Category Archives: Medical

Data Visualizations in Healthcare

A couple of weeks ago I attended HIMSS 2017 in Orlando (Healthcare Information and Management Systems Society), the largest annual Healthcare IT event in the US. One of the big tenets of the show was system interoperability. There are lots of different vendors, few standards, and vast amounts of data being collected. There is an emerging set of APIs (such as HL7 FHIR) to ensure data can be shared among systems and follows a patient properly through the various providers she encounters during her episodes of care.

Somewhat serendipitously I came across a booth which had large prints of beautiful data visualizations on it. The booth was from Arcadia Healthcare Solutions. Given my background on data visualization and my being employed at Rennova Health Technology Solutions and responsible for our healthcare IT products and services, I was drawn to interpret these prints. They are also featured in an online data gallery, which I encourage you to explore.

One of these visualizations created by Jeff Solomon is called “The Health IT Space“. It displays highly aggregated data from various EHR (Electronic Health Record) systems. From the gallery:

The Electronic Health Record is a data gold mine. Each patient you see generates millions of detailed records in real time that can be extracted and analyzed for improved predictive algorithms, increased operational efficiency, better care quality, and so much more.


These graphs are stylized Entity Relationship diagrams from seven different EHRs. Nodes are data tables, and edges are relationships between these tables inferred from shared attributes.


The color-highlighted nodes are referring to patient data. The size of the node corresponds to the amount of records in the respective table.


Again, from the gallery description:

In each cluster, the core patient entity – the nucleus around which the rest of the data revolve – can be identified by its contrasting color. The tables containing the bulk of the clinically and operationally valuable data tend to form clusters of large, interconnected nodes, while a larger number of satellite tables house system configurations and other low-volume metadata that has very few relationships to the nucleus.

At the large end of entire health systems, the graph starts to look very busy:


It is pretty amazing how much data is being aggregated into these graphs. Nearly 5,000 database tables – hence the black areas where there are too many dots to separate them at this resolution. A combined number of 18 billion records! Nearly 300,000 relationships between these tables (again, the lines are too numerous to be distinguishable).

The Health IT SpaceI find it somewhat humbling to review these graphs. Our own MedicalMime EHR falls into the small category by these standards. Major and Large EHRs are at least one, maybe two orders of magnitude larger and more complex.

Interpreting the large amount of data contained in the EHR opens up many ways to improve healthcare, both medically for the patient as well as operationally for the providers. Visualizations can help us to better understand patterns and trends which otherwise would remain hidden.

The entire big picture of the above visualization is indicated on the right. For a Hi-Res version please contact the friendly folks from Arcadia Health Solutions directly from their website.

Another big trend at HIMSS’17 was Artificial Intelligence. Machine learning and predictive analytics received a lot of attention. Solutions like IBM’s Watson Health promise to bring world-class expertise into ordinary physician practices through subscription to hosted specialty knowledge in the cloud – whether curated by scientists or machine-learned using statistical techniques from big data. Health Catalysts is an open platform to make machine learning techniques more accessible and bring them to small SW houses, not just the large companies with large R&D budgets. While certainly overhyped at the moment, acceptance for obtaining a “second medical opinion from the cloud / app” to improve clinical decisions is rising.

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Posted by on May 20, 2017 in Medical


Apple’s Health App and HealthKit – Platforms for Next Gen Healthcare?

Business Analytics 3.0

mobile-applicationsGame on….I think we just witnessed a big next generation leap in Healthcare Data and Analytics.  Apple jumped into the health information business on June 2, 2014, launching both a new health app and a cloud-based health information platform with IOS 8.

The new App, called simply “Health”, will collect a number of body metrics including blood pressure, heart rate, and stats on diet and exercise.  Health will constantly monitor key health metrics (like blood sugar or blood pressure), and if any of them begin to move outside the healthy range, the app can send a notification to the user’s doctor.

