Mock on, Mock on, Voltaire, Rousseau

Mock on, mock on, Voltaire, Rousseau;

Mock on, mock on: ‘tis all in vain!

You throw the sand against the wind,

And the wind blows it back again.


And every sand becomes a Gem,

Reflected in the beam divine;

Blown back they blind the mocking Eye,

But still in Israel’s paths they shine.


The Atoms of Democritus

And Newton’s Particles of Light

Are sands upon the Red Sea shore,

Where Israel’s tents do shine so bright.


— William Blake

Happy ~3.14159… Day!

Today is Pi Approximation Day. This day celebrates the fractional representation of π, which is 22/7 = 3.14285….

The date originates from day and month nomenclature, rather than month and day nomenclature.

Let’s look closer at π:

When we measure the distance around a circle (starting and stopping at the same point) compared to the distance measured across the circle’s center, we are computing a ratio (and calculating a number). As curious as this intuitive measurement seems — a simple ratio of girth versus breadth — the resulting number is the mathematical constant π, defined as π = C/d. Here C represents the circumference of the circle, and d is the diameter of the circle. We learn that the distance around any given circle is a little more than three times the distance across it.

Pi itself is an irrational number. Irrational numbers are numbers that have no terminating digit after its decimal point, including no terminal repeating digits or terminal sequence of digits. Nevertheless, only the first 39 digits of π are needed to accurately calculate the spherical volume of our entire universe. Thankfully, however, when thinking about π or invoking its use during hand calculations, most people (including many math students) are safe using the first 5 decimal places, such that π = 3.14159.

Pi is used in the following non-exhaustive list of formulas:

  • Circumference, C, of a circle: C = 2πr
  • Area, A, of a circle: A = πr2
  • Volume, V, of a cylinder: V = πr2h
  • Volume, V, of a sphere: V = (4/3)πr3

For each of the aforementioned equations r is radius, and pertaining specifically to the volume of a cylinder, h is height.

Celebrate Pi Approximation Day!

Biomimicry 101: Turbulence and Chaos Theory

eagles-wingsFigure: The upward curvature (called winglets) found on the tips of wings in certain bird species, such as the bald eagle, increases aerodynamic efficiency by helping reduce drag.

When you ponder biomimicry, think design, intelligent design, and creation, but please don’t think evolution. And when considering biomimetic applications, let your imagination know no bounds.

Turbulence is the name for the small eddies that break off of larger ones; it is dissipative; it is unstable and dynamical. In fact, the study of turbulence is at the core of chaos and non-linear, dynamical systems – a subfield within mathematics with special appeal to mathematical physicists. For instance, the vortices (i.e., turbulence) that whirl off the wings of Boeing or Airbus passenger jets will differ greatly from those off the most sophisticated jet fighters, such as the F-18 Super Hornet. No matter what, each plane has its own “fingerprint” when it comes to air flow dynamics across their wings. And this characteristic signature is even more complex and dynamical for sweep-wing planes, such as the now retired but amazing F-14 Tomcat.

Of interest, just yesterday, July 19th, 2019, Airbus released a conceptual model of a large passenger prop plane with splayed wingtips and a fanned tail. This “hybrid” design attempts to reduce as much of the turbulent air flow as possible by mimicking the wings of soaring eagles.

Remark: Current models of many mid-sized to large passenger jets and cargo planes already have winglets to minimize the swirling eddies at the tips of their wings.

What is more, to help promote mathematical thinking and biomimicry, Andrew McIntosh, professor of thermodynamics and combustion theory, at the University of Leeds has held paper airplane design contests. These contests offer students a hands-on approach to help creativity form in the minds of future engineers.

Something completely different but related: aerospace and aviation

Today marks the 50th anniversary of the Apollo 11 moon landing!

On July 20, 1969, Neil Armstrong and Buzz Aldrin navigated the lunar module they piloted, named the Eagle, down onto the surface of the moon. Within moments of their landing, Armstrong radioed NASA Mission Control in Houston, Texas, his now infamous message, “Houston, Tranquility Base here. The Eagle has landed.” Soon afterwards, Armstrong made a more profound statement when he became the first person to set foot on the moon, saying, “That’s one small step for man, one giant leap for mankind.”

Three years later, on July 20, 1972, the Armstrong Air and Space Museum in Wapakoneta, Ohio, — the birthplace of Armstrong — opened its doors.

