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]

Biomimicry 101: Cardiovascular Medicine: Part 2: Cardiac Tissue Engineering and Other Novel Biomimetic Research

coronary-angioFigure 1: Coronary angiogram depicting adequate perfusion of the myocardium via the left coronary vasculature: the left main trunk branching out to form the left anterior descending and circumflex arteries. Among the areas of the heart that these arteries perfuse, the left-sided vasculature ultimately feeds – supplies oxygen to – the left ventricle.

Cardiovascular disease accounts for more deaths per year than all forms of cancer combined.

– American Heart Association, 2016

Given the complex yet interrelated structure and physiological design of the heart, we now center our discussion on biomimicry and bioengineering in cardiovascular medicine. First, we discuss multipotent and pluripotent stem cell therapy with respect to tissue engineering and regenerative science in cardiovascular research. Second, we expand briefly on the concept of cell plasticity related to cardiovascular medicine. Third, we point out the evolving role of protein therapy in cardiology, such as efforts to treat heart attack (i.e., myocardial infarction) by reprogramming/regenerating heart muscle cells (i.e., the cardiac myocytes). Fourth, we highlight a novel approaches to reperfusion therapy. Finally, we explore a variety of other biomimetic applications that have promising potential to impact cardiac and endovascular patient care.

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.

Multipotent and pluripotent (induced pluripotency) stem cell therapy for tissue engineering and regenerative science in cardiovascular research

Cardiovascular disease (both coronary and cerebrovascular disease) accounts for more deaths per year than all forms of cancer combined (American Heart Association, 2016). Given that cardiomyocytes have a rate of turnover of 1% in youth to 0.5% in old age (Tchao et al., 2013), the heart is one of the least regenerative organs in the body. Currently, efforts remain ongoing for repopulating damaged/injured cardiac muscle tissue (the myocardium) via stem cell therapy (Naumova & Yarnykh, 2014). Moreover, it is often the case that tissue injury or damage results from ischemic events, such as heart attacks (also known as a myocardial infarctions). In fact, therapeutic goals and clinical outcomes driving much of the work behind regenerative cardiovascular research have to do with preventing the post-infarct heart from sliding into a low-functioning state of utility by regenerating the cardiomyocytes. One such approach gaining favor in recent years is the use of multipotent and pluripotent stem cells, as opposed to totipotent stem cells. Whereas totipotent stem cells are taken from embryonic tissue, multipotent and pluripotent stem cells (as well as induced pluripotency stem cells) are harvested from adult tissue and are less problematic to the recipient heart (Baldassarre, Cimetta, Bollini, Gaggi, & Ghinassi, 2018; Hirt, Hansen, & Eschenhagen, 2014; Purdom, 2007). However, because of the ability to perpetually divide, pluripotency is more advantageous with respect to the heart. Below we survey progress made in the use of pluripotent-derived cardiomyocytes. In addition, we review advances made in cardiac DTI that allow this non-invasive imaging technique to gain favor as the leading platform for the evaluation of infarct healing (via stem cell therapy) after ischemic injury in patients post-heart attack.

— Multipotent and (induced) Pluripotent Stem Cell Therapy —

With each ischemic insult that fully manifests as a heart attack, the myocardium will lose approximately one billion cardiomyocytes (i.e., the cardiac muscle cells) (Naumova & Yarnykh, 2014). What is more, such robust, immediate loss of myocardial tissue dramatically affects cardiac hemodynamics (including reduced cardiac output). Furthermore, after the initial ischemic injury, as well as the initial change in hemodynamics, a functional decline occurs over time (such as further reduced cardiac output) that can limit the physical capacity of a patient due to left ventricular remodeling. Such anatomical and physiological decline is termed heart failure. However, therapeutic strategies based on “patching” the cardiac muscle damage at or near the time of event onset (given that the patient is hemodynamically stable) by means of stem cell therapy can curb the detrimental progression of heart attack-induced heart failure, and this is especially the case with induced pluripotent-derived cardiomyocytes (Baldassarre, Cimetta, Bollini, Gaggi, & Ghinassi, 2018).