The Health app will share all its information with a new cloud platform called “HealthKit.” The new health cloud platform is designed to act as a global repository for all the user’s health information. It will accept data collected by a variety of third-party devices and apps. For instance Nike is now working to…

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Posted by on June 2, 2014 in Medical


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Visualizing Voting Preferences for World Values

The other day I listened to a presentation by Melinda Gates prepared for the United Nations to deliver an update about progress towards the Millennium Development Goals (MDG). The eight goals of the MDG had been embraced by the UN back in 2005 for the time target of 2015. So it is reasonable to see whether the world is on track to reach each of these eight goals. To summarize, from the MDG Wikipedia page:

  1. Eradicating extreme poverty and hunger
  2. Achieving universal primary education
  3. Promoting gender equality and empowering women
  4. Reducing child mortality rates
  5. Improving maternal health
  6. Combating HIV/AIDS, malaria, and other diseases
  7. Ensuring environmental sustainability
  8. Developing a global partnership for development

A good listing of reports, statistics and updates can be found on the UN website here.

Sample Vote for 6 of 16 MDG choices

Sample Vote for 6 of 16 MDG choices

At the end of Melinda’s presentation is a link to a UN global survey on the MDG goals after 2015. I took this survey and found the visualization of voting results quite interesting. First, one is asked to select six out of a list of sixteen (6 of 16) goals which one thinks have the highest impact for a future better world. (The survey methodology is described in more detail here.) Here is a sample vote:

A nice touch is that for each of the sixteen goals there is a different color and when you check that goal, one of the sixteen areas on the stylized globe is filled with that color. Personal data such as name is optional, but some demographic information is required, including age, gender, educational level and country. Next, one can look at a summary of all currently tallied votes and compare them interactively to ones own vote (checkmarks on the right).


It is perhaps not surprising that I voted very similar to others in similar demographic cohorts.

  • Country: I picked five of the Top five goals like all other voters living in the US. I included ‘Political freedoms’ in my top six, which in the US only ranks 11th.
  • Age: I shared five of the Top six goals with people in my age group (world-wide). The one I did not check was ranked 4th (Better job opportunities). When you mouse over one of the goals, the display changes to highlight this goal in all columns:
Interactive Vote Analysis with highlighted goal

Interactive Vote Analysis with highlighted goal

  • Gender: Here I picked four of the Top five goals (did not include the ‘Better job opportunities’).
  • Education: I voted very similar to people with very high HDI (Human Development Index, a visualization of which we covered in a previous post) with five of the Top six.

From the above, it seems somewhat surprising that voters in the US did not ascribe a higher value to ‘Better job opportunities’, given how much economic values and topics like unemployment seem to dominate the media. That said, these votes should be a reflection about which goals are most valuable for making the world a better place – not just your own home country. Worldwide it seems that other, more fundamental goals are judged by voters in the US to be more important than ‘Better Job opportunities’.

Another chart on the results page is showing a heat map of the world countries based on how many votes have been submitted. I thought it was interesting that Ghana had submitted about twice as many votes as all of the US, and Nigeria about 7x as many. The country with most voters at this time is India, but not far ahead of Nigeria.


A fairly useless dynamic animation in this map is a map pin drop of four people who voted similarly to me. I found this too anecdotal to be of any real interest and downright annoying that I couldn’t turn it off. and just focus on the vote heat map. For example, the total number of votes should be displayed in the Legend. I vaguely remember that it was several hundred thousand from 194 countries prior to starting the survey, but couldn’t get that data to display again without clicking on the Vote Again:


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Posted by on September 21, 2013 in Education, Medical, Scientific


Trends in Health Habits across the United States

Trends in Health Habits across the United States

This week Scientific American published an interesting article about trends in health habits across the United States. The article includes both a large composite chart as well as a page with an interactive chart. Both are well done and a great example of using a visualization to help telling a story. I personally find the most useful part of the graphic to be the comparison column on the right with shades of color indicating degree of improvement (blue) or deterioration (red).

US health habits 1995 vs. 2010 (Source: Scientific American)

From the article:

Americans are imbibing alcohol and overeating more yet are smoking less (black lines in center graphs).