We invite you to return to our 2018 visit to the museum (click here).

Can you imagine a career in mathematics that might even help mimic nature – God’s great creation?

Starting out now on your very own discovery of the intricacies of God’s creation through scientific study might very well help you in discerning what path you should take in the future. Christian scholarship that extends into professional roles — such as mathematicians, engineers, and physicists who work in chaos and non-linear dynamics or aerospace and aviation to biologists and zoologists who study ornithology — is sincerely needed in education and society.

Biomimicry 101: Biosensors and Biomimicry: From Edison’s Fluoroscope to a Biomimetic X-Ray Detector Design



When you ponder biomimicry, think design, intelligent design, and creation, but please don’t think evolution. And when considering biomimetic applications, let your imagination know no bounds.

Biosensors use biological agents and/or processes in the detection of other biological agents and/or processes. Microfluidic chips for the detection of malaria and a microelectromechanical system (often abbreviated MEMS) that detects Dengue virus are two such examples. These types of devices may be referred to as “lab-on-a-chip technology” or “point-of-care testing.”

Yet biosensors also consist of specialized machinery for the detection of biological states and diseases (i.e., physiological abnormalities). Examples of these types of sensors include molecular imaging scanners, such as magnetic resonance imaging (MRI exams), positron emission tomography (PET scans), and single-photon emission computed tomography (SPECT scans). In fact, researchers driving the new paradigm – i.e., the next frontier – in biosensing and diagnostic medical imaging are attempting to combine – i.e., fuse – MRI and PET imaging techniques (so-called fusion imaging). Moreover, only recently the fusion of PET and x-ray computed tomography (CT) held this distinguished honor as the new frontier. Nevertheless, the success of any PET, SPECT, CT, and PET-CT modality is predicated on designs of image detector plates, and over the past several decades we have clearly witnessed advances in detector plate technology.

TECHNICAL INSERT: MRI is possible through the detection of hydrogen atoms at the molecular level. PET is possible due to the detection of gamma-rays, which arise from molecular processes occurring after the injection of a radionuclide coupled to a radiotracer (usually a sugar molecule). SPECT is also possible as a result of gamma-rays detection from processes that, again, take place at the molecular level after the injection of a radionuclide – radiotracer pair. CT is possible because of the detection of x-rays.

Here we discuss a novel biomimetic concept that improved x-ray detector plate sensitivity (Pignalosa, Liu, Chen, Smith, & Yi, 2012). Given this exciting idea – an x-ray detector plate with features that mimic the eye of a month – we speculate that such enhanced detector plate technology can be extrapolated and tested for feasibility of use in CT, PET, and SPECT imaging. Importantly, however, our discussion will focus on x-ray fluoroscopy because we consider key technological advances in the history of fluoroscopy as a proper backdrop through which future ideas for detector plate technology in molecular imaging can be properly motivated.

Thus, this installment in our biomimicry series considers the uniquely designed aspects of God’s great creation in the following way:

  • First, we offer a brief tutorial on x-ray production.
  • Second, we describe the traditional fluoroscopic imaging chain.
  • Third, we briefly relate points concerning the production of x-rays and the fluoroscopic imaging chain (i.e., focusing on one aspect of the latter, that is, the image intensifier).
  • Finally, we discuss a biomimetic approach that uses the inherent design of the miner moth’s eye to improve the resolution of an x-ray image.

Fluoroscopic x-ray equipment and improved image resolution

What is fluoroscopy? To answer this question, it is best to simply define fluoroscopy as “imaging with light,” or better yet “to view with light.” The term is derived from the word fluorescence, which means “light,” and the word scope, which means “to view.” Moreover, the fundamental process of fluoroscopic imaging involves x-ray imaging in real-time. Therefore, fluoroscopy enables x-ray imaging when a physician desires to view a dynamic, moving part. Notably, since fluoroscopy is one of two common modalities physicians may choose from when real-time image guidance is needed (the other being ultrasound imaging), it falls more along the along the lines of an interventional tool rather than a diagnostic instrument (although certain, limited diagnostic methods are possible with fluoroscopy). A suitable analogy of fluoroscopic imaging would be the beam of a flashlight (i.e., the fluoroscopic beam) aimed at a specific part of an engine (i.e., an area of the body) that the mechanic (i.e., the physician) is working on (i.e., intervening on).