What do we mean when we say totipotent, multipotent, pluripotent, or induced pluripotent?

Totipotent – The state of a cell that is capable of giving rise to all types of differentiated cells found in an organism, as well as the supporting extra-embryonic structures of the placenta. A single totipotent cell could, by division in utero, reproduce the whole organism.

Multipotent – Having the ability to develop into more than one cell type of the body.

Pluripotent – The state of a single cell that is capable of differentiating into all tissues of an organism, but not alone capable of sustaining full organismal development. In other words, pluripotent stem cells can give rise to any type of cell in the body except those needed to support and develop a fetus in the womb.

Induced pluripotent stem cell – A type of pluripotent stem cell, similar to an embryonic stem cell, formed by the introduction of certain embryonic genes into a somatic cell, in which somatic cells are differentiated, mature cells. What is more, somatic cells are commonly referred to as “adult” cells.

Why pluripotent is important!

According to the National Institutes of Health website (n.d.):

In late 2007, scientists identified conditions that would allow some specialized adult human cells to be reprogrammed genetically to assume a stem cell-like state. These stem cells are called induced pluripotent stem cells (iPSCs). IPSCs are adult cells that have been genetically reprogrammed to an embryonic stem cell–like state by being forced to express genes and factors important for maintaining the defining properties of embryonic stem cells. Although these cells meet the defining criteria for pluripotent stem cells, it is not known if iPSCs and embryonic stem cells differ in clinically significant ways. Mouse iPSCs were first reported in 2006, and human iPSCs were first reported in late 2007. Mouse iPSCs demonstrate important characteristics of pluripotent stem cells, including expressing stem cell markers, forming tumors containing cells from all three germ layers, and being able to contribute to many different tissues when injected into mouse embryos at a very early stage in development. Human iPSCs also express stem cell markers and are capable of generating cells characteristic of all three germ layers.

Although additional research is needed, iPSCs are already useful tools for drug development and modeling of diseases, and scientists hope to use them in transplantation medicine. Viruses are currently used to introduce the reprogramming factors into adult cells, and this process must be carefully controlled and tested before the technique can lead to useful treatments for humans. In animal studies, the virus used to introduce the stem cell factors sometimes causes cancers. Researchers are currently investigating non-viral delivery strategies.

Non-embryonic (including adult and umbilical cord blood) stem cells have been identified in many organs and tissues. Typically there is a very small number of multipotent stem cells in each tissue, and these cells have a limited capacity for proliferation, thus making it difficult to generate large quantities of these cells in the laboratory. Stem cells are thought to reside in a specific area of each tissue (called a “stem cell niche”) where they may remain quiescent (non-dividing) for many years until they are activated by a normal need for more cells, or by disease or tissue injury. These cells are also called somatic stem cells.

— Bioengineering Applications of Engineered Heart Tissue —

  • Screening for drug discovery (i.e., pharmacodynamics) and cardiotoxicity testing
  • Cardiovascular disease modeling
  • Regenerative medicine: cell-based heart regeneration
    • Importance of avoiding arrhythmias
    • Immunological favorability
  • Evidence indicates that immunological tolerance to iPSC-derived tissues is favorable for utilization. Moreover, the evidence suggests that such tissues may actively participate in their own survival.

Examples of adult tissue-derived, pluripotent-derived stem cells

Cardiac progenitor cells naturally form functional, fully-fledged cardiomyocytes. However, harvesting suitable numbers of cardiac progenitor cells for the treatment of injured or failing myocardium is an insurmountable task via cardiac biopsy. For this reason, various adult stem cell sources have been identified from other human tissue, including bone marrow, adipose tissue, connective tissue, umbilical cord blood, and skeletal muscle. Notably, given these tissue types, stem cells induced from skeletal muscle present an intriguing opportunity for the treatment of debilitating myocardial ischemia that leads to myocardial infarction. In fact, stem cells associated with skeletal muscle cells are resistant to hypoxia, fibrosis, and easily achieve contractile characteristics (Tchao et al., 2013).

