Brian Naughton // Sun 02 August 2020 // Filed under stats // Tags cgm quantifiedself pymc3 numpyro jax

This post is a numpyro-based probabilistic model of my blood glucose data (see my original blogpost for necessary background). The task is, given my blood glucose readings, my heart rate data, and what I ate, can I figure out the contribution of each food to my blood glucose.

This is a classic Bayesian problem, where I have some observed data (blood glucose readings), a model for how food and heart rate influence blood glucose, and I want to find likely values for my parameters.

Normally I would use pymc3 for this kind of thing, but this was a good excuse to try out numpyro, which is built on JAX, the current favorite for automatic differentiation.

To make the problem a little more concrete, say your fasting blood glucose is 80, then you eat something and an hour later it goes to 120, and an hour after that it's back down to 90. How much blood glucose can I attribute to that food? What if I eat the same food on other day, but this time my blood glucose shoots to 150? What if I eat something else 30 minutes after eating this food so the data overlap? In theory, all of these situations can be modeled in a fairly simple probabilistic model.

Imports

I am using numpyro, and jax numpy instead of regular numpy. In most cases, jax is a direct replacement for numpy, but sometimes I need original numpy, so I keep that as onp.

#!pip install numpyro
import jax.numpy as np
from jax import random
from jax.scipy.special import logsumexp

import numpyro
import numpyro.distributions as dist
from numpyro.diagnostics import hpdi
from numpyro import handlers
from numpyro.infer import MCMC, NUTS

import numpy as onp
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt

import glob
import json
import io

from tqdm.autonotebook import tqdm
from contextlib import redirect_stdout

%config InlineBackend.figure_format='retina'

Some simple test data

Simple test data is always a good idea for any kind of probabilistic model. If I can't make the model work with the simplest possible data, then it's best to figure that out early, before starting to try to use real data. I believe McElreath advocates for something similar, though I can't find a citation for this.

To run inference with my model I need three 1D arrays:

  • bg_5min: blood glucose readings, measured every 5 minutes
  • hr_5min: heart rate, measured every 5 minutes
  • fd_5min: food eaten, measured every 5 minutes
def str_to_enum(arr):
    foods = sorted(set(arr))
    assert foods[0] == '', f"{foods[0]}"
    mapk = {food:n for n, food in enumerate(foods)}
    return np.array([mapk[val] for val in arr]), foods

bg_5min_test = np.array([91, 89, 92, 90, 90, 90, 88, 90, 93, 90,
                         90, 100, 108, 114.4, 119.52, 123.616, 126.89, 119.51, 113.61, 108.88, 105.11,
                         102.089, 99.67, 97.73, 96.18, 94.95, 93.96, 93.16, 92.53, 92.02, 91.62, 91.29, 91.03, 90.83, 90.66, 90.53,
                         90, 90, 90, 90, 90, 90, 90, 89, 90, 90, 89, 90, 90, 90, 90, 90, 90, 90, 90, 95, 95, 95, 95, 100])

_fd_5min_test = ['', '', '', '', '', 'food', '', '', '', '', '', '',
                 '', '', '', '', '', '', '', '', '', '', '', '',
                 '', '', '', '', '', '', '', '', '', '', '', '',
                 '', '', '', '', 'doof', '', '', '', '', '', '', '',
                 '', '', '', '', '', '', '', '', '', '', '', '', '']

fd_5min_test, fd_5min_test_key = str_to_enum(_fd_5min_test)
hr_5min_test = np.array([100] * len(bg_5min_test))

bg_5min_test = np.tile(bg_5min_test, 1)
fd_5min_test = np.tile(fd_5min_test, 1)
hr_5min_test = np.tile(hr_5min_test, 1)

print(f"Example test data (len {len(bg_5min_test)}):")
print("bg", bg_5min_test[:6])
print("heart rate", hr_5min_test[:6])
print("food as enum", fd_5min_test[:6])

assert len(bg_5min_test) == len(hr_5min_test) == len(fd_5min_test)
Example test data (len 60):
bg [91. 89. 92. 90. 90. 90.]
heart rate [100 100 100 100 100 100]
food as enum [0 0 0 0 0 2]

Read in real data as a DataFrame

I have already converted all my Apple Health data to csv. Here I process the data to include naive day and date (local time) — timezones are impossible otherwise.

df_complete = pd.DataFrame()

for f in glob.glob("HK*.csv"):
    _df = (pd.read_csv(f, sep=';', skiprows=1)
             .assign(date = lambda df: pd.to_datetime(df['startdate'].apply(lambda x:x[:-6]),
                                                      infer_datetime_format=True))
             .assign(day = lambda df: df['date'].dt.date,
                     time = lambda df: df['date'].dt.time)
          )

    if 'unit' not in _df:
        _df['unit'] = _df['type']
    df_complete = pd.concat([df_complete, _df[['type', 'sourcename', 'unit', 'day', 'time', 'date', 'value']]])