TECHNICAL INSERT: A static image operating technique is possible with fluoroscopic imaging. Operators use this technique, called last image hold, in tandem with other fluoroscopic features (i.e., low dose and pulsed settings) to lower radiation dose.

Fluoroscopy: x-ray production and imaging chain

— The Physics of X-Ray Production —

X-rays were discovered by the German physicist Wilhelm Conrad Röntgen in 1895. If we dig a little deeper, we realize that what Röntgen actually discovered was a correlation between lights illuminated (scintillating) from a fluorescent screen (placed on a workbench in his laboratory) and x-ray photons coming into contact with it. Röntgen came to understand that the x-rays were being generated from a point elsewhere in his laboratory. In fact, it was for his discovery of x-rays in 1895 that Röntgen became the first recipient of the Nobel Prize in Physics (awarded in 1901).

To help us better understand the fascinating physics of x-ray production, we quote Wininger (2012), as follows:

When the x-ray tube is activated, electrons are “boiled off” from the wire element (i.e., a thin filament of tungsten) to form an electron cloud [see Figure 1]. The wire element is strategically located opposite from the spinning target anode as part of a built-in concavity (of which the rim is slightly more negatively charged to concentrate the electrons in the cloud) on the cathode. The number of electrons boiled off is directly related to the tube current. Occurring nearly simultaneously with tube activation, the electrons in the electron cloud are forcefully attracted to the target anode due to the potential difference between the cathode and anode. The rate of speed and the efficiency of attraction are dependent on the potential difference across the tube.

fluoroscopic-x-ray-productionFigure 1: A closer look inside the x-ray tube. When tube current is applied the filament heats up to boil off electrons into a cloud. X-rays are produced as the tube potential forces the incident (free) electrons to strike the target on the anode at a high-speed.

When high-speed (incident) electrons strike the target, the change in kinetic energy produces only less than 1% of x-rays, with most of the change occurring in the form of heat production (99% or greater) (Dowd & Tilson, 1999). More specifically, x-rays are generated by two processes. The first process involves the interaction of electrons with the nucleus of an atom of tungsten in which the incident electron slows down to change direction (called bremsstrahlung, or “braking radiation”). Bremsstrahlung radiation is emitted from zero to the maximum energy (operating kV). The second process is a collision of the incident electron and an outer shell electron of the tungsten atom. The collision knocks the outer shell electron out of orbit (producing characteristic radiation). Characteristic radiation is the term used to reference the fact that the x-ray energy produced is related to the binding energy between the outer shell electron and the nucleus of the target atom, and is always the same for a specific target atom (again, tungsten in the case of x-ray production in fluoroscopy) (Dowd & Tilson, 1999). (pp. 126-127)

— The Fluoroscopic Imaging Chain —

In 1896 –  just one year following Röntgen’s discovery of x-rays – the American inventor Thomas Edison (known best for inventing the incandescent light bulb, yet not to be overlooked for his pioneering work on the motion picture camera as well as battery technology) perfected the fluoroscope. According to Tselos (1995):

Thomas Edison played a major role in the development of early x-ray technology in 1986, notably increasing tube power and reliability and making the fluoroscope a practical instrument. Eventually, Edison would move x-ray technology from the laboratory to the marketplace.

Of course, the marketplace alluded to by Tselos included the medical industry.

Given this history, what follows is a description of the traditional fluoroscopic imaging chain easily recognized and appreciated across the medical industry by the latter half of the 20th century (as well as into the 21st century).

In fact, Wininger (2012) described the fluoroscopic imaging chain with an emphasis on radiographic quality, as follows:

Overall radiographic quality is based on two principal properties, photographic quality (i.e., visibility of detail) and geometric quality (i.e., sharpness of detail) (Carlton & Adler, 2006; Bushong, 2004). Photographic quality is determined by density and contrast, whereas geometric quality is governed by recorded detail (i.e., resolution) and image distortion. In fluoroscopic image acquisition, the term “density” (a term derived from static film-based radiography) is replaced by the term “brightness” to be congruent with the language used to describe the visibility of images on a display monitor. The notion of an imaging chain makes reference to highly integrated instrumentation (together with the patient), regardless of the modality of interest. The fluoroscopic imaging chain denotes the x-ray generator, x-ray tube, collimator and filtration, table and patient, grid, image intensifier, optical coupler, and the image viewing system (Schueler, 2000). To this end, while each link in the chain is of equal importance, an understanding of fluoroscopic image quality relative to the image intensifier will be emphasized. The image intensifier functions as a “pass-through” device by converting x-rays to light (fluorescence) and then to electrons by way of its input phosphor-screen with adjoined photocathode backing [see Figure 2]. This design effectively and efficiently reduces overall radiation exposure (Wang & Blackburn, 2000), and at the same time, allows physicians to dynamically view anatomy with a relatively high degree of resolution due to the total brightness gain. It is the ability to view dynamically with excellent image resolution—that underpins the role of fluoroscopy in many of the modern disciplines of medicine.