From myocyte to pluripotent-derived cardiomyocyte stem cell

Tchao et al. (2013) investigated the practicality of using human muscle cells (i.e., myocytes) for engineering cardiac muscle tissue by means of pluripotency induction given that cardiac and skeletal muscle share major transcription factors as well as sacromere proteins that are generally regarded as significant to either cardiac or skeletal muscle tissue but not both muscle types. In fact, skeletal muscle and cardiac muscle are known to have similar embryonic developmental pathways. What is more, according to Lewandowski et al. (2018), this similarity implies that skeletal muscle cells induced for pluripotency have what it takes to achieve greater myocardial development, compared to other tissue types, such as, for example, fibroblast cells from connective tissue.

The state of plasticity of a cell: review of Lewandowski et al.’s attempt to derive heart cells from muscle cells

In this section, we look closely at a study conducted by Lewandowski et al. (2018), who investigated the feasibility, significance, and practicality of cardiomyocytes derived from induced pluripotent stem cells of myogenic origin.

  • The work by Lewandowski et el. (2018):
  • Biochemical (regulatory) pathways and epigenetic memory
    • Importance of the Wnt signaling
    • Importance of the epigenetic memory
  • Morphological and functional properties, including electrophysiological analysis
    • Importance of mismatches between iPSC and native cardiac muscle cells
  • Paracrine effects
  • Study limitations

Cardiac muscle microarchitecture: innovative evaluation of stem cell therapy structural outcomes by cardiac DTI

Introduced in the mid-1990’s, diffusion tensor imaging (DTI) is a MRI technique capable of visualizing cardiac microstructure (Naumova & Yarnykh, 2014). One distinguishing feature of DTI is its ability to image fiber trajectories – a method known as tractography. Although tractography has been widely used in brain imaging (as well as musculoskeletal imaging), Sosnovik et al. (2014) recently published a landmark study showing the capacity of cardiac DTI tractography to characterize the integrity and spatial organization of cardiac myofibers in live mice after stem cell therapy for ischemic heart damage. According to Naumova and Yarnykh (2014):

The study [by Sosnovik et al. (2014)] establishes DTI as a new approach for assessment of the effect of stem cell therapy in a preclinical setting, in which it could prove whether cardiomyocytes derived from stem cells are actually aligned with host myofibers to regenerate heart structure and function. (p. 1720)

Furthermore, Naumova and Yarnykh (2014) stated the following:

Collectively, the present [study by Sosnovik et al. (2014)] and earlier studies have established the feasibility of DTI tractography in the human heart in vivo. However, a significant amount of work remains to translate this challenging technology to serial applications in clinical trial settings. (p.1721)

What is more, quality control protocols are a critical part of all imaging programs. With respect to protocols for cardiac DTI tractography, a dedicated phantom has only recently been developed that incorporates microtubules that allow the phantom to mimic the heart itself, specifically, the microarchitecture of the heart (Teh, Zhou, Hubbard Cristinacce, Parker, & Schneider, 2016). Testing of this phantom has been successful, and it is our conjecture that the device will help bring clinical trials utilizing serial cardiac DTI tractography a step closer to reality for assessment of the myocardium for patients with post-ischemic heart damage treated by regenerative stem cell therapy (preferably, pluripotent-derived cardiomyocytes).

Protein therapy in cardiology

Whereas protein engineering refers to various ways of modifying proteins, the benefit of protein therapy is its affinity for targeted interventions.

Protein-mediated paracrine effects identified through stem cell-derived cardiac muscle analysis, have spurred interest in protein therapy as a viable approach for cardiac muscle proliferation and myocardium repair (Jay & Lee, 2013).