# clean up the names a bit and sort
df_complete = (df_complete.assign(type = lambda df: df['type'].str.split('TypeIdentifier', expand=True)[1])
                          .sort_values(['type', 'date']))
df_complete.sample(4)

I can remove a bunch of data from the complete DataFrame.

df = (df_complete
        .loc[lambda r: ~r.type.isin({"HeadphoneAudioExposure", "BodyMass", "UVExposure", "SleepAnalysis"})]
        .loc[lambda r: ~r.sourcename.isin({"Brian Naughton’s iPhone", "Strava"})]
        .loc[lambda r: r.date >= min(df_complete.loc[lambda r: r.sourcename == 'Connect'].date)]
        .assign(value = lambda df: df.value.astype(float)))
df.groupby(['type', 'sourcename']).head(1)
type sourcename unit day time date value
ActiveEnergyBurned Connect kcal 2018-07-08 21:00:00 2018-07-08 21:00:00 8.00
BasalEnergyBurned Connect kcal 2018-07-08 21:00:00 2018-07-08 21:00:00 2053.00
BloodGlucose Dexcom G6 mg/dL 2020-02-24 22:58:54 2020-02-24 22:58:54 111.00
DistanceWalkingRunning Connect mi 2018-07-08 21:00:00 2018-07-08 21:00:00 0.027
FlightsClimbed Connect count 2018-07-08 21:00:00 2018-07-08 21:00:00 0.00
HeartRate Connect count/min 2018-07-01 18:56:00 2018-07-01 18:56:00 60.00
RestingHeartRate Connect count/min 2019-09-07 00:00:00 2019-09-07 00:00:00 45.00
StepCount Connect count 2018-07-01 19:30:00 2018-07-01 19:30:00 33.00

I have to process my food data separately, since it doesn't come from Apple Health. The information was just in a Google Sheet.

df_food = (pd.read_csv("food_data.csv", sep='\t')
             .astype(dtype = {"date":"datetime64[ns]", "food": str})
             .assign(food = lambda df: df["food"].str.split(',', expand=True)[0] )
             .loc[lambda r: ~r.food.isin({"chocolate clusters", "cheese weirds", "skinny almonds", "asparagus"})]
             .sort_values("date")
            )
df_food.sample(4)
date food
2020-03-03 14:10:00 egg spinach on brioche
2020-03-11 18:52:00 lentil soup and bread
2020-02-27 06:10:00 bulletproof coffee
2020-03-02 06:09:00 bulletproof coffee

For inference purposes, I am rounding everything to the nearest 5 minutes. This creates the three arrays the model needs.

_df_food = (df_food
              .assign(rounded_date = lambda df: df['date'].dt.round('5min'))
              .set_index('rounded_date'))

_df_hr = (df.loc[lambda r: r.type == 'HeartRate']
            .assign(rounded_date = lambda df: df['date'].dt.round('5min'))
            .groupby('rounded_date')
            .mean())

def get_food_at_datetime(datetime):
    food = (_df_food
              .loc[datetime - pd.Timedelta(minutes=1) : datetime + pd.Timedelta(minutes=1)]
              ['food'])

    if any(food):
        return sorted(set(food))[0]
    else:
        return None

def get_hr_at_datetime(datetime):
    hr = (_df_hr
            .loc[datetime - pd.Timedelta(minutes=1) : datetime + pd.Timedelta(minutes=1)]
            ['value'])
    if any(hr):
        return sorted(set(hr))[0]
    else:
        return None


df_5min = \
(df.loc[lambda r: r.type == "BloodGlucose"]
   .loc[lambda r: r.date >= pd.datetime(2020, 2, 25)]
   .assign(rounded_date = lambda df: df['date'].dt.round('5min'),
           day = lambda df: df['date'].dt.date,
           time = lambda df: df['date'].dt.round('5min').dt.time,
           food = lambda df: df['rounded_date'].apply(get_food_at_datetime),
           hr = lambda df: df['rounded_date'].apply(get_hr_at_datetime)
          )
)


bg_5min_real = onp.array(df_5min.pivot_table(index='day', columns='time', values='value').interpolate('linear'))
hr_5min_real = onp.array(df_5min.pivot_table(index='day', columns='time', values='hr').interpolate('linear'))
fd_5min_real = onp.array(df_5min.fillna('').pivot_table(index='day', columns='time', values='food', aggfunc=lambda x:x).fillna('')).astype(str)
assert bg_5min_real.shape == hr_5min_real.shape == fd_5min_real.shape, "array size mismatch"