fluoroscopic-image-intensifierFigure 2: Inside the image intensifier tube, x-rays photons are converted to light photons at the input screen and then to electrons at the photocathode. Flowing through the image intensifier tube the electron stream is repelled by the negatively charged electrostatic lenses and is attracted to the positively charged anode. Electrons are converted back to light at the output screen in order to proceed to the image viewing system. The output quantity of light photons is significantly greater than the input quantity of x-ray photons due to total brightness gain.

The potential for x-rays to penetrate an object (i.e., soft tissue or bone) and create an image is related to the quality of the x-ray beam as a result of the operating kilovoltage (kV) at the x-ray tube, and may simply be referred to as the “x-ray tube intensity,” “tube intensity,” or “tube potential.” The amount of x-rays produced is related to tube current (in milliamperage (mA)) and time (in seconds (s)). Whereas the operator presets these factors in static filmbased radiography, producing kilovoltage peak (kVp) and milliamperage seconds (mAs) upon exposure, this is not commonplace in fluoroscopic imaging due to automatic brightness control and real-time intended-use. Automatic brightness control is a type of automated “negative feedback” commonly set by most operators to ensure a proper amount of x-rays in order to image patients with thin to average body types. Because of its real-time imaging capability, extended exposure times are possible when operating fluoroscopy systems, and thus, the amount of tube current is substantially less compared to that used in static film-based radiography, 1 to 5 mA versus 100 to 500 mA, respectively (Carlton & Adler, 2006; Bushong, 2004). However, the physician has likely encountered degradation of recorded detail while using fluoroscopy due to a blotchy or grainy appearance that is directly related to an insufficient amount of radiation to create a uniform image (a phenomenon common to all electromagnetic imaging modalities) (Carlton & Adler, 2006). This is referred to as quantum noise or quantum mottle, as “quantum” means counted or measured. According to Carlton and Adler (2006):

With fluoroscopy, the time factor is controlled by the length of time the eye can integrate, or accumulate, light photons from the fluoro imaging chain. Because this period is 0.2 seconds, fluoroscopy must provide sufficient photons, through mA, to avoid mottle. Quantum mottle is also a large part of video noise and is a special problem during fluoroscopy because the units operate with the minimum number of photons possible to activate the fluoro screen. The factors that influence mottle are those that affect the total number of photons arriving at the retina of the eye. This includes radiation output, beam attenuation by the subject, the conversion efficiency of the input screen, minification gain, flux gain, total brightness gain, viewing system, and the distance of the eye from the viewing system. Increasing the efficiency of any of these factors can assist in reducing quantum mottle, but the most common solution is to increase the fluoro tube mA.

Image degradation from quantum mottle not only presents patient safety concerns due to challenges surrounding needle placement, particularly in patients with hypersthenic body habitus, but can also be a concern to the interventional pain physician and staff members inside the fluoroscopy suite, especially when team members are standing near the patient. We turn to x-ray attenuation physics to help us better understand this (McKetty, 1998). We see that in most fluoroscopically-guided pain procedures, the primary beam is directed at bony structures (i.e., material with a large content of calcium atoms, atomic number-20, which efficiently attenuates the beam) as opposed to soft tissues (i.e., material containing more atoms of carbon, oxygen, and hydrogen, producing an effective atomic number-7.4 and thus allowing more of the beam to transmit to the image intensifier). [Moreover, the differences in the atomic numbers and densities of matter found in the makeup of the human body can be striking.] It follows that in order to compensate for the attenuated beam within the field-of-view for bony imaging compared to soft tissue imaging, radiation output ramps up either as a result of adjustments to technique factors via automatic brightness control or by means of manual technique adjustments or activation of high-fluoro/boost mode by the operator. It is also important to note that most manufacturers incorporate an increase in mA during pulsed fluoroscopy to maintain equivalent image perception (Mahesh, 2001). With this in mind, a study on perceptual comparison between pulsed and continuous fluoroscopy concluded that the average absolute differences in the equivalent-perception dose is approximately 3% (Aufrichtig et al., 1994), where the equivalent-perception dose is defined as the dose of radiation in pulsed mode needed to give the visual equivalence in continuous mode. Thus, we find, importantly, an average radiation dose savings of 22%, 38%, and 49% for pulsed-15 frames per second, pulsed-10 frames per second, and pulsed-7.5 frames per second, respectively (Aufrichtig et al., 1994). (pp. 124-126)

