Improving laser Doppler aided diagnostics of burn injuries: Mathematica in clinical use and biomedical research I

Stanislav ((Hledík)^a)
 
in collaboration with Iveta ((Bryjová)^(a,b)), Jiří ((Štětinský)^c) & Hana ((Klosová)^c)

aInstitute of Physics, Faculty of Phil. & Science, Silesian University in Opava, Czech Republic
bDept. of Cybernetics and Biomedical Engineering, Technical Univ. of Ostrava, Czech Republic
cBurn Center, University Hospital Ostrava, Czech Republic

Burn wounds medical care

Initial period

Up to 48 hrs; 12–24 hrs: microcirculation most compromised. Not covered here.

Medium-term (healing) period

48 hrs: repair processes create high perfusion that can meet metabolic requirements

Time ~ days up to 2-3 weeks

Blood perfusion assessment:

Long-term period

Time ~ weeks up to months/years

Discussed in the next talk: The assessment of skin viscoelastic data related to post-burn scarring

Laser Doppler Perfusion Imaging

Laser Doppler Imaging (LDI): diagnostics method based on Doppler frequency shift of laser beam backscattered by moving blood cells.

Blood perfusion and burns

({{, }, {Normal skin, Superficial dermal burn: epidermis + <1/3 of dermis}})

({{, , }, {Mid dermal burn, Deep dermal burn, Full thickness burn}})

Perfusion imaging using laser Doppler principle

({{, , }, {Scattering on moving blood cells,  Δν ≡ ν-(Subscript[ν, 0]) = -2 (Subscript[ν, 0])((v cosθ)/c), }})

Wavelength 650-690 nm, output power 1 mW, beam diameter 1 mm

Bandwidth filter 50 Hz - 15 kHz   ⇒  maximum flow velocity ~ 5 mm/s   ⇒  entire microvascular velocity range

Typical LDI output of a burn area

Clinically proven: skin microcirculation (therefore perfusion) in burns is related to burn depth and healing time [Kloppenberg FWH, Beerthuizen GIJM, ten Duis HJ, Burns 27 (2001), 359-363]

LDI provides quantitative maps of blood perfusion (perfusion images)

Excellent tool for estimating burn depth and reinforcing the clinical judgement of a burn wound

University Hospital Ostrava: Data archives since January 2010 from patients who incurred variously extensive and severe burns

Perfusion changes over time

Burn area averaged perfusion values and their dependence on time

Criteria to be met for spontaneous healing within 3 weeks:

perfusion ≿ critical value

(d/(dt))perfusion ≿ critical value

How can Mathematica be helpful?

Constructing maps of perfusion temporal evolution

Maps of perfusion change not implemented yet by manufacturer-supplied software

Promising tool to improve topographic accuracy of burn surgery (avoiding unnecessary early necrectomy locally)

Project Perfusion Image Progression and Prognosis Assesment (PIPPA)

Creating overlays and device calibration

Three components (b, c combined in proprietary *.ldi format):

Camera image (JPEG)

Intensity map - shares morphological features with camera image

Perfusion map - no common features

Imperfections of LDI scanner

Device calibration (go to |->)

(Target notebooks are not available with this presentation but can be requested at hlediks@gmail.com)

The task of obtaining subtraction under clinical conditions presents a challenge since the two perfusion scans separated by a time span of several days usually differ more than the algorithms for image registration can cope with. At this point the Mathematica' s extensive interactive and image processing capabilities gain ground in the form of Digital Subtraction Perfusion Topography Analysis (DSPTA) method.