print(f"Real data (len {bg_5min_real.shape}):")
print("bg", bg_5min_real[0][:6])
print("hr", hr_5min_real[0][:6])
print("food", fd_5min_real[0][:6])
Real data (len (30, 288)):
bg [102. 112. 114. 113. 112. 111.]
hr [50.33333333 42.5        42.66666667 43.         42.66666667 42.5       ]
food ['' '' '' '' '' '']

numpyro model

The model is necessarily pretty simple, given the amount of data I have to work with. Note that I use "g" as a shorthand for mg/dL, which may be confusing. The priors are:

  • baseline_mu: I have a uniform prior on my "baseline" (fasting) mean blood glucose level. If I haven't eaten, I expect my blood glucose to be distributed around this value. This is a uniform prior from 80–110 mg/dL.
  • all_food_g_5min_mu: Each food deposits a certain number of mg/dL of sugar into my blood every 5 minutes. This is a uniform prior from 8–16 mg/dL per 5 minutes.
  • all_food_duration_mu: Each food only starts depositing glucose after a delay for digestion and absorption. This is a uniform prior from 45–100 minutes.
  • all_food_g_5min_mu: Food keeps depositing sugar into my blood for some time. Different foods may be quick spikes of glucose (sugary) or slow release (fatty). This is a uniform prior from 25–50 minutes.
  • regression_rate: The body regulates glucose by releasing insulin, which pulls blood glucose back to baseline at a certain rate. I allow for three different rates, depending on my heart rate zone. Using this simple model, the higher the blood glucose, the more it regresses, so it produces a somewhat bell-shaped curve.

Using uniform priors is really not best practices, but it makes it easier to keep values in a reasonable range. I did experiment with other priors, but settled on this after failing to keep my posteriors to reasonable values. As usual, explaining the priors to the model is like asking for a wish from an obtuse genie. This is a common problem with probabilistic models, at least for me.

The observed blood glucose is then a function that uses this approximate logic:

for t in all_5_minute_increments:
  blood_glucose[t] = baseline[t] # blood glucose with no food
  for food in foods:
    if t - time_eaten[food] > food_delays[food]: # then the food has started entering the bloodstream
      if t - (time_eaten[food] + food_delays[food]) < food_duration[food]: # then food is still entering the bloodstream
        blood_glucose[t] += food_g_5min[food]

  blood_glucose[t] = blood_glucose[t] - (blood_glucose[t] - baseline[t]) * regression_rate[heart_rate_zone_at_time(t)]

This model has some nice properties:

  • every food has only three parameters: the delay, the duration, and the mg/dL per 5 minutes. The total amount of glucose (loosely defined) can be easily calculate by multiplying food_duration * food_g_5_min.
  • the model only has two other parameters: the baseline glucose, and regression rate
MAX_TIMEPOINTS = 70 # effects are modeled 350 mins into the future only
DL = 288 # * 5 minutes = 1 day
SUB = '' # or a number, to subset
DAYS = [11]

%%time
def model(bg_5min, hr_5min, fd_5min, fd_5min_key):

    def zone(hr):
        if hr < 110: return "1"
        elif hr < 140: return "2"
        else: return "3"

    assert fd_5min_key[0] == '', f"{fd_5min_key[0]}"
    all_foods = fd_5min_key[1:]

    # ----------------------------------------------

    baseline_mu = numpyro.sample('baseline_mu', dist.Uniform(80, 110))

    all_food_g_5min_mu = numpyro.sample("all_food_g_5min_mu", dist.Uniform(8, 16))
    food_g_5mins = {food : numpyro.sample(f"food_g_5min_{food}",
                                          dist.Uniform(all_food_g_5min_mu-8, all_food_g_5min_mu+8))
                    for food in all_foods}

    all_food_duration_mu = numpyro.sample(f"all_food_duration_mu", dist.Uniform(5, 10))
    food_durations = {food : numpyro.sample(f"food_duration_{food}",
                                            dist.Uniform(all_food_duration_mu-3, all_food_duration_mu+3))
                      for food in all_foods}

    regression_rate = {zone : numpyro.sample(f"regression_rate_{zone}", dist.Uniform(0.7, 0.96))
                       for zone in "123"}

    all_food_delay_mu = numpyro.sample("all_food_delay_mu", dist.Uniform(9, 20))
    food_delays = {food : numpyro.sample(f"food_delay_{food}", dist.Uniform(all_food_delay_mu-4, all_food_delay_mu+4))
                   for food in all_foods}