Some of the behaviors have patterns; others do not. Obesity is heaviest in the Southeast (2010 maps). Smoking is concentrated there as well. Excess drinking is high in the Northeast.

Comparing 2010 and 1995 figures provides the greatest insight into trends (maps, far right). Heavy drinking has worsened in 47 states, and obesity has expanded in every state. Tobacco use has declined in all states except Oklahoma and West Virginia. The “good” habit, exercise, is up in many places—even in the Southeast, where it has lagged.

A more detailed visual analysis is possible using the interactive version of these graphs on the related subpage Bad Health Habits are on the rise. Here one can compare up to three arbitrary states against top, median, and bottom performing states by health habit.

The following examples show tobacco use, exercise and obesity by state with line charts for the three arbitrarily selected states of Florida, California and Hawaii.

Tobacco Trend By State

Exercise Trend By State

Obesity Trend By State

Leading the exercise statistics are citizens in states offering attractive outdoor sports opportunities, like Oregon or Hawaii. Such correlation seems intuitive in both causal directions: People interested in exercise tend to move to those states with the most attractive outdoor sports. And people living in those states may end up exercising more due to the opportunity.

When looking at the average trend line, exercise seems to have leveled off after a bump in the early 2000’s, whereas the decline in smoking over the last decade continues unabated.

15 years is half a generation. During that time, Americans have in almost every state smoked less, exercised more in many states, but obesity is sharply on the rise in every state! From a health and policy debate the latter seems to be the most alarming trend. Most people want the next generation to be better off than the previous one. This has to some extent been true with wealth, at least until the great recession of 2008. But these data show that at population levels, more wealth is not necessarily more health.

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Posted by on October 19, 2012 in Medical


Software continues to eat the world

Software continues to eat the world

One year ago Marc Andreessen, co-founder of Netscape and venture capital firm Andreessen-Horowitz, wrote an essay for the Wall Street Journal titled “Why Software Is Eating The World“. It is interesting to reflect back to this piece and some of the predictions made back at a time when Internet company LinkedIn had just gone public and Groupon was just filing for an IPO.

Andreessen’s observation was simply this: Software has become so powerful and computer infrastructure so cheap and ubiquitous that many industries are being disrupted by new business models enabled by that software. Examples listed were books (Amazon disrupting Borders), movie rental (NetFlix disrupting Blockbuster), music industry (Pandora, iTunes), animation movies (Pixar), photo-sharing services (disrupting Kodak), job recruiting (LinkedIn), telecommunication (Skype), video-gaming (Zynga) and others.

On the infrastructure side one can bolster this argument by pointing at the rapid development of new technologies such as cloud computing or big data analytics. Andreessen gave one example of the cost of running an Internet application in the cloud dropping by a factor of 100x in the last decade (from $150,000 / month in 2000 using LoudCloud to about $1500 / month in 2011 using Amazon Web Services). Microsoft now has infrastructure with Windows Azure where procuring an instance of a modern server at one (or even multiple) data center(s) takes only minutes and costs you less than $1 per CPU hour.

Likewise, the number of Internet users has grown from some 50 million around 2000 to more than 2 billion with broadband access in 2011. This is certainly one aspect fueling the enormous growth of social media companies like Facebook and Twitter. To be sure, not every high-flying startup goes on to be as successful after its IPO. Facebook trades at half the value of opening day after three months. Groupon trades at less than 20% of its IPO value some 9 months ago. But LinkedIn has sustained and even modestly grown its market capitalization. And Google and Apple both trade near or at their all-time high, with Apple today at $621b becoming the most valuable company of all time (non inflation-adjusted).

The growing dominance and ubiquitous reach of software shows in other areas as well. Take automobiles. Software is increasingly been used for comfort and safety in modern cars. In fact, self-driving cars – once the realm of science fiction such as flying hover cars – are now technically feasible and knocking on the door of broad industrial adoption. After driving 300.000 miles in test Google is now deploying its fleet of self-driving cars for the benefit of its employees. Engineers even take self-driving cars to the racetracks, such as up on Pikes Peak or the Thunderhill raceway. Performance is now at the level of very good drivers, with the benefit of not having the human flaws (drinking, falling asleep, texting, showing off, etc.) which cause so many accidents. Expert drivers still outperform the computer-driven cars. (That said, even human experts sometimes make mistakes with terrible consequences, such as this crash on Pikes Peak this year.) The situation is similar to how computers got so proficient at chess in the mid-nineties that finally even the world champion was defeated.

