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Emanated from the idea of reinvestigating ancient medical system of Ayurveda—Traditional Indian Medicine (TIM), our recent study had shown significant applications of analysis of arterial pulse waveforms for non-invasive diagnosis of cardiovascular functions. Here we present results of further investigations analyzing the relation of pulse-characteristics with some clinical and pathological parameters and other features that are of diagnostic importance in Ayurveda.

Pulse-examination for diagnosis/prognosis is an important component of traditional Chinese and Indian medical system. Considering that the traditional method of pulse-examination relies upon sensation of the pulse by the doctor, standardization and validation by modern scientific approaches poses formidable challenge in reviving this ancient non-invasive and comprehensive method of diagnosis/prognosis of diseases and psychosomatic disorders. Instrumentation based standardized techniques of pulse-signal recording offer feasible solution in this regard. Digitization of the signal makes room for wide-range of computational analysis and modeling and validation of this method. Our recently reported and tested algorithm of efficient filtering of noise and base-line drift made significant contribution in augmenting this potential [

In our most recent paper we had given a review of important approaches that re-establish and provide novel applications of the ancient Indian and Chinese techniques of diagnosis/prognosis using pulse-examination [

In the present paper we consider further study on analysis of spectral parameters of the radial arterial pulse (hereafter mostly referred as pulse) and certain clinical, physiological and pathological features that are crucial to Ayurvedic method of diagnosis/prognosis of ailments/disorders of the mind-body system.

The features and data-set are described in the next Section. Analysis and results are presented in Section 3. Significance of results and scope are highlighted in the last Section.

The dataset used in our earlier study on pulse morphology variation [

For nearly 65% of this sample there also were observations provided for all of the following features.

TIM Diagnostic Features: Age (years), Body-weight (kg.), BP (Diastolic, Systolic), Pulse-rate (per min.), Bala, Guna-1, Guna-2, Guna-3, Depth, Doshas.

The features Bala, etc., are specific to Ayurvedic pulse-examination.

Bala indicates perceived force of artery. It has two categories: Balwaan—fullness of artery (pulse coming up with force hence easily palpable); or Ksheen—weakness or diminished flow of artery (pulse needs deep palpation to be felt by the Physician).

Gunas indicate three specific characters of pulse as sensed by the Ayurvedic Physicians. Each has two categories. Guna-1: sthool (broadness usually accompanied by heaviness) or sooksham (subtlety, does not rise against the entire midst of palpating surface of fingertips); Guna-2: guru (heaviness in movement) or laghu (lightness in movement); Guna-3: mridu (soft in touch) or kathin (hard in touch).

Depth identifies superficial or deep status of the pulse: uttaan (palpable easily upon superficial touch) or gambheer (not palpable easily, palpable upon deep touch).

Doshas in Ayurvedic terminology are supposed to indicate natural tendency (Prakrati) of the functional (physiological and biochemical including metabolic) state of the mind-body system [

Hereafter we will refer the above-described TIM diagnostic features simply as “Features”. In the data given to us, the features Bala and Depth were described as categorical so, as per standard practice in statistical quantitative representation, each was converted into two-dimensional variables: namely balwaan = (0, 1); ksheen = (1, 0); & uttaan = (0, 1); gambheer = (1, 0). Other qualitative features were provided in the data set as scaled integer weights on a scale 0 to 6 assigned by the Ayurvedic Physicians.

We had carried out multivariate hierarchical clustering of the given data on above-described features. The results showed good relevance of the features in terms of distinct clusters of different health conditions and disease types [

For further insight into the covariance structure of the features in different classes of healthy and diseases cases, we have also conducted Principal Component Analysis [

Following results were found in terms of loadings for first eight principal components, which explained nearly 92% of the variation in the data.

Features measuring pulse properties and doshas were found most important factors in representing the variation in data set. Interestingly, Bala = (0, 1) and Depth = (0, 1) depth were dominating in this respect among the males as well as females. The features BP, Age and body-weight were found to play above-average role in this respect. However Guna-2 and Pitt were dominant features only in Males and Bala = (1, 0) was important in Females. Vaat and Kaph were found to have comparable impact on both males and females.

Disease-wise Roles: Bala, and Depth and Vaat were found prominent in distinguishing the subgroup of patients suffering from Hypertension (HT) and/or Ischemic Heart Disease (IHD) from other subjects. Guna-2 had partially significant role in this respect. In case of Diabetes Mellitus (DM), the features Bala, Depth, and body-weight were prominent. Though, less prominent, Guna-1 & Guna-2 also had significant role in classifying DM from others.

Further relevance of the features with respect to pulse waveform was found in terms of Spectral Analysis of the pulse signal records. Plots of power spectral density (PSD) of pulse-signals were found to have distinct patterns in certain diseases [

Accuracy of PSD-based estimation of Vaat, Pitt, and Kaph levels vis-à-vis the integer-weights assigned by the experts for these features of doshas, was found about 72% on an average.