    food_g_totals = {food : numpyro.deterministic(f"food_g_total_{food}", food_durations[food] * food_g_5mins[food])
                     for food in all_foods}

    result_mu = [0 for _ in range(len(bg_5min))]
    for j in range(1, len(result_mu)):
        if fd_5min[j] == 0:
            continue

        food = fd_5min_key[fd_5min[j]]
        for _j in range(min(MAX_TIMEPOINTS, len(result_mu)-j)):
            result_mu[j+_j] = numpyro.deterministic(
                f"add_{food}_{j}_{_j}",
                (result_mu[j+_j-1] * regression_rate[zone(hr_5min[j+_j])]
                 + np.where(_j > food_delays[food],
                            np.where(food_delays[food] + food_durations[food] - _j < 0, 0, 1) * food_g_5mins[food],
                            0)
                )
            )


    for j in range(len(result_mu)):
        result_mu[j] = numpyro.deterministic(f"result_mu_{j}", baseline_mu + result_mu[j])

    # observations
    obs = [numpyro.sample(f'result_{i}', dist.Normal(result_mu[i], 5), obs=bg_5min[i])
           for i in range(len(result_mu))]

def make_model(bg_5min, hr_5min, fd_5min, fd_5min_key):
    from functools import partial
    return partial(model, bg_5min, hr_5min, fd_5min, fd_5min_key)

Sample and store results

Because the process is slow, I usually only run one day at at time, and store all the samples in json files. It would be much better to run inference on all days simultaneously, especially since I have data for the same food on different days. Unfortunately, this turned out to take way too long.

assert len(bg_5min_real.ravel())/DL == 30, len(bg_5min_real.ravel())/DL

for d in DAYS:
    print(f"day {d}")
    bg_5min = bg_5min_real.ravel()[int(DL*d):int(DL*(d+1))]
    hr_5min = hr_5min_real.ravel()[int(DL*d):int(DL*(d+1))]
    _fd_5min = fd_5min_real.ravel()[int(DL*d):int(DL*(d+1))]
    fd_5min, fd_5min_key = str_to_enum(_fd_5min)

    #
    # subset it for testing
    #
    if SUB != '':
        bg_5min, hr_5min, fd_5min = bg_5min[-SUB*3:-SUB*1], hr_5min[-SUB*3:-SUB*1], fd_5min[-SUB*3:-SUB*1]

    open(f"bg_5min_{d}{SUB}.json",'w').write(json.dumps(list(bg_5min)))
    open(f"hr_5min_{d}{SUB}.json",'w').write(json.dumps(list(hr_5min)))
    open(f"fd_5min_key_{d}{SUB}.json",'w').write(json.dumps(fd_5min_key))
    open(f"fd_5min_{d}{SUB}.json",'w').write(json.dumps([int(ix) for ix in fd_5min]))

    rng_key = random.PRNGKey(0)
    rng_key, rng_key_ = random.split(rng_key)
    num_warmup, num_samples = 500, 5500

    kernel = NUTS(make_model(bg_5min, hr_5min, fd_5min, fd_5min_key))
    mcmc = MCMC(kernel, num_warmup, num_samples)
    mcmc.run(rng_key_)
    mcmc.print_summary()
    samples_1 = mcmc.get_samples()
    print(d, sorted([(float(samples_1[food_type].mean()), food_type) for food_type in samples_1 if "total" in food_type], reverse=True))
    print(d, sorted([(float(samples_1[food_type].mean()), food_type) for food_type in samples_1 if "delay" in food_type], reverse=True))
    print(d, sorted([(float(samples_1[food_type].mean()), food_type) for food_type in samples_1 if "duration" in food_type], reverse=True))

    open(f"samples_{d}{SUB}.json", 'w').write(json.dumps({k:[round(float(v),4) for v in vs] for k,vs in samples_1.items()}))

    print_io = io.StringIO()
    with redirect_stdout(print_io):
        mcmc.print_summary()
    open(f"summary_{d}{SUB}.json", 'w').write(print_io.getvalue())
day 11


sample: 100%|██████████| 6000/6000 [48:58<00:00,  2.04it/s, 1023 steps of size 3.29e-04. acc. prob=0.81]