In this post I want to look at some other areas specifically impacting my own life, such as digital photography. I am not a professional photographer, but over the years my wife and I have owned dozens of cameras and have followed the evolution of digital photography and its software for many years. Of course, there is an ongoing development towards chips with higher resolution and lenses with better optic and faster controls. But the major innovation comes from better software. Things like High Dynamic Range (HDR) to compensate for stark contrast in lighting such as a portrait photo against a bright background. Or stitching multiple photos together to a panorama, with Microsoft’s PhotoSynth taking this to a new level by building 3D models from multiple shots of a scene.

One recent innovation comes in the form of the new Sony RX100 camera, which science writer David Pogue raved about in the New York Times as “the best pocket camera ever made”. My wife bought one a few weeks ago and we both have been learning all it can do ever since. Despite the many impressive features and specifications about lens, optics, chip, controls, etc. what I find most interesting is the software running on such a small device. The intelligent Automatic setting will decide most settings for your everyday use, while one can always direct priorities (aperture, shutter, program) or manually override most aspects. There are a great many menus and it is not trivial to get to use all capabilities of this camera, as it’s extremely feature-rich. Some examples of the more creative software come in modes such as ‘water color’ or ‘illustration’. The original image is processed right then and there to generate effects as if it was a painting or a drawing. Both original and processed photo are stored on the mini-SD card.

Flower close-up in ‘illustration’ mode

One interesting effect is to filter to just the main colors (Yellow, Red, Green, Blue). Many of these effects are shown on the display, with the aperture ring serving as a flexible multi-functional dial for more convenient handling with two hands. (Actually, the camera body is so small that it is a challenge to use all dials while holding the device; just like the BlackBerry keyboard made us write with two thumbs instead of ten fingers.) The point of such software features is not so much that they are radically new; you could do so with a good photo editing software for many years. The point is that with the ease and integration of having them at your fingertips you are much more likely to use them.

Example of suppressing all colors except yellow

The camera will allow registering of faces and detect those in images. You can set it up such that it will take a picture only when it detects a small/medium/large smile on the subject being photographed. One setting allows you to take self-portrait, with the timer starting to count down as soon as the camera detects one (or two) faces in the picture! It is an eerie experience when the camera starts to “understand” what is happening in the image!

There is an automatic panorama stitching mode where you just hold the button and swipe the camera left-right or up-down while the camera takes multiple shots. It automatically stitches them into one composite, so no more uploading of the individual photos and stitching on the computer required.

Beach panorama stitched on the camera using swipe-&-shoot

I have been experimenting with panorama photos since 2005 (see my collection or my Panoramas from the Panamerican Peaks adventure). It’s always been somewhat tedious and results were often mixed (lens distortions, lighting changes sun vs. cloud or objects moving during the individual frames, not holding the camera level, skipping a part of the horizon, etc.) despite crafty post-processing on the computer with image software. I have read about special 360 degree lenses to take high-end panoramas, but who wants to go to those lengths just for the occasional panorama photo? From my experience, nothing moves the needle as much as the ease and integration of taking panoramas right in the camera as the RX100 does.

Or take the field of healthcare. Big Data, Mobility and Cloud Computing make possible entirely new business models. Let’s just look at mobility. The smartphone is evolving into a universal healthcare device for measuring, tracking and visualizing medical information. Since many people have their smartphone with them at almost all times, one can start tracking and analyzing personal medical data over time. And for almost any medical measurement, “there is an app for that”. One interesting example is this optical heart-rate monitor app Cardiio for the iPhone. (Cardio + IO ?)

Screenshots of Cardiio iPhone app to optically track heart rate

It is amazing that this app can track your heart rate just by analyzing the changes of light reflected from your face with its built-in camera. Not even a plug-in required!