The key component: the image intensifier

Compared to the discovery of x-rays (and x-ray production), the history that surrounds the imaging chain of fluoroscopy is equality fascinating. As Wininger described above, the image intensifier acts as a pass-through device. Notably, given that only 1% of the energy at the x-ray tube is transformed into x-rays (with the remainder of the energy released as heat), the introduction of the phosphor-screen and photocathode backing in the mid-twentieth century greatly improved image quality, while at the same time, lowered x-ray dose.

Future trends: from image intensifiers to flat panel detectors and biomimicry

Today, whether we are talking about fluoroscopy or detectors for x-ray imaging, the image intensifier has been mostly supplanted by flat panel detectors.

To improve the quality of flat panel detectors with respect to x-ray systems, researcher looked at what might be possible if we were to mimic the anti-reflective, light-collecting ability associated with the compound eye of a moth (Pignalosa, Liu, Chen, Smith, & Yi, 2012).

moth-and-x-ray-biosensorFigure 3: As a way to reduce radiation exposure, features associated with the leaf miner moth’s compound eye (pictured above) have been mimicked and incorporated into scintillator designs for medical x-ray detectors.

Accordingly, a news release on this topic was issued by the Optical Society (2012), as follows:

Using the compound eyes of the humble moth as their inspiration, an international team of physicists has developed new nanoscale materials that could someday reduce the radiation dosages received by patients getting X-rayed, while improving the resolution of the resulting images.

The work, led by Yasha Yi – a professor of the City University of New York, who is also affiliated with Massachusetts Institute of Technology and New York University – was published today in the Optical Society’s (OSA) journal, Optics Letters.

Like their Lepidopteran cousins the butterflies, moths have large compound eyes [see Figure 3], made up of many thousands of ommatidia – structures made up of a primitive cornea and lens, connected to photoreceptor cells. But moth eyes, unlike those of butterflies, are remarkably anti-reflective, bouncing back very little of the light that strikes them. The adaptation helps the insects be stealthier and less visible to predators during their nocturnal flights. Because of this feature, engineers have looked to the moth eye to help design more efficient coatings for solar panels and antireflective surfaces for military devices, among other applications.

Now Yi and his colleagues have gone a step further, using the moth eye as a model for a new class of materials that improve the light-capturing efficiency of X-ray machines and similar medical imaging devices.

In particular, the researchers focused on so-called “scintillation” materials: compounds that, when struck by incoming particles (say, X-ray photons), absorb the energy of the particles and then reemit that absorbed energy in the form of light. In radiographic imaging devices, such scintillators are used to convert the X-rays exiting the body into the visible light signals picked up by a detector to form an image.

One way to improve the output (the intensity of light signals read by the detector, and thus the resolution of the resulting images) is to increase the input – that is, to use a higher x-ray dosage. But that’s not healthy for patients because of the increased levels of radiation. An alternative, Yi and colleagues figured, is to improve the efficiency with which the scintillator converts X-rays to light. Their new material does just that.

Can you imagine a career researching and developing tissue scaffolds that might even mimic nature – God’s great creation?

Christian scholarship extending into professional roles is sincerely needed in education and culture. Chemical engineering and bioengineering can be a promising career for those who like to study physiology, microbiology, biochemistry, radiological sciences, and nuclear medicine. If such fields of study connect with your interests, we at Ashland Creation Colloquium (and wholeheartedly encourage you to discover the fascinating areas of radiology (MRI, ultrasound, x-ray, CT, and fluoroscopy) and nuclear medicine (PET and SPECT), and to pick up where Pignalosa, Liu, Chen, Smith, and Yi left off.


