Functional-thermoregulatory model for the differential diagnosis of psoriatic arthritis
© Ismail et al.; licensee BioMed Central. 2014
Received: 11 July 2014
Accepted: 5 December 2014
Published: 11 December 2014
Psoriasis arthritis (PsA) is a chronic inflammatory arthritis of joints of uncertain pathogenesis. PsA may lead to severe disabilities even in the absence of any clinical symptom. Therefore, PsA diagnosis in its early stages is critical.
Material and methods
This study uses Control System theory to model finger skin thermoregulatory processes overlying the hand joint in response to an isometric exercise. The proposed model is based on a homeostatic negative feedback loop characterized by four distinct parameters that describe how the control mechanisms are activated and maintained. Thermal infrared imaging was used to record a total of 280 temperature curves of 14 finger joints for each of 11 PsA patients and 9 healthy controls.
Result and conclusion
PsA patients presented delayed and prolonged re-warming processes characterized by the undershoot onset after the end of the isometric exercise followed by a faster temperature increase. Region classification on the basis of the model parameters demonstrated that the interphalageal joint region of thumb better discriminates between patients and controls, providing 100% true-positive discrimination for PsA affected regions and 88.89% of correct classification of healthy regions. Even proved over a limited number of subjects, the proposed method may provide useful hints for early differential diagnosis in the IR assessment of PsA disease.
KeywordsControl system Cutaneous temperature Modeling Psoriatic arthritis Thermal infrared imaging Isometric exercise Multinomial logistic regression
Psoriasis (PsO) is a chronic, complex, immuno-inflammatory disease involving the skin and the musculoskeletal structures . Psoriasis arthritis (PsA) is a chronic inflammatory arthritis of uncertain pathogenesis that affects around 25% of worldwide psoriatic patients . PsA commonly affects the tips of fingers and toes . Psoriasis skin lesions typically precede the onset of joint symptoms, damage peripheral and axial joints by 10 months of symptom onset in around 27% of patients and 2 years of symptom onset in 47% of patients . After that period, patients experience severe disabilities such as difficulty with grasping their hand [1, 2]. The diagnosis of PsA is not always immediate since there are not specific circulating markers and its symptoms are frequently unstable. Ultrasonography (US) and magnetic resonance (MRI) are considered the gold standard imaging methods for documenting clinical and sub-clinical PsA . However, their use in clinical routine for early diagnosis of PsA may be limited by their cost (especially MRI) or dependency on the operator’ skill (especially US) [2, 3]. Local thermoregulatory malfunctions were found to be manifested by the presence of PsA disorder . In fact, psoriatic skin vascular features may induce large thermal changes in skin temperature in psoriatic plaques [3–5], however little is known about the effect of the joint inflammatory process of PsA on normal skin overlying affected joints in PsA patients. Infrared (IR) imaging is a non-invasive diagnostic technique that is able to provide two-dimensional maps of the cutaneous temperature distribution of a given body by measuring emitted infrared energy [6, 7]. Moreover, since the cutaneous temperature depends on the local blood perfusion and thermal tissue properties, functional Infrared imaging (fIR) provides a dynamical and functional indirect evaluation of local haematic flow, thermal properties and the functionality of thermoregulatory effectors of the cutaneous tissue in both basal conditions or in response to stimuli [6, 7]. Many inflammatory joint diseases such as Rheumatoid Arthritis (RA) and Juvenile Arthritis have been studied with fIR [8, 9]. In RA for example a direct relationship between disease activity (Ritchie score, morning stiffness) and skin temperature as for the heat distribution index was demonstrated. Several IR imaging studies have been performed to differentiate PsA plaque skin [1, 4, 10]. However, to our best knowledge, no study with the exception of our pilot study (Capo et al., ) has ever been performed to study the thermal changes of skin overlying joint in PsA that may be manifested by the PsA inflammatory condition that may present on the distal interphalangeal joints as well as larger joints. Moreover, while most of the IR diagnostic studies of PsA were usually performed on the basis of static IR evaluation (without performing any Challenge/diagnostic test) of the abnormalities in the corresponding thermal pattern [1, 4, 10], a dynamic and functional IR evaluation of temperature changes of skin overlying the proximal and distal interphalangeal Joints of PsA patients in both basal conditions or in response to functional (isometric) exercise, is