                                             mean       std    median      5.0%     95.0%     n_eff     r_hat
                      all_food_delay_mu     10.39      0.29     10.40      9.95     10.86     10.32      1.04
                   all_food_duration_mu      9.22      0.20      9.22      8.93      9.51      2.77      2.28
                     all_food_g_5min_mu      9.81      0.37      9.78      9.16     10.32      5.55      1.44
                            baseline_mu     89.49      0.37     89.47     88.89     90.09      9.89      1.00
          food_delay_bulletproof coffee      7.59      0.86      7.51      6.37      8.98     23.44      1.02
      food_delay_egg spinach on brioche     13.75      0.41     13.92     13.04     14.26      4.81      1.08
              food_delay_milk chocolate      6.70      0.21      6.74      6.38      7.00     17.39      1.00
     food_delay_vegetables and potatoes     12.03      0.93     12.15     10.52     13.44     16.36      1.08
       food_duration_bulletproof coffee      9.92      1.36      9.72      8.27     12.09      2.72      2.68
   food_duration_egg spinach on brioche     11.42      0.34     11.42     10.94     11.93      2.51      2.59
           food_duration_milk chocolate      7.01      0.22      6.98      6.58      7.34     16.01      1.00
  food_duration_vegetables and potatoes      8.56      1.40      8.52      6.55     10.43      4.89      1.37
         food_g_5min_bulletproof coffee      2.45      0.38      2.41      1.86      3.01      7.07      1.58
     food_g_5min_egg spinach on brioche      7.38      0.33      7.39      6.86      7.92      9.65      1.36
             food_g_5min_milk chocolate     11.38      0.38     11.40     10.70     11.94     21.69      1.06
    food_g_5min_vegetables and potatoes     14.46      2.99     15.55      9.90     18.17     10.31      1.17
                      regression_rate_1      0.93      0.00      0.93      0.92      0.93     24.68      1.04
                      regression_rate_2      0.74      0.03      0.73      0.71      0.78      3.68      1.69
                      regression_rate_3      0.78      0.03      0.77      0.73      0.82      4.28      1.60

Plot results

Plotting the data in a sensible way is a little bit tricky. Hopefully the plot is mostly self-explanatory, but note that baseline is set to zero, the y-axis is on a log scale, and the x-axis is midnight to midnight, in 5 minute increments.

def get_plot_sums(samples, bg_5min, hr_5min, fd_5min_key):
    samples = {k: onp.array(v) for k,v in samples.items()}
    bg_5min = onp.array(bg_5min)
    hr_5min = onp.array(hr_5min)

    means = []
    for n in tqdm(range(len(bg_5min))):
        means.append({"baseline": np.mean(samples[f"baseline_mu"])})
        for _j in range(MAX_TIMEPOINTS):
            for food in fd_5min_key:
                if f"add_{food}_{n-_j}_{_j}" in samples:
                    means[n][food] = np.mean(samples[f"add_{food}_{n-_j}_{_j}"])

    plot_data = []
    ordered_foods = ['baseline'] + sorted({k for d in means for k, v in d.items() if k != 'baseline'})
    for bg, d in zip(bg_5min, means):
        tot = 0
        plot_data.append([])
        for food in ordered_foods:
            if food in d and d[food] > 0.1:
                plot_data[-1].append(round(tot + float(d[food]), 2))
                if food != 'baseline':
                    tot += float(d[food])
            else:
                plot_data[-1].append(0)
    print("ordered_foods", ordered_foods)
    return pd.DataFrame(plot_data, columns=ordered_foods)
for n in DAYS:
    print(open(f"summary_{n}{SUB}.json").read())
    samples = json.load(open(f"samples_{n}{SUB}.json"))
    bg_5min = json.load(open(f"bg_5min_{n}{SUB}.json"))
    hr_5min = json.load(open(f"hr_5min_{n}{SUB}.json"))
    fd_5min = json.load(open(f"fd_5min_{n}{SUB}.json"))
    fd_5min_key = json.load(open(f"fd_5min_key_{n}.json"))

    print("fd_5min_key", fd_5min_key)
    plot_data = get_plot_sums(samples, bg_5min, hr_5min, fd_5min_key)
    plot_data['real'] = bg_5min
    plot_data['heartrate'] = [hr for hr in hr_5min]

    baseline = {int(i) for i in plot_data['baseline']}
    assert len(baseline) == 1
    baseline = list(baseline)[0]
    log_plot_data = plot_data.drop('baseline', axis=1)
    log_plot_data['real'] -= plot_data['baseline']

    display(log_plot_data);

    f, ax = plt.subplots(figsize=(16,6));
    ax = sns.lineplot(data=log_plot_data.rename(columns={"heartrate":"hr"})
                                        .drop('hr', axis=1),
                      dashes=False,
                      ax=ax);
    ax.set_ylim(-50, 120);
    ax.set_title(f"day {n} baseline {baseline}");
    ax.lines[len(log_plot_data.columns)-2].set_linestyle("--");
    f.savefig(f'food_model_{n}{SUB}.png');
    f.savefig(f'food_model_{n}{SUB}.svg');

png

Total blood glucose

Finally, I can rank each food by its total blood glucose contribution. Usually, this matches expectations, and occasionally it's way off. Here it looks pretty reasonable: the largest meal by far contributed the largest total amount, and the milk chocolate had the shortest delay.