Pignalosa, P., Liu, B., Chen, H., Smith, H., & Yi, Y. (2012). Giant light extraction enhancement of medical imaging scintillation materials using biologically inspired integrated nanostructures. Optics Letters, 37, 2808-2810. [View abstract] [View in PubMed]

The Optics Society. (2012, July 3). Insects inspire x-ray improvements: Nanostructures modeled after moth eyes may enhance medical imaging. The Optical Society website. [View news release]

Tselos, G.D. (1995). New Jersey’s Thomas Edison and the fluoroscope. New Jersey Medicine, 92, 731-733. [View in PubMed]

Wininger, K.L. (2012). Applied radiologic science in the treatment of pain: Interventional pain medicine. In Racz, G. (Ed.). Pain management – current issues and opinions (pp. 123-158). [View chapter]

Previous articles in this series:

Please stay tuned! Winglets – and their impact on aviation – are featured in the next installment of our biomimicry series!

Biomimicry 101: Other Biomimetic Medical Advances: Progress and Steps to Diabetic Solutions and Spinal Cord Regeneration

other-biomimetic-solutionsFigure: The islets of Langerhans (left panel), and a spinal cord neuron (right panel).

When you ponder biomimicry, think design, intelligent design, and creation, but please don’t think evolution. And when considering biomimetic applications, let your imagination know no bounds.

Given our claim that the heart’s design is inherently unique and complex, an argument concerning the uniqueness of the pancreas can likewise be made, and is equally valid. Both arguments stem from knowledge that we are a special creation of God’s creative work. What is more, many features of the pancreatic organ-system are conducive to biomedical mimicry, which is important for people whose pancreas is limited functionally. Therefore, as we continue this series, we want to spotlight the work by Fournier, Goldblatt, Horner, and Sarver (1995) on patenting a bioartificial pancreas for combating diabetes (with the patent first filed in 1993). As we shed light on their process, our hope is students will not only gain valuable insight into ways to approach innovative ideas in health care, but also through God’s leading develop enthusiasm about career choices in mathematics and medicine, including more heavily-weighted bioengineering disciplines, such as microbiology and biochemistry. In our view, a general familiarity with the steps taken to patent a bioartificial pancreas can be used to engineer other devices that also fight diabetes or other diseases or disorders, such as cancer or spinal cord injury, via biomimetic solutions. Ultimately, the key to any medical endeavor is to get ideas into the clinical trial stage.

Biomimetic diabetic solutions

According to an educational web-based forum about the pancreas, as sponsored by the National Institutes of Health (2018), this organ has two important functions:

  • Production of enzymes (collectively, lipases, proteases, and amylases) that break down food in the digestive tract
  • Production the hormones insulin and glucagon to regulate blood sugar

— Mathematical Model —

Having a mathematical model in your tool belt is always a good thing. There are occasions when both invention and mathematics resolve themselves simultaneously. Sometimes the invention logically comes first, and the underpinning mathematics comes later. However, mathematical models can be generated prior to pressing forward with an invention.

In the 1990 article “Mathematical Modeling of a Novel Bioartificial Pancreas Design for the Control of Type I Diabetes,” Sarver and Fornier apply numerical analysis to their work on a bioartificial pancreas. We will leave it to you to decide the way in which Fournier, Goldblatt, Horner, and Sarver applied the mathematics to solve their case for a bioartificial pancreas patent (before, simultaneously, or after).

What is Numerical Analysis?

Numerical analysis is the iterative application of mathematics. Prior to the development of computers, numerical methods were necessary for solving engineering-based problems. With the aid of computers, numerical methods (i.e., iterative processes) have become a much more powerful tool because computers can perform the iterations much faster than we can calculate them. Numerical analysis takes advantage of algorithms to attain an approximation; it may be best defined as a branch of mathematics that places emphasis on the numbers rather than the symbols.

Numerical methods can be a beneficial component to any college undergraduate study in the STEM (science, technology, engineering and mathematics) majors. What is more, a numerical methods course is oftentimes recommended for junior-level (i.e., third-year) college STEM undergraduates. Prerequisites include high school algebra, differential calculus, integral, calculus, and ordinary differential equations.

Please click here to learn more about numerical methods.

The Bioartificial Pancreas

The first page of U.S. Patent No. 5,387, 237 (1995), shows Fournier, Goldblatt, Horner, and Sarver’s patent summary (i.e., the abstract) for their bioartifical pancreas, as follows:

An implantable bioartificial pancreas device having an islet chamber containing glucose responsive and insulin-secreting islets of Langerhans or similar hormone secreting cells, the islet chamber having baffle means inside thereof to assist in even distribution of the islets in the chamber, one or more vascularizing chambers open to surrounding tissue, a semi-permeable membrane between the islet and vascularizing chambers that allows passage of small molecules including insulin, oxygen and glucose and does not allow passage of agents of the immune system such as white cells and antibodies, the vascularizing chambers containing a growth factor soaked fibrous or foam matrix having a porosity of about 40 to 95%, the matrix providing small capillary growth and preventing the blood from clotting in the lower chamber.