Another system comes from Withings, this one designed to turn the iPhone into a blood pressure monitor. A velcro sleeve with battery mount and cable plugs into the iPhone and an app controls the inflation of the sleeve, the measurement and some simple statistics.

Blood pressure monitor system from Withings for iPhone

Again, it’s fairly simple to just put the sleeve around one upper arm and push the button on the iPhone app. The results are systolic and diastolic blood pressure readings and heart rate.

Sample blood pressure and pulse measurement

Like many other monitoring apps this one also keeps track of the readings and does some simple form of visual plotting and averaging.

Plot of several blood pressure readings

There is also a separate app which will allow you to upload your data and create a more comprehensive record of your own health over time. Withings provides a few other medical devices such as scales to add body weight and body fat readings. The company tagline is “smart and connected things”.

One final example is an award-winning contribution from a student team from Australia called Stethocloud. This system is aimed at diagnosing pneumonia. It is comprised of an app for the iPhone, a simple stethoscope plug-in for the iPhone and on the back-end some server-based software analyzing the measurements in the Windows Azure cloud according to standards defined by the World Health Organization. The winning team (in Microsoft’s 2012 Imagine Cup) built a prototype in only 2 weeks and had only minimal upfront investments.

StethoCloud system for iPhone to diagnose pneumonia

This last example perhaps illustrates best the opportunities of new software technologies to bring unprecedented advances to healthcare – and to many other fields and industries. I think Marc Andreessen was spot on with his observation that software is eating the world. It certainly does in my world.

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Posted by on August 20, 2012 in Industrial, Medical, Socioeconomic


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Futuristic TouchScreen Visualization

Futuristic TouchScreen Visualization

Glass manufacturer Corning has published the second YouTube video in its series “A Day Made of Glass”. It provides a glimpse into the future of ubiquitous touchscreen glass displays, from the car dashboard to the kitchen refrigerator and wall-to-wall home display, the large school community table to the medical laboratory, even the glass wall in an outdoor theme park.

Corning Day Of Glass 2

Mashable writes in its story about the video that it “will blow your mind”. Hyperbole aside, it is worth watching (click on image above). The script goes through a typical day and shows various display applications; then it pauses the scenes and mentions the underlying technological challenges and whether the depicted displays are possible and feasible with today’s technology. From the video:

“Of course, this is not just a story about glass. It’s a story about a shift in the way we will communicate and use technology in the future. It’s a story about ubiquitous displays, open operating systems, shared applications, cloud media storage and unlimited bandwidth. We know there are many obstacles to be overcome before what we’ve just seen will become an attainable, reliable reality. But at Corning, we believe in this vision – and we are not waiting.”

Besides being a great corporate promotional piece, the 11 min video is a great example of how interactive, even immersive visualizations can change how we consume and interact with information and with one another.
Apple created a video back in 1987 titled “Knowledge Navigator” which seemed similarly futuristic at the time. Today, 25 years later, the iPad is in common use. Interactive touch screens have become the norm for smart phones since Apple launched the iPhone in 2007, just 5 years ago. Larger form factors exist, but are still expensive to build.

Regardless of how long it will take for touch screen displays to get bigger and become ubiquitous, the notion of interactive data visualization will only become more valuable.

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Posted by on February 5, 2012 in Industrial, Medical, Recreational, Scientific


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Nonlinearity in Growth, Decay and Human Mortality

Nonlinearity in Growth, Decay and Human Mortality

Processes of Growth and Decay abound in natural and economic systems. Growth processes determine biological structure and pattern formation, selection of species or ideas, the outcome of economic competition and of savings in financial portfolios. In this post we will examine a few different types of quantitative growth / decay and their qualitatively different outcomes.


In the media we often hear about nonlinear, exponential, or explosive growth as popular references to seemingly unstoppable increases. Buzzwords like “tipping point” or “singularity” appear on book titles and web sites. Mathematical models can help analytical understanding of such dynamic processes, while visualization can support a more intuitive understanding.