Harmonic analysis also led to significant inference rules, with statistical confidence above 90%, in terms the ratio (technically called the 5^{th} K-ratio; denoted) of power energy ratio of the first five harmonics. These rules provide potential applications for non-invasive and quick diagnosis of cardio-vascular risks, if any [

Fisher’s Ratio (FR) is a likelihood ratio of cumulative eperiodogram of a signal (arterial pulse signal in our study). Our recently reported research had shown significant application of FR in—(i) classifying the abnormal and normal morphology-patterns in any selected time-interval of the record; (ii) accurate detection of morphological variations over time that were found to have important role in diagnosis/prognosis of cardiac disorders [

In view of these findings, the main focus of our present study is to analyze the relationship between the FR and the TIM Diagnostic Features.

Typical PSD of a Vaatdosha dominance case. Here the peak is highest in the frequency range (LF) of Vaat

The following inferences for FR values for specific portion of the pulse waveform are statistically significant. Here, the Min and Max are of the FR values for 5^{th} to 45^{th} period of the pulse signal records.

(i) if Gunas = (2, 0, 0), a sufficient condition for pulse strength = “balwaan” is:

FR_min = ~ 11.34 and FR_max = ~14.107

(ii) if Gunas = (2, 0, 0) a sufficient condition for pulse strength = “ksheen” is:

FR_min = ~9.34 and FR_max = ~11.27

For Female subjects having Ischemic Heart Disease (IHD), Diabetes Mellitus (DM), and/or Hypertension (HT):

(i) if Gunas = (1, 0, 0) & pulse strength = “ksheen”, a necessary and sufficient condition for pulse Depth = “uttaan” is:

FR_min = ~10.7 and FR_max = ~14.11

(ii) if Gunas = (1, 0, 0) & nadi strength = “ksheen”, a sufficient condition for pulse Depth = “gambheer” is:

FR_min = ~13.06 and FR_max = ~18.04

Our analysis for FR for the entire pulse record from 5^{th} period onwards, shows distinct range of values of FR for different intervals or categories of Feature values. We have also found distinct probability curves of FR for different categories (intervals) of several features that are regarded important in pulse-based diagnostic practices of Ayurveda. This indicates significant relationship between different Features and FR. We have analyzed male and female data separately for homogeneity of individual samples which was necessary for substantial (>90%) statistical confidence in the statistical estimates.

The probability density function of FR estimated using the empirical plots of relative frequency in our data under different intervals/categories of certain features show distinct types or parameters. Significant results are shown in the

. Significant results for the probability distribution of FR for data set of females

Feature Interval/Category | Approx. pdf of FR | Feature Interval/Category | Approx. pdf of FR |
---|---|---|---|

Sys. BP < 100 Sys. BP > 110 | Bi-modal: peaks at FR = 10.5 & FR = 14.5 Uniform [8, 16] | Depth = uttaan Depth = gambheer | Truncated N (11.5, 9) Gamma: k ≈ 14; α ≈ 0.8 |

Guna_1 < 2 Guna_1 = 2 Guna_1 > 2 | Gamma: k ≈ 14; α ≈ 0.84 Truncated Normal in the interval [6.5, 12.5); Cumulative of Uniform in [12.5, 17.5] (Figure 2) Gamma: k ≈ 12; α ≈ 0.9 | Vaat ≤ 1 Vaat > 2 | Gamma: k ≈ 18; α ≈ 0.6 Bi-modal: peaks at FR = 11 & FR = 16 |

Guna_2 = 0 Guna_2 = 1 | Truncated N (11.6, 8.6) Gamma in interval [6.5, 16.5); triangular in [16.5, 21.5] | Pitt = 1 Pitt > 1 | Truncated N (11.7, 7.7) Truncated N (10.9, 6.3) |

Bala = balwaan Bala = ksheen | Gamma: k ≈ 13; α ≈ 0.9 Truncated N (11.6, 3.8) | Kaph = 0 Kaph > 0 | Truncated N (11.4, 9.5) Truncated N (11, 1.8) |

. Significant results for the probability distribution of FR for data set of males

Feature Interval/Category | Approx. pdf of FR | Feature Interval/Category | Approx. pdf of FR |
---|---|---|---|

Sys. BP < 110 Sys. BP Î [110, 125] Sys. BP > 125 | Gamma: k ≈ 13; α ≈ 0.9 Bi-modal: peaks at FR = 9 & FR = 14 (Figure 3) Uniform [8, 17.5] | Depth = uttaan Depth = gambheer | Truncated N (11.4, 5.4) Gamma: k ≈ 10; α ≈ 1 |

