nN/µm as indicated at the top of the graph. The traction rate and contraction velocity rapidly change with a step change in stiffness. A segmented linear regression fit is plotted highlighting the change in traction rate (inset). Data displayed in (c) and (d) are compiled from this trace. (c) Traction rate increases with apparent stiffness while corresponding contraction velocity decreases. The rates are determined from a linear regression fit where the 95% confidence interval for each slope is within 0.4 nN/min and 20 nm/min for the force and height, respectively. (d) Plot of force versus cell height. The three linear, distinct traces each have slopes that indicate that the desired apparent stiffnesses were achieved. The * marks the trace without any feedback loop. Each interval was translated to begin at the origin for comparison.</p

Conceptual design of the AFM stiffness clamp.

<p>(a) A stiff spring can be simulated using a spring of a smaller stiffness. A cell applying a given force against a stiff spring achieves a smaller change in height than a softer spring. Moving the spring base up as the cell contracts makes a softer spring appear stiffer to the contracting cell. Plotting contractile traction force versus cell height produces a trace whose steep slope is the apparent stiffness, (dotted line) and is greater than the native spring stiffness, (solid line). (b) A soft spring can be simulated using a spring of a greater stiffness. A cell applying a given force against a soft spring achieves a greater change in height than a stiffer spring. Moving the spring base down as the cell contracts makes a stiffer spring appear softer to the contracting cell. Plotting traction force versus cell height produces a trace whose gradual slope is the apparent stiffness, (dotted line) and is less than the native spring stiffness, (solid line).</p

Feedback control can change the apparent stiffness a cell experiences.

<p>(a) A contracting cell in a soft extracellular matrix (ECM) experiences little resistance to its contraction and can be modeled with a soft spring. (b) A contracting cell in a stiff ECM experiences a large resistance to its contraction and can be modeled with a stiff spring. Using the AFM stiffness clamp, a soft spring can be made to appear stiff (or vice-versa) by controlling the spring's extension as a function of the cell's contraction. This approach can be broadly applied to make springs appear stiffer or softer than their actual value.</p

Illumination of the reversed lens microscope.

<p>A) Cartoon schematic of the illumination optics together with the collection optics. Red and blue brackets indicate optics outside and inside the phone, respectively. Green brackets indicate the illumination system. A single LED illuminates the sample through an illumination shaping filter (ISF, dashed line) and a diffuser (solid line). B) Methods for correcting image intensity variation caused by vignetting. Columns correspond to the method used. For each column, the top panel is an image of a blank sample showing the illumination uniformity (or lack thereof). The middle panel is a line scan of this image from corner to corner. The lower panel is the standard deviation of a 10×10 pixel box at the indicated positions. Column 1 shows the results of using an LED to directly illuminate the sample. Column 2 shows the results of adding a diffuser between the LED and the sample. Column 3 shows the results of adding illumination shaping filters between the LED and the diffuser. Column 4 shows the results of incorporating a modified form of high-dynamic-range imaging with the diffuser and illumination shaping filters. Images at multiple illumination levels are taken and combined into a single image. Parts of the sample that fall into vignetted regions on the sensor are substituted with the corresponding region of the images taken with brighter illumination levels (see Methods). Note that this image has not yet been flat fielded based on the calibration image. C) An image of a 0.05 mm spacing Ronchi ruling taken with the reversed lens microscope and the combined illumination correction methods described in B). A 10X zoom of a portion of the Ronchi ruling is shown in the upper right corner.</p

Resolution of the reversed lens microscope.

<p>A) Ray-tracing model of a reversed mobile phone camera lens as an objective for a mobile phone microscope. Performance is predicted to be best on axis (α), falling off by >2X at the edge of the field (δ) for a 1.0 mm spacing between lenses. Optical resolution is in microns; to account for variations in sagittal and tangential point-spread at higher field angles, resolution was defined as the first-zero radius of an Airy disk chosen such that its 70% encircled energy radius is the same as that computed for the sample point via ZEMAX. Field positions for α, β, γ, and δ are 0.0, 0.7, 1.5, and 2.1 mm, respectively. B) Measurements of resolution achieved by the reversed lens microscope. The resolution measurements are based on the smallest resolvable group of a 1951 USAF resolution target imaged at different radial distances from the optic axis; asymmetric NA at high field angles (and thus field radii) results in differing sagittal and tangential resolution, as seen in c and d. The dashed line connects to enlargements of the target at the different field positions.</p

Spatial resolution of mobile phone microscopy is dependent on microscope optics.

<p><b>A</b> The resolution that can be captured with a mobile phone microscope approaches that of a scientific camera coupled to the same optics across a range of numerical apertures. Inset shows the measured intensity profile across bars of non-transmitting chrome spaced at 512 line pairs per millimeter and taken with a 10×/0.25 NA objective, as well as the ideal target profile. The Michelson contrast calculated for this example group is 41%, indicating that features with this spacing are resolved. <b>B</b> Wright stained blood smear with an inset of a granulocyte and red blood cells taken with a 10×/0.25 NA objective and iPhone 4. <b>C</b> Image of the same sample and region of interest taken with a 40×/0.65 NA objective and iPhone 4 showing improved resolution.</p

Proposed steps to enable quantitative, reproducible imaging with a mobile phone microscope.

<p><b>A</b> Standardize illumination source and brightness. <b>B</b> Set focal state on a field with known dimensions or features. <b>C</b> Set exposure and gain using a clear field of view. Use this field to set or select a white balance state; may require resetting exposure and gain to ensure changes in white balance do not result in saturation of a color channel. <b>D</b> Acquire images of samples while keeping capture settings constant. <b>E</b> Information content can be preserved by selecting lossless or high quality compression settings. In addition, multiple images can be used to record additional z planes or expand the effective dynamic range of the image. While many of the features required to implement these steps are not directly accessible in the default camera, they are built into commonly available third-party camera applications or can be incorporated into custom applications.</p

Spatial resolution of mobile phone microscopy has improved with mobile phone advancement.

<p><b>A</b> The spatial resolution of mobile phone microscopy with iPhone and Android phones is plotted as a function of the effective pixel size for images taken with a 10×/0.25 NA objective. The theoretical constraints on resolution imposed by pixel spacing on the Bayer color sensor array are plotted along with the empirically determined resolution limit of the underlying microscope optics. <b>B</b> The spatial resolution of mobile phone microscopy with the same iPhone and Android phones is plotted as a function of megapixel count. <b>C</b> Spatial resolution of the iPhone family of phones is plotted over time, together with the dates of significant camera advancements.</p