Let’s look three different growth processes: Linear, exponential, and hyperbolic (rows below) by specifically considering three different quantities (columns below):
The absolute amount (as a function of time),
the absolute rate of increase (derivative of that function), and
the relative rate of increase (relative to the amount)

Amounts, Rates, and Relative Rates of three growth processes: Linear, Exponential, Hyperbolic

Linear growth (blue lines) is the result of a constant rate or increment per time interval. The relative rate (size of increment in relation to existing quantity) is decreasing to zero.

Exponential growth (red lines) is the result of a linearly growing rate or increment per time interval. The relative rate is a constant. Think accrual of savings with fixed interest rate. Urban legend has it that Albert Einstein once declared compound interest – an exponential growth process – to be “the most powerful force in the universe”. Our intuition is ill-suited to deal properly with exponential effects, and in many ways it seems hard to conceive of even faster growth processes. However, even with exponential growth it takes an infinite time to reach an infinitely large amount.

Hyperbolic growth (brown lines) is the result of a quadratically growing rate. In this type of growth even the relative rate is increasing. This can be caused by auto-catalytic effects, in other words, the larger the amount, the larger the growth of the rate. As a result, such growth leads to infinite values at a finite value of t – also called a discontinuity or singularity.

When multiple entities grow and compete for limited resources, their growth will determine the outcome as a distribution of the resource as follows:

  • Linear growth leads to coexistence of all competitors; their ratios determined by their linear growth rates.
  • Exponential growth leads to reversible selection of a winner (with the highest relative growth rate). Reversible since a competitor with a higher relative growth rate will win, regardless of when it enters the competition.
  • Hyperbolic growth leads to irreversible selection of a winner (first to dominate). Irreversible since the relative growth rate of the dominant competitor dwarfs that of any newcomer.

Such processes have been studied in detail in biology (population dynamics, genetics, etc.) It’s straightforward to imagine the combination of random fluctuations, exponential (or faster) growth and ‘Winner-take-all’ selection as the main driving processes of self-organized pattern formation in biology, such as in leopard spots or zebra stripes, all the way to the complex structure-formation process of morphogenesis and embryology.

Yet such processes tend to also occur in economics. For example, the competition for PC operating system platforms was won by Microsoft’s Windows due to the strong advantages of incumbents (applications, tools, developers, ecosystem, etc.) Similar effects can be seen with social networks, where competitors (like FaceBook) become disproportionately stronger as a result of the size of their network. I suspect that it also plays a central role in the evolution of inequality, which can be viewed as the dynamic formation of structure (viewed as the unequal allocation of wealth across a population).

Two popular technology concepts owe their existence to nonlinear growth processes:

  • Exponential Growth: The empirical Moore’s Law states that computer power doubles every 18 months or so (similar for storage capacity, transistors on chips and network bandwidth). This allows us to forecast fairly accurately when machines will have certain capacities which seem unimaginable only a few decades earlier. For example, computer power increases by a factor of 1000 in only 15 years, or a million-fold in 30 years or the span of just one human generation!
  • Hyperbolic Growth: Futurist Ray Kurzweil has observed that the doubling period of many aspects of our knowledge society is shrinking. From this observation of an “ever-accelerating rate of technological change” he concludes in his latest book that “The Singularity Is Near“, with profound technological and philosophical implications.

In many cases, empirical growth observations and measurements can be compared with mathematical models to either verify or falsify hypothesis about the underlying mechanisms controlling the growth processes. For example, world population growth has been tracked closely. To understand the strong increase of world population as a whole over the last hundred years or so one needs to look at the drivers (birth and mortality rates) and their key influencing factors (medical advances, agriculture). Many countries still have high birth rates, while medical advances and better farming methods have driven down the mortality rates. As a result, population has grown exponentially for many decades. (See also the wonderful 2min video visualization of this concept linked to from the previous post on “7 Billion“.) Short of increasing the mortality rate, it is evident that population stabilization (i.e. reduction of growth to zero) can only be achieved by reducing the birth rate. This in turn influences the policy debates, for example to empower women so they have less children (better education and economic prospects, access to contraception, etc.). Here is a graphic on world population growth rates:

Population growth rates in percent (source: Wikipedia, 2011 estimates)

Compare this to the World maps showing population age structure in the Global Trends 2025 post. There is a strong correlation between how old a population is and how high the birth rates are. (Note Africa standing out in both graphs.)