Detecting artieral stenosis/occlustion: coronary angiography, coronary CT angiography, myocardial perfusion imaging, and reperfusion therapy and biomimicry

Conventional coronary angiography is the gold standard for detecting and treating coronary artery stenosis (Jiangping et al., 2013). Nevertheless, recent advances made in non-invasive, diagnostic methodologies, such as coronary CT angiography (with slice standards of 64 slices or greater) and myocardial perfusion imaging studies, are contributing to the earlier detection of the underlying pathology (i.e., earlier detection of coronary artery disease) (Gorenol, Schönermark, & Hagen, 2012; Tamarappoo et al., 2010). With respect to stress and rest myocardial perfusion imaging, according to Smith (2018):

If the coronary artery narrows less than 50% of the original vessel diameter, the effect on blood flow is clinically insignificant, but at 70% narrowing, blood flow is significantly affected during stress. During rest, the vessel must be narrowed 90% or more to reduce blood f low significantly. A cardiac event is not likely to be detected unless the coronary artery is narrowed to these degrees under stress or rest. Myocardial perfusion studies detect stress-induced myocardial schemia approximately 80% to 90% of the time, which is more sensitive than exercise electrocardiography at 60% to 70% sensitivity. This is because of the high rate of patients that undergo nondiagnostic exercise ECG tests because of baseline electrocardiographic abnormalities or inadequate stress.

What is more, a luminal stenosis at 70% to 80%, as assessed by coronary CT angiography, was correlated with electrocardiographic rhythm strips that revealed robust ST-segment depression (Lipinski, Morise, & Froelicher, 2002).

— Stents/Camouflaged Coating of Sugar —

Significant coronary artery narrowing is quantified as luminal narrowing at 70% or greater, although 50% narrowing is significant for the left main coronary artery (Bovin, Klausen, & Petersen, 2013). Given this percentage of narrowing (and the chronic nature of coronary artery disease), when cardiologists talk with patients and family members about reperfusion interventions, such as coronary artery ballooning and stenting, the discussion inevitably comes around to the likelihood of restenosis of treated vessels (including in-stent restenosis). One way to reduce the potential of in-stent restenosis, however, is a stent design that mimics the luminal lining of the tunica intima (the innermost layer of the coronary artery comprised entirely of endothelial cells) (Perez et al., 2009). In fact, such biomimetic-inspired stents have been modeled on the native coating found on endothelial cells of the tunica intima (i.e., the native glycocalyx). Production of these stents involves laser-etching technology that patterns the inside surface of the stent’s struts after these glycocalic fibers. This means that the surface area inside the stent effectually becomes camouflaged against vascular inflammatory and injury cycles that are associated with the patients’ coronary disease. The net-outcome for this design has reduced the body’s foreign body response to the stent.

monarch-caterpillar-cvcuFigure 2: The segmented structure of the monarch caterpillar has inspired a novel coronary stent concept that offers segmented movement relative to pulsatile blood flow through the coronary arteries, as well as movement related to the heart’s squeezing action.

— Stents/Dynamical, Flexible Cardionature and the Caterpillar’s Skeleton —

At rest, average heart rate is approximately 72 beats per minute, and with exercise, the typical range falls between 112 and 146 beats per minute. Therefore, we are clearly beneficiaries of the heart’s dynamical nature (including the constant movement of its surface) (Jiangping et al., 2013). What is more, the heart’s constant movement places high mechanical loads (i.e., mechanical stress and strain) on the functionality of stents, and this movement can ultimately damage the stent’s integrity. In their efforts to support the demands of this environment, Singh and Wang (2014) introduced a “flexible” stent that offers an unparalleled advantage over common, “stiff” stents. Their design mimics the flexible yet rigid skeletal structure of a monarch caterpillar. The end product is a biomimetic stent capable of flexing and bending with the movement of the heart, which, once again, is dynamical in nature as the heart adapts to the demands to supply oxygen to the body’s muscles and organs.