Guna_1 < 2 Guna_1 = 2 Guna_1 > 2 | Gamma: k ≈ 14; α ≈ 0.85 Gamma: k ≈ 15; α ≈ 0.71 Cumulative of Uniforms in [5, 11) & [11, 19]. | Vat ≤ 1 Vat Î [2, 3] Vaat > 4 | Gamma: k ≈ 13 ; α ≈ 0.9 Truncated N (11, 6.7) Uniform [9.5, 15.5] |

Guna_2 = 0 Guna_2 = 1 | Truncated N(11.3, 7.7) Bi-modal: peaks at FR = 10 & FR = 16 | Pitt ≤ 1 Pitt > 2 | Truncated N (11.3, 7.4) Combination of two truncated Normals in intervals [6.5, 11.5) & [11.5, 21.5] |

Bala = balwaan Bala = ksheen | Gamma: k ≈ 14; α ≈ 0.78 Truncated N (12, 8.6) | Kaph = 0 Kaph > 0 | Uniform [7.5, 17.5] Truncated N (11.4, 4.5) |

Relative frequency (shown along the vertical axis) of different values (intervals shown along the horizontal axis) of FR for pulse records of females who had Guna_1 = 2

Relative frequency (shown along the vertical axis) of different values (intervals shown along the horizontal axis) of FR for pulse of males whose systolic BP was between 110 and 125 when their pulse signals were recorded

Renewed interest in the non-invasive, holistic diagnostic approach of pulse-examination followed in the traditional Chinese and Indian medicine has gained momentum with advanced instrumentation and digital recording (e.g. [

Hierarchical clustering and multivariate statistical analysis has supported the relevance and utility of these TIM diagnostic features in classifying the healthy and diseased/pathological cases and also in differential diagnosis of the later [

Recent research on pulse signals shows that spectral properties of pulse waveform are import in pulse-based diagnosis [

Our recently developed algorithm for accurate automatic detection of different patterns of pulse morphology and its variation over time as well the detection of consecutive patches of specific patterns/pattern-combination validated a crucial aspect of TIM practice of pulse-examination. It also made a notable, first ever contribution towards automated pulse-based diagnostic application [

As a particular spectral parameter, viz., the Fisher’s likelihood Ratio (FR), was found important in our algorithm for computational detection of different patterns of pulse waveform, it was a natural extension to analyze the possible relation between FR and the TIM diagnostic features. The features called gunas pertaining to “pulse properties perceived through touch”, by definition, “qualitatively” represent the pulse morphology. Interestingly, our results show a correlation between FR values for specific portion of the pulse (namely, between the 5^{th} and 45^{th} period) and the gunas.

Similar to other clinical/physiological/bio-chemical/bioelectrical features or parameters of the human mind- body system, pulse variation too is non-deterministic in nature. Whence, variation in FR should also be ideally analyzed as a random variable. We have therefore analyzed the empirical Probability Density Function (pdf) of FR. (These functions were estimated by best fitting of different theoretical/standard probability density functions to the relative frequency curve obtained from the data.) The results show significant distinction in the form and/or parameters of the pdf with respect different intervals or categories of several features.

It is interesting to note that non-standard or mixture of two standard distributions (e.g. in

The pdf obtained as “Uniform [a, b]” shows that FR would take any value within [a, b] with equal probability. This practically means no inference on the pulse morphology patterns (and hence on diagnosis) in terms of the mode or other statistical parameter of FR. Which means either the subject is healthy; e.g. in the group of Males having “Kaph” = 0; or there are different pathological conditions e.g. in the group of Males having systolic BP > 125 or in the groups of Males having Vaat > 4. In such a case, higher likelihood of distinct values of FR (i.e., the possibility of different patterns of pulse morphology) may be found by considering the specific range or category of the particular feature along with other feature(s) known as related with certain pathological condition. For example, high systolic BP together with higher body-weight and age would indicate risk of HT or cardiac problem, etc.

In the case of truncated Normal or Gamma, the most likely value (mode) of FR could be used for diagnostic inference in terms of pulse morphology provided the probability of this value is above certain threshold.

It should be noted that it was not our objective here to develop diagnostic rule or inference in terms of FR and/or any TIM feature. The aforesaid interpretation of the different forms of pdf against respective feature intervals or categories is mainly to underline the additional importance and future applications of this approach.

For real application, the pdf should be estimated for FR of consecutive segments (that define pulse morphology patterns [

As mentioned earlier, our objective and focus here was to analyze the relevance and importance, if any, of the TIM features for pulse-based diagnosis/prognosis. We have done it by analyzing the relation of these features with the spectral parameters of pulse that were found significant in recent instrumentation-based and computa- tional research on pulse-based diagnosis/prognosis. Results show significant relation and hence validate the relevance, significance and utility of the TIM diagnostic features. In addition, this study also highlights new possibilities of development of comprehensive diagnostic techniques to authenticate, support and expand the traditional approach of pulse-examination in a consistent and objective manner.

The author thanks summer intern Aporupa Bose for assistance in probability-curve fitting.