Efforts toward spinal cord regeneration

To help us navigate toward a delivery method for spinal cord tissue regeneration, we consider a bioengineering survey and literature review by Wininger, Deshpande, and Bester (2012), who examined suitable ideas for delivery methods for the regeneration of the lumbar disc based on vascular supply/penetration, as follows:

Kloth et al issued a report on patient selection criteria for IDET in 2008.17 Notably, the criteria outlined in the report supports our decision to refrain from pursuing IDET in this case. Furthermore, similar to discography, percutaneous intradiscal radiofrequency thermocoagulation, and intradiscal biacuplasty, IDET requires needle placement into the disc.

When considering needle placement into a disc, it is important to consider the long-term effects of disc puncture. On this point, the biological effects of disc puncture continue to be debated in the literature. A recently published 10-year follow-up study on provocative lumbar discography by Carragee et al claims accelerated disc degeneration was associated with disc penetration injuries during discography.18

Perhaps more interesting is consideration of the knowledge gleaned from investigations on central disc vascular supply relative to disc puncture. A prospective study conducted by Deshpande et al on lumbar discography first confirmed real-time intravascular uptake of iodinated contrast media in 14.3% of the studied patient population.19 Further, although such episodes of uptake continue to be observed,2 it has long been observed in the radiological community that the intervertebral disc might enhance on MR images if examination start is delayed over a 30-minute window after gadolinium administration.20 Furthermore, serial MR images clearly demonstrate the phenomenon known as diffusion march (ie, the diffusion of gadolinium across the vertebral endplates and into the disc) with no intradiscal enhancement noted at 24 to 48 hours after contrast administration.21 Thus, for interventional pain physicians, broader implications of these vascular supply studies may help remedy delivery challenges related to bioengineering designs to regenerate the intervertebral disc, such as tissue scaffolds, mesenchymal stem cell therapy, or biomolecules to act as biochemical mediators within the disc.22-31

Finally, we highlight a forward-thinking concept of “direct” electrical stimulation of the intervertebral disc to induce analgesia. This novel technique places a percutaneous SCS lead inside or just outside the confines of the disc, thus sparing as much disc tissue as possible.32 However, the idea of electrically stimulating the disc in this manner has yet to be proven surgically feasible or provide clinically acceptable pain control. Thus, members of the interventional pain medicine community interested in neuroaugmentive techniques are involved in a truly transformative era of research.11,12 Electrical stimulation of the intervertebral disc could provide benefit for the disc’s cells and tissue, or provide beneficial synergies. For example, electromagnetic field stimulation has been shown in vitro to promote human intervertebral disc DNA synthesis. In addition, electrical stimulation applications could be used to promote cellular proliferation as an amplification process in autogenous disc cell therapy to regenerate disc tissue.33 (p. 434)

With this survey in mind, however, the hope for regeneration of spinal cord tissue hinges on demonstrable safety in crossing the blood and central nervous system barrier (better known as the “blood-brain barrier”).

Can you imagine a career advancing medicine through insight into solutions that might mimic nature? Nature and the universe in its entirety is God’s great creation; as His special creation, we can certainly look upon our Creator as Physician!

Christian scholarship extending into professional roles is sincerely needed in education and culture. Chemical engineering, bioengineering, and medicine can be promising careers for those who like to study physiology, microbiology, biochemistry, and mathematics.


Fournier, R.L., Goldblatt, P.J., Horner, J.M., & Sarver, J.G. (1995). Bioartificial pancreas. U.S. Patent No. 5,387, 237. Washington, D.C.: U.S. Patent and Trademark Office. [View patent]

National Institutes of Health. (2018). Informed health online. How does the pancreas work? Retrieved from

Sarver, J.G., & Fornier, R.L. (1990). Mathematical modeling of a novel bioartificial pancreas design for the control of type I diabetes. Mathematical and Computer Modelling, 14, 551-556. [View in article]

Wininger, K.L., Deshpande, K.K., & Bester, M.L. (2012). Persistent pain following lumbar disc replacement. Radiologic Technology, 83(5), 430-436. [View abstract] [View in PubMed]

Previous articles in this series:

Biosensors will be featured in the next installment of our biomimicry series!