Endovascular angiography: reperfusion therapy and biomimicry

— Stents/High Shear Wall Flows and the Swirling Flow of Water Currents —

What about biomimicry in peripheral vascular studies? Has any attention been given to reperfusion therapy in this area of medicine? The answer to both of these questions is “yes.” For example, the superficial femoral artery (SFA) is a lower extremity artery susceptible to luminal narrowing secondary to atheromas and plaque build-up. Moreover, stents indicated for this vessel can be quite long, with lengths up to 15 cm commonly deployed. Recently, a novel stent design for the reperfusion of an occluded segment of the SFA was modeled on the flow of blood through the aorta, given that the aorta is quite resistant to atherosclerotic disease (Gaines, 2015). This intrinsic resistance identified with the aorta has been correlated with high-grade, pulsatile blood flow, which in part is also associated with the structural nature of the aortic arch. In other words, hemodynamics at the aorta not only imposes a high shear wall stress on the aorta’s inner wall (the tunica intima layer of this artery), but blood flow analysis reveals that the curvature of the aortic arch also helps give rise to a swirling, turbulent component of this high-grade, pulsatile flow.

TECHNICAL INSERT: For a conceptual image of the aforementioned dynamics in the healthy aorta, imagine that the turbulent and swirling nature of blood flow through the aortic arch repeatedly washes and rinses the luminal lining in this region of the artery. The best analogy comes from the flow of water that washes the banks along a somewhat sharp, curving bend (effectually, a U-turn) of a river as the current transits downstream.

With respect to the SFA, the stent that captures the nature of aortic blood flow has a subtle corkscrew design. Notably, such design helps impose a swirling effect on the flow of blood through the stented region of the SFA that also induces higher shear wall stress, which reduces the chances for in-stent restenosis.

— Stents/Vascular Smooth Muscle Cell Biomimetic Surface Patterns —

Because normal wound healing in the tissues surrounding a deployed stent is delayed, design schemes for stents have included antibody coatings to attract endothelial progenitor cells as a means to promote healing. However, testing of these stents has revealed that the associated lesions are often more complex than those associated with other stents, such as drug-eluting stents (whereas drug-eluting stents are known to be cytotoxic). Therefore, to address these challenges, and in a novel design twist to the aforementioned glycocalyx-mimicked stent, researchers recently introduced a stent that is designed to mimic vascular smooth muscle cells (VSMCs) at the nanometer level on the stent struts (Liang, et al., 2016). Methods similar to those used to obtain the glycocalic coating (i.e. laser-etching) were used to achieve the VSMC pattern. Testing performed on the iliac arteries of rabbits showed that a VSMC-biomimetic surface pattern was effective for rapid re-endothelialization (which translates as distinctly effective for promoting normal wound healing), as well as reducing the likelihood of in-stent restenosis.

Clearly the heart is uniquely designed! Can you imagine a career researching and developing engineered heart tissues?

The Heart is Uniquely Designed: Part of God’s Special Creation!

Quintessentially Mimicking the Structure and Function of the Human Heart:

Christian scholarship extending into professional roles is sincerely needed in education and culture, including mathematics and the sciences (including medicine). Chemical engineering and bioengineering can be a promising career for those who like to study physiology, microbiology, and biochemistry. And a well-developed understanding of anatomy and physiology plays a crucial role.

Insert: myocardial squeezing problem or atrial/ventricular filling problem

For many years echosonographers and cardiologists understood heart failure as a mechanical-type squeezing problem due to myocardial remodeling or enlargement; only recently did they learn it may also be a filling problem. The latter became known as diastolic heart failure.

As Christians, we ought to ask ourselves if we walk around with filling defects. In fact, the sermon “Why is my Heart not Filling?” given at Maranatha Baptist Church by Pastor Todd Grover (2018), gives us perspective on whether or not our own hearts might be suffering spiritually.