Some key building blocks

Image Geometric Operations

i1=

ImageResize[i1, Scaled[0.6]]

ImageTrim[i1, {{128, 52}, {302, 265}}]

ImageRotate[i1, 15 Degree,#]&/@{Automatic,All,Full}

Image Manipulation and Arithmetic

i2=;

α=0.4;
ImageCompose[i1,{i2,α}]

ImageCompose[i1,{i2,α},Scaled[{.7,.3}]]

ImageDifference vs ImageSubtract

g = Image[DensityPlot[#, {x, 0., 1.}, {y, 0., 1.}, ColorFunction -> GrayLevel, ColorFunctionScaling -> False, PlotRange -> {0., 1.}, BoundaryStyle -> None, PlotRangePadding ->None, Frame ->False, FrameTicks -> None, Mesh -> None, PerformanceGoal -> "Quality"], "Real", ColorSpace -> "Grayscale", ImageSize -> 60] & /@ {y, x}
b = Map[ImagePad[Binarize[#, .5],1,Black] &, g]

ImageDifference

gdif=ImageDifference@@g;
Row[Insert[Insert[Flatten[{g,gdif}]," - ",2]," = ",4]]
#[ImageData@gdif]&/@{Min,Max}
Column[Short/@(#[ImageData@gdif]&/@{First,Last})]

bdif=ImageDifference@@b;(* logical XOR *)
Row[Insert[Insert[Flatten[{b,bdif}]," - ",2]," = ",4]]
#[ImageData@bdif]&/@{Min,Max}

ImageSubtract

gsub=ImageSubtract@@g;
Row[Insert[Insert[Flatten[{g,gsub}]," - ",2]," = ",4]]
#[ImageData@gsub]&/@{Min,Max}
Column[Short/@(#[ImageData@gsub]&/@{First,Last})]

bsub=ImageSubtract@@b;(* ! ⇒ *)
Row[Insert[Insert[Flatten[{b,bsub}]," - ",2]," = ",4]]
#[ImageData@bsub]&/@{Min,Max}

ImageSubtract ≠ | ImageSubtract | = ImageDifference (grayscale/color images)

Image/@{ImageData@gsub,Abs[ImageData@gsub],ImageData@gdif}

ImageSubtract = | ImageSubtract | ≠ ImageDifference (binary images)

Image/@{ImageData@bsub,Abs[ImageData@bsub],ImageData@bdif}

Image Filtering

igs=;

{MedianFilter[igs, 2], GaussianFilter[igs, {4, 3}]}

Extending low-resulution LDI scan to image

(* ukázka visualizace dat *)
data={{0,0,0,0},{0,1,0,1},{0,0,2,0},{0,1,0,3}};
rdata=Reverse[data];
GraphicsRow[Flatten[{Style[MatrixForm[rdata],24],ArrayPlot[rdata],MatrixPlot[rdata],#[data, Mesh -> None, Frame -> None, ColorFunction -> "TemperatureMap",InterpolationOrder -> 3]&/@{ListDensityPlot,ListContourPlot}}],ImageSize->800]

Dynamic interactivity

Manipulate[ImageCompose[i1,{i2,alpha},Scaled[{tx,ty}]],
{{alpha,0,"α"},0,1},{{tx,.5},0,1},{{ty,.5},0,1}]

... and many others

Masking (morphological processing)

Interpolation

Calibration for overlays positioning purposes

Mathematica implementation

Go to PIPPA notebook |->

(Target notebooks are not available with this presentation but can be requested at hlediks@gmail.com)

Conclusion

PIPPA

Standard methods allow the assessment of blood perfusion statistics globally or within a ROI

Allows calculation and display of subtraction maps, i.e. maps that show the result of subtraction of two successive perfusion maps with a time lapse between

Enables more precise spatial and temporal analysis of blood LDI perfusion scans

Improvement of diagnostics and topographical accuracy in treatment planning, particularly the reduction of unnecessary surgery

Things to do

Solve the influence of ambient light

Motion artifacts correction

Assesement of the influence of fluid residuals in burns

Reproducibility of scanner head positioning (markers?)

Correction of surface curvature

More advanced filtering methods (Savitzky-Golay 2D?)

Automatic/semiautomatic image registration

Mathematica package development

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