from pprint import pprint
print("### total grams of glucose")
pprint(sorted([(round(float(samples_1[food_type].mean()), 2), food_type) for food_type in samples_1 if "total" in food_type], reverse=True))
print("### food delays")
pprint(sorted([(round(float(samples_1[food_type].mean()), 2), food_type) for food_type in samples_1 if "delay" in food_type], reverse=True))
print("### food durations")
pprint(sorted([(round(float(samples_1[food_type].mean()), 2), food_type) for food_type in samples_1 if "duration" in food_type], reverse=True))
### total blood glucose contribution
[(123.52, 'food_g_total_vegetables and potatoes'),
 (84.24, 'food_g_total_egg spinach on brioche'),
 (79.69, 'food_g_total_milk chocolate'),
 (23.88, 'food_g_total_bulletproof coffee')]
### food delays
[(13.75, 'food_delay_egg spinach on brioche'),
 (12.03, 'food_delay_vegetables and potatoes'),
 (10.39, 'all_food_delay_mu'),
 (7.59, 'food_delay_bulletproof coffee'),
 (6.7, 'food_delay_milk chocolate')]
### food durations
[(11.42, 'food_duration_egg spinach on brioche'),
 (9.92, 'food_duration_bulletproof coffee'),
 (9.22, 'all_food_duration_mu'),
 (8.56, 'food_duration_vegetables and potatoes'),
 (7.01, 'food_duration_milk chocolate')]

Conclusions

It sort of works. For example, day 11 looks pretty good! Unfortunately, when it's wrong, it can be pretty far off, so I am not sure about the utility without imbuing the model with more robustness. (For example, note that the r_hat is often out of range.)

The parameterization of the model is pretty unsatisfying. To make the model hang together I have to constrain the priors to specific ranges. I could probably grid-search the whole space pretty quickly to get to a maximum posterior here.

I think if I had a year of data instead of a month, this could get pretty interesting. I would also need to figure out how to sample quicker, which should be possible given the simplicity of the model. With the current implementation I am unable to sample even a month of data at once.

Finally, here is the complete set of plots I generated, to see the range of results.

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Brian Naughton // Sun 19 April 2020 // Filed under health // Tags quantifiedself health cgm

Blood glucose control, and specifically how steady your blood glucose levels are after eating, is an important indicator of health. According to a paper from the Segal lab:

"Postprandial hyperglycemia is an independent risk factor for the development of TIIDM, cardiovascular disease, and liver cirrhosis and is associated with obesity, and enhanced all-cause mortality in both TIIDM and cancer."

In this paper they showed there was individual variation in response to foods, which they related to the microbiome and other features, and showed that dietary changes could improve blood glucose control. This work led to the publication of a fascinating book called The Personalized Diet, whose results can be summarized as "find out which foods spike your blood glucose and don't eat them".

There isn't that much other data out there on blood glucose control in non-diabetics. The other relevant paper I know of is a recent PLoS Biology paper from the Snyder group at Stanford. They also showed significant variation in how non-diabetics responsed to the same foods.

There is also an appealing, intuitive connection of blood glucose to cancer progression and prevention, which rests on the fact that cancer benefits from readily available energy sources in the blood.

I thought it was worth knowing my personal food response profile, so I wore a Dexcom G6 CGM for 30 days.


CGM

A Continuous Glucose Monitor (CGM) is a device that samples your blood glucose continuously. The technology has been around for a few years, but from what I understand, the latest iteration (Dexcom G6) is a pretty big advance over the G5 — mainly in size and accuracy — and is arguably more accurate than competitors like the Freestyle Libre. Dexcom is not a hugely well known company, but it is large (market cap of around $25B at the time of writing.)

The G6 is available by prescription only (I have never heard an explanation for why, but this is partially why we don't have useful preventive data for non-diabetics...) and the cost is approximately $10-20 per day without insurance. The G6 reads out blood glucose in mg/dL every 5 minutes, and transmits directly to an app on your smartphone.

I have done finger prick tests intermittently, and while that's inexpensive and pretty accurate, there are issues: specifically, it hurts and you can't do it often enough to really see granular responses to foods.