Consider 2 Corinthians 6:11-13 (ESV), in which the Apostle Paul expressed to the Christians living in Corinth: “We have spoken freely to you, Corinthians; our heart is wide open. You are not restricted by us, but you are restricted in your own affections. In return (I speak as to children) widen your hearts also.”

According to Pastor Grover (2018): “Here Paul revealed his heart’s condition to the Corinthians, that his heart is wide-open or enlarged, or that his heart is full and does not suffer from a filling problem.” Grover also pointed out that Paul stated he has spoken freely, and reminded listeners that Jesus said, “What comes out of the mouth proceeds from the heart.” However, Pastor Grover acknowledged that verse 11 of 2 Corinthians 6 is also clearly implying that Paul has a welcoming spirit toward the Corinthians, but not because Paul is outgoing, and has a warm and inviting personality. Rather, the reason is spiritual, since only a couple of years earlier Paul would have been killing these same Corinthians for their faith he is now trying to nurture.

So, a natural question to ask is what fills the heart. Some at Corinth were blaming Paul for their bad spiritual condition, but Paul is telling them that it is not he that should be blamed. Then, how did Paul’s heart become filled? To answer this, Pastor Grover quoted three verses from the very same epistle, and offered the applications of these verses, as follows:

  • The Spirit unveils, as we read according to 2 Corinthians 3:16 (ESV), “But when one turns to the Lord, the veil is removed.” Thus, if we don’t understand, then we can turn to the Lord, and the Lord will remove our veil of not understanding.
  • The Spirit writes, since we learn from 2 Corinthians 3:3 (ESV), “And you show that you are a letter from Christ delivered by us, written not with ink but with the Spirit of the living God, not on tablets of stone but on tablets of human hearts.” Therefore, we cannot live in the flesh and expect the Spirit to teach us.
  • Finally, the Spirit does not mix with sin, as we know according to 2 Corinthians 4:2 (ESV), “But we have renounced disgraceful, underhanded ways. We refuse to practice cunning or to tamper with God’s word, but by the open statement of the truth we would commend ourselves to everyone’s conscience in the sight of God.” And thus, we cannot allow sin to soil our hearts.

To summarize, Pastor Grover remarked: “So if our heart is not filling properly, we must develop a skill set as a Bible reader, because a heart fills as we read, learn, and know that the Spirit unveils, the Spirit writes, and the Spirit does not mix with sin.”

May the God of hope fill you with all joy and peace in believing, so that by the power of the Holy Spirit you may abound in hope.

– Romans 15:13 (ESV)


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Tchao, J., Jin Kim, J., Lin, B., Salama, G., Lo, C.W., Yang, L., & Tobita, K. (2013). Engineered human muscle tissue from skeletal muscle derived stem cells and induced pluripotent stem cell derived cardiac cells. International Journal of Tissue Engineering, 198762. [View in PubMed]

Teh, I., Feng-Lei, Z., Hubbard Cristinacce, P.L., Parker, G.J.M., & Schneider, J.E. (2016). Biomimetic phantom for cardiac diffusion MRI. Journal of Magnetic Resonance Imaging, 43(3), 594-600. [View in article] [View in PubMed]

Wininger, K.L. (2018, September 14). Biomimicry 101: Biomaterials and tissue engineering. [blog post]. Retrieved from

Previous articles in this series:

Other medical applications are featured in the next installment in our biomimicry series!

In our next installment on biomimicry, we will touch finally on cardiac function and fractal behavior via the area of concentration we have coined mathematical cardiology. We then move forward from our focus on the heart, as we turn our attention to two unrelated fields in medicine where biomimetic solutions have garnered exciting outcomes: diabetic solutions and work towards spinal cord regeneration.