50th anniversary of Apollo 8: Christmas Eve reading from the Book of Genesis during lunar orbit


Apollo 8 was the first manned mission to the moon. The crew, Commander Frank Borman, Command Module Pilot Jim Lovell, and Lunar Module Pilot William Anders, left the earth on December 21, 1968. On Christmas Eve, December 24, 1968, the three astronauts did a live television broadcast from lunar orbit, which ended with a reading from the Book of Genesis. What follows is a transcript of that reading:

William Anders:

“We are now approaching lunar sunrise, and for all the people back on Earth the crew of Apollo 8 has a message we would like to send you.”

“In the beginning God created the heaven and the earth.
And the earth was without form, and void; and darkness was upon the face of the deep.
And the Spirit of God moved upon the face of the waters. And God said, Let there be light: and there was light.
And God saw the light, that it was good: and God divided the light from the darkness.”

Jim Lovell:

“And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.
And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so.
And God called the firmament Heaven. And the evening and the morning were the second day.”

Frank Borman:

“And God said, Let the waters under the heavens be gathered together unto one place, and let the dry land appear: and it was so.
And God called the dry land Earth; and the gathering together of the waters called he Seas: and God saw that it was good.”

“And from the crew of Apollo 8, we close with good night, good luck, a Merry Christmas, and God bless all of you – all of you on the good Earth.”


NASA Goddard Space Flight Center. (n.d.). The Apollo 8 Christmas Eve broadcast. Retrieved from

Biomimicry 101: Special Insert: Mathematical Cardiology

mandelbrot-set-x2Central illustration: At the heart of the Mandelbrot set lies the cardioid, a well-defined mathematical representation (left panel). On the cardioid’s boundary exists an assortment of circles, with each of these circles further continuing its own fractal pattern (right panel; zoomed-in view for illustrative purposes).

When you ponder biomimicry, think design, intelligent design, and creation, but please don’t think evolution. And when considering biomimetic applications, let your imagination know no bounds.

Here we touch briefly on cardiac function and fractal behavior via what we have coined mathematical cardiology. Our intent is to glorify God as the universe’s greatest mathematician.

Mathematical cardiology – a unique pattern

While we have argued that the heart itself is complex and uniquely designed, others offer claims suggesting that the heart is seminally prototypical. In part, evidence in either case points to the intrinsic fractal behavior of the heart. Specifically, fractal descriptions mark the quintessential characteristic of non-linear, dynamical systems, and with respect to the heart such behavior is clearly present. The preeminent example deals with the heart’s electrophysiology. The rhythmic impulse that is ultimately carried through the heart’s conduction pathway can, at times, become quite irregular. In these cases, the rhythm (the irregularity) is called an arrhythmia. What is more, two somewhat related arrhythmias, known as atrial fibrillation and atrial flutter, are regarded as irregularly irregular. This pattern of irregular irregularity is understood to be a chaotic temporal disturbance of atrial origin. Furthermore, although dynamical systems are non-linear and chaotic by nature, at the center of any such system is simple, identifiable deterministic activity (despite a behavior seemingly acting in an erratic way) (Bassingthwaighte & van Beek, 2002). What this means for patients with atrial fibrillation or atrial flutter is that algorithms can be developed to mathematically identify these arrhythmias based on the deterministic, fractal character. This identification translates into a more proactive means of rhythm identification and possible correction. In fact, in the case of an urgent, life-threatening arrhythmia, attempts to convert to normal sinus rhythm via implantable defibrillators become possible sooner (or even anticipated), due to resultant mathematical interpretation of the rhythm’s fractal behavior (Captur, Karperien, Hughes, & Moon, 2017).


Bassingthwaighte, J.B., & van Beek, J.H.G.M. (2002). Lightning and the heart: Fractal behavior in cardiac function. Proceedings of the IEEE: Institute of Electrical and Electronics Engineering, 76(6), 693-699. [View in article] [View in PubMed]

Captur, G., Karperien, A.L., Hughes, A.D., Francis, D.P., & Moon, J.C. (2017). The fractal heart – embracing mathematics in the cardiology clinic. Nature Reviews: Cardiology, 14(1), 56-64. [View in article] [View in PubMed]