Applying the CGM

The process of applying the G6 is very simple, and surprisingly almost entirely painless (less painful than a finger prick). Each "sensor" (the part that samples blood glucose) comes with its own applicator, which inserts the sensor interstitially, surrounded by a large adhesive bandaid. The transmitter (the grey lozenge) then snaps into the sensor, and relays data back to your phone via bluetooth.

The G6 is only approved for use when applied to the abdomen, though many users apply it to the backs of their arms. Since I do not depend on the readings for anything critical, I can be a bit more relaxed about this part, so I stuck it to my arm. Overall, it's very unobtrusive, and with the exception of worrying about getting it wet in the shower, I mostly just forgot it was there.


Glucose readings

The G6 integrates with Apple Health, which helps a lot with data wrangling. For some pseudomedical reason the readout is delayed by three hours, but that's not a big deal. To get all my Apple Health data, I can just click the export data button on the Apple Health app, then convert from xml to csv using this handy in-browser converter.

Apple Health also includes data from my Garmin vivosport. The main datatypes here are steps, heart rate, and sleep data.


Get to the graphs

My main questions were: how does my blood glucose change with my diet, sleep, and exercise?

First, what was my average blood glucose over the 30 days? Surprisingly high. A fasting blood glucose reading of above 100 indicates prediabetes. I believe that a really good number would be hovering around 75-85 with food-induced spikes of 100-120. (Note the graph below includes all readings, fasting and non-fasting so it's not as bad as it may seem.)

over the course of the day

Here I show my average blood glucose over the day, and I have marked my estimated sleep and waking times from my Garmin data with grey lines (it's not terribly accurate). By 3am I am usually at a good fasting glucose number (~85) but during the day I have a pretty consistently high number (>100) that depends a lot on the foods I eat, and this can persist past midnight.

coffee spike

There's a clear spike when I wake up. Is that due to circadian rhythms, or morning coffee? These two charts show my glucose by time of day, and by time of first coffee (which varied +/- 45m). The two charts look almost the same, but time of day is a more consistent pattern than minutes after drinking coffee, so I don't think this is a coffee- or breakfast-specific effect.

Foods that spike my blood glucose

Over the 30 days, I took a photo of everthing I ate using an app (BiteSnap). This heatmap that shows when my glucose went high, and it's annotated with the foods I ate from 30 minutes to three hours before. The most intense red is due to an impossible burger (mainly the bun...)

blood glucose trajectories

After eating each food type, what does my blood glucose response look like? Some foods quickly spike (sugary foods like oatmeal with honey), some do not spike at all (fatty foods like chocolate mousse), and others contribute a large amount of blood glucose over time (carby foods like dutch crunch bread). One caveat here is that foods eaten in the evening (e.g., milk chocolate) appear to have lower spikes, but partially this is due to starting at a higher value after dinner. This effect is hard to account for except by manually binning breakfast, lunch, and dinner. The foods are sorted from highest mean increase over four hours to lowest.


Exercise can help drive blood glucose down

There have been a few publications on post-meal exercise and blood glucose. For example, a 2017 study found that exercise at 60% of VO2 max for 50 minutes was effective at driving down blood glucose. This squares with my own observations.

Anecdotally, I observed that being sedentary post-meal (<90bpm) led to a prolonged high-glucose plateau, zone 2 exercise (approximately 110-140pm) led to rapid post-meal glucose reduction — down to just below my typical fasting level after 45 to 60 minutes — and prolonged, higher intensity exercise (>140bpm) led to flat or increased glucose, I assume due to the physical stresses involved.

The charts below show my change in blood glucose over 30 minutes, at a given heart rate, starting at >110 (i.e., post-meal). The second chart shows only the subset of data where my blood glucose is going down; this is because post-meal you will hit 110 twice, on the way up and on the way down, and only the latter is really informative here. Unfortunately, I do not have enough data at higher heart rates to make much of a claim there.


Was this experiment worthwhile?

I didn't find too many unexpected responses to food (carbs are bad; greens, protein and fat are good), though the same food could produce quite different results on different days or different times of day. In a podcast, CGM enthusiast Peter Attia noted that after 3 years of CGM use he was still learning his patterns, and I believe he also recommends his patients collect a minimum of 90 days of CGM data.

Despite all that, this was probably the most useful health intervention I have done. I learned a bunch of actionable things:

  • my blood glucose is too high for too much of the day. At the very least, it would be good to have glucose levels go down to fasting level at bedtime and stay there all night. Therefore I have tried to stop eating late in the day.

  • bread triggered an especially bad response for me. It was not surprising that bread is bad, but the magnitude of the effect was. Some bready but fatty foods (butter-heavy deep dish pizza) were tolerated much better, thankfully.