Diamond Caverns – the true gem among the Mammoth Cave caving system


A trip to Diamond Caverns in Park City, Kentucky, off of Exit 48 on I-65, just on the outskirts of Mammoth Cave National Park, is quite an adventure. The cave has a particularly abundant source of large flowstone formations, as well as beautiful “bacon” formations. Undoubtedly, though, visitors get to enjoy their caving while exploring one of the most beautifully laid-out cave tails in Kentucky’s caving system. Oh, and be on the lookout for cave crickets!

Fun Fact: As a product of the Flood’s aftermath, some of Diamond Caverns’ flowstones are thought to be the byproducts of underground waterfalls. (Flowstones are estimated to deposit at rates of 1-cubic centimeter every 150 years.)

Creation Science High School and Undergraduate Essay Contests

The third question in our series of writing prompts for our creation science writing contest asks students to consider the growth and formation of stalactites and stalagmites, including consideration of factors influential on their rates of growth. For instance, the 1932 article “An Unusual Occurrence of Stalactites and Stalagmites” by Karl Ver Steeg serves as a credible reference offering such valued information. In fact, for students choosing this question, a summary that highlights any differences between stalactites exposed to the elements (like the kind mentioned in Ver Steeg’s 1932 article) and stalactites formed underground (like those formed within Diamond Caverns, see the picture above) is encouraged. Such contrasted settings may show intriguing results with respect to stalactite growth rates. (Hint: Ver Steeg’s article will help with such a comparison.)

diamond-caverns-2Diamond Caverns – discovered in 1859, and rediscovered daily.

Just maybe the writing prompt that deals with geology (as well as the fossil record) was developed specifically for you!

We invite you to browse the aforementioned question here, as follows: “essay contests.”

Could you consider yourself in a role that helps improve our understanding of the geology of the planet?

Starting out now on your very own discovery of the intricacies of God’s creation today through scientific study might very well help in discerning what path you should take in the future. For example, for a possible career path, such study could help you better understand the activities of geologists. And one of your first activities ought to be growing your very own stalactites. In fact, in the book 77 Fairly Safe Science Activities for Illustrating Bible Lessons by Professor Donald B. DeYoung (2013), lesson #74 called “Cave Icicles” allows readers to do this very thing.

This blog is the third blog entry related to this year’s caving expeditions. Please click below to see the other two sites we explored.


DeYoung, D.B. (2013). 77 fairly safe science activities for illustrating Bible lessons. Grand Rapids, MI: Baker Books.

Ver Steeg, K. (1932). An unusual occurrence of stalactites and stalagmites. The Ohio Journal of Science, 32(2), 69-84. Retrieved from

Christmas Greetings – iterations of the Koch snowflake

koch-snowflake-2-uChristmas greetings – the 0th through 5th iterations of the Koch snowflake (2018).

For unto you is born this day in the City of David a Saviour, which is Christ the Lord. And this shall be a sign unto you; Ye shall find the babe wrapped in swaddling clothes, lying in a manger. And suddenly there was with the angel a multitude of the heavenly host praising God, and saying, Glory to God in the highest, and on earth peace, good will toward men.

– Luke 2:11-14 (KJV)

We at Ashland Creation Colloquium want to wish everyone Merry Christmas and Happy Holidays!

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The Koch snowflake is a recursive, self-similar mathematical pattern, with the zeroth through fifth iterations shown above. In other words, the Koch snowflake is a fractal.

According to Weisstein (n.d.):

The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral triangle, removing the inner third of each side, building another equilateral triangle at the location where the side was removed, and then repeating the process indefinitely.

The 2018–2019 Creation Science Essay Contests

Challenge yourself this Christmas break by exploring our 2018-2019 creation science essay contests for high school students and college undergraduates. Select from informative writing prompts with diverse subject matter. For more information, please see our contest flyer (or download our printer friendly version of the writing prompts and contest submission guidelines).

The truth Ashland Creation Colloquium adheres to is that the Bible is the inerrant Word of God, and although it is not a book of science, everything the Bible says about science is true.


Weisstein, E.W. (n.d.). Koch snowflake. WolframMathWorld. [View in online article]