Conversely one can study processes of decay or decline, again with qualitatively different outcomes for given rates of decline such as linear or exponential. One interesting, mathematically inspired analysis related to decay processes comes from the ‘Gravity and Levity’ Blog in the post “Your body wasn’t built to last: a lesson from human mortality rates“. The article starts out with the observation that our likelihood of dying say in the next year doubles every 8 years. Since the mortality rate is increasing exponentially, the likelihood of survival is decreasing super-exponentially. The empirical data matches the rates forecast by the Gompertz Law of mortality almost perfectly.

Death and Survival Probability in the US (Source: Wolfram Alpha)

If the death rate were to grow exponentially – i.e. with a fixed increase per time interval – the resulting survival probability would follow an exponential distribution. If, however, the death rate is growing super-exponentially – i.e. with a doubling per fixed time interval – the survival probability follows a Gompertz distribution.

Lets look at a table similar to the above, this time contrasting three decay processes (rows below): Linear, Exponential, Super-Exponential. (Again we consider the amount, absolute rate and relative rate (columns below) as follows (constants chosen to match initial condition F[0] = 1):

Amounts, Rates, and Relative Rates of three decay processes: Linear, Exponential, Super-Exponential

The linear decay (blue lines) is characterized by a constant rate and reaches zero at a time proportional to the initial amount, at which the relative rate has a discontinuity.

The exponential decay (red lines) is characterized by a constant relative rate and thus leads to a steady, but long-lasting decay (like radio-active decay).

The super-exponential decay (brown lines) leads to the amount following a Gompertz distribution (matching the shape of the US survival probability chart above). For a while the decay rate remains very small near zero. Then it ramps up quickly and leads to a steep decline in the amount, which in turn reduces the rate down as well. The relative rate keeps growing exponentially.

The above linked article goes on to analyze two hypotheses on dominant causes of human death: The single lightning bolt and the accumulated lightning bolt model. If the major causes of death were singular or cumulative accidents (like lightning bolts or murders), the resulting survival probability curves would have a much longer tail. In other words, we would see at least some percentage of human beings living to ages beyond 130 or even 150 years. Since such cases are practically never observed, the underlying process must be different and the lightning bolt model is not able to explain human mortality.

Instead, a so called “cops and criminals” model is proposed based upon biochemical processes in the human body. “Cops” are cells who patrol the body and eliminate bad mutations (“criminals”) which when unchecked can lead to death. From the above post:

 The language of “cops and criminals” lends itself very easily to a discussion of the immune system fighting infection and random mutation.  Particularly heartening is the fact that rates of cancer incidence also follow the Gompertz law, doubling every 8 years or so.  Maybe something in the immune system is degrading over time, becoming worse at finding and destroying mutated and potentially dangerous cells.

Unfortunately, the full complexity of human biology does not lend itself readily to cartoons about cops and criminals.  There are a lot of difficult questions for anyone who tries to put together a serious theory of human aging.  Who are the criminals and who are the cops that kill them?  What is the “incubation time” for a criminal, and why does it give “him” enough strength to fight off the immune response?  Why is the police force dwindling over time?  For that matter, what kind of “clock” does your body have that measures time at all?

There have been attempts to describe DNA degradation (through the shortening of your telomeres or through methylation) as an increase in “criminals” that slowly overwhelm the body’s DNA-repair mechanisms, but nothing has come of it so far.  I can only hope that someday some brilliant biologist will be charmed by the simplistic physicist’s language of cops and criminals and provide us with real insight into why we age the way we do.

A web calculator for death and survival probability based on Gompertz Law can be found here.

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Posted by on January 12, 2012 in Medical, Scientific, Socioeconomic


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