  • post-meal, zone 1 or especially zone 2 exercise is a good way to modulate glucose levels. I now associate that food coma feeling with a spike of glucose that needs to be corrected with exercise. Even a short, brisk walk seems to help.

  • as you might expect, some foods, like bread and oatmeal, dropped way down my food pecking order, but less obviously I now know that some "treats" like dark chocolate mousse or almond flour cookies are fine to eat. Finding foods that strike the balance between tasting sweet (unsavory?) without triggering glucose spikes is a fun diversion.

The graphs posted here are the highlights, but I did a bunch of other analyses. The most interesting is a pymc3/numpyro probabilistic model of glucose response that works reasonably well. The main purpose of this model is try to explain each reading by a mixture of contributions from time-of-day, food, etc. I will probably publish this as a separate post.

I plan to do this exercise again in six months or so, to see if my interventions are generating better numbers. In general it's pretty simple, Michael Pollan and the paleo people were right: eat clean unprocessed food, not too much....


ADDENDUM: CGM-approved desserts

Almond flour chocolate chip cookies:

  • 6 Tbs. butter, softened
  • 2 Tbs. coconut oil
  • 1/4 cup brown sugar, packed
  • 1 tsp. vanilla extract
  • 1 large eggs
  • 1/4 tsp. baking soda
  • 1/4 tsp. salt
  • 1 1/2 cups almond flour
  • 1 cup dark chocolate chips (we use Pascha 85%)

Preheat oven to 350°F. Line a baking sheet with parchment paper (or use a Silpat).

In the bowl of a stand mixer, cream together the butter, coconut oil, and brown sugar. Add the vanilla and eggs, mixing until incorporated.

Mix in the baking soda and salt. Add the almond flour, 1 cup at a time, beating well after each addition. Fold in the chocolate chips and walnuts with a wooden spoon.

Form the dough into ~2-3 tablespoon rounds and place on the lined baking sheet about 3 inches apart (~24 cookies). Flatten them a bit with the spatula, they do not flatten very much while baking. Bake for 13 minutes, or until golden brown around edges. Cool and enjoy! Cookies will be fragile until completely cooled.

Adapted from: https://meaningfuleats.com/almond-flour-chocolate-chip-cookies-grain-free/

Almond flour brownies:

  • 100 g 85%+ chocolate bar, broken into squares (we use Lindt 90%)
  • 8 Tbs. unsalted butter
  • 1/4 cup granulated sugar
  • 2 large eggs
  • 1 teaspoon vanilla extract
  • 1/2 teaspoon salt
  • 1 cup almond flour

Preheat oven to 350°F. Line an 8×8-inch square baking pan with foil to use as a sling for removing the brownies. Butter the foil or spray it with a nonstick cooking spray.

Melt chocolate and butter together in the microwave in 30-second bursts, stirring between each. When only a couple unmelted bits remain stir to finish melting. Whisk in sugar, then eggs, one at a time, then vanilla and salt. Stir in almond flour with a spoon or flexible spatula. Scrape batter into prepared pan, spread until even. Bake for 25 minutes, or until a toothpick inserted into the center comes out batter-free.

Let cool 5 min in the pan, then lift out gently using the foil. Brownies will be fragile until completely cooled.

Adapted from: https://smittenkitchen.com/2012/08/my-favorite-brownies/

Breakfast cookies:

  • 3 large ripe bananas
  • 1 tsp. vanilla extract
  • 1/4 cup coconut oil, melted
  • 2 cups rolled oats
  • 2/3 cup almond meal
  • 2/3 cup coconut (finely shredded & unsweetened)
  • 1 tsp. cinnamon
  • 1/2 tsp. kosher salt
  • 1 tsp. baking powder
  • 7 ounces very dark chocolate chips, or a chopped very dark chocolate bar

Preheat oven to 350°F.

Thoroughly mash the bananas in a large bowl. Add the vanilla extract and coconut oil, and stir to combine. Add the oats, almond meal, and shredded coconut, and mix well to fully moisten the dry ingredients. Add the cinnamon, salt, and baking powder, and mix until well combined. Fold in the chocolate chunks/chips.

Drop dollops of the dough, each about 2 teaspoons in size, an inch apart, onto a parchment (or Silpat) lined baking sheet. A cookie scoop works very well for this. Bake for about 20 minutes, until lightly browned.

Adapted from: https://www.101cookbooks.com/healthy-cookie-recipe/

Chocolate Mousse

https://chocolatechocolateandmore.com/easy-whipped-dark-chocolate-mousse/ but modified with with 1/3rd the sugar and using (Alter Eco) 85% chocolate.

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