rare. Studies have shown that skin blood flow (and thus indirectly cutaneous temperature) during isometric exercise undergoes a limitation due to cutaneous vasoconstriction . Recently, isometric exercise was evident to be potentially able to elicit significantly different thermal responses in both healthy and PsA patient groups . However, such evidence was based on a qualitative study without providing a broad understanding of the complex mechanism underlying thermoregulation malfunctions in this disease . Therefore, a quantitative evaluation of the cutaneous temperature of the skin overlying the proximal and distal Interphalangeal Joints of PsA patients in both basal conditions and in response to functional (isometric) exercise, could provide a functional indicator of the hypothetical PsA-related thermoregulatory malfunctions of skin overlying joints due to their inflammation thus providing a mean to assess indirectly PsA disease activity and help its primary diagnosis. Recently, control theory has been used to model different thermal responses due to pathological, functional, and morphological alterations in the skin thermoregulation system associated with vascular diseases like Raynaud’ phenomenon (RP) [6, 7, 12, 13]. Ismail et al. [12, 13] adopted a prototype second-order control system to model the skin thermal recovery response to a mild cold challenge. They suggested that the direct estimation of its time domain characteristics could provide an effective description of the local thermoregulatory malfunctions in the percense of RP disease and Varicocele. Mariotti et al. [6, 7] proposed a thermoregulatory model based on a homeostatic negative feedback loop characterized by four distinct functional parameters, which describe how thermal control mechanisms are activated and maintained in response to a cold challenge in the percense of RP disease and Varicocele. Due to the model limitation of the direct estimation approach [12, 13], in this study, we propose to implement the model proposed by Mariotti et al.  to evaluate how the PsA joint inflammatory characteristics affect the skin thermal recovery capability in response to isometric exercise. We expect that the application of such model may help in the primary diagnosis of PsA.
Modeling cutaneous thermoregulatory effectors for isometric exercise
Where s is the Laplace variable, Y(s), r and d are the output, reference input, and the disturbance inputs, respectively. Moreover, the set of parameters (i.e. a, k, d, and LT) could provide an insight on the dynamics and activity level of thermoregulatory effector mechanisms during both healthy state and the presence of a disease. In fact, the reciprocal of the plant time constant (a) represents the speed of the response of the thermal process to external and internal stimuli. The integral gain (k) could be considered as a descriptor of an active and systemic vasodilation process in restoring and maintaining the reference basal temperature conditions , since it refers to the control action and determines the efficiency of the feedback control system in achieving the steady state. The disturbance input (d) represents a passive heat exchange with the environment and, therefore, depends on room temperature and y(t). LT is a time required for the thermoregulatory processes to access the internal re-warming process after the end of the isometric exercise. During this time, the thermal variations are mostly attributable to the passive heat exchange with the environment. Once LT is finished, there is the onset of the re-warming process and the controller starts to restore the reference basal conditions T.
Where is the vector of experimental finger re-warming curves’ data points and is the vector of the estimated model’s data points. The data points are defined from i =1 to number of data points NE, and is the vector of the model parameters, i.e. a, k, d, and LT. From equations 5 and 6, the finger thermoregulatory model (Figure 3) is uniquely described by a, k, d, and LT, which can be estimated based on measurements of T and y(t) [6, 7] by solving the optimization problem defined by the cost function stated in equation 7.
Materials and methods
No. of subjects
Age (Mean ±Std) (Years)
This study was approved by the Human Board Review and conducted according to the Helsinki’s Declaration. All the subjects signed an informed consent and could withdraw from the study at any moment.
A total of 280 experimental temperature curves from 14 regions of interest were collected. Each curve included a baseline and a recovery time-course after a controlled isometric exercise. 154 and 126 curves were collected from PsA patients and HCs, respectively. Selected Areas (AR) for the fourteen Regions of Interest (ROIs) located on the hand’s dorsum corresponding to the interphalangeal joints (IP): both proximal and distal (IPP and IPD respectivily), metacarpophalangeal joints (MCP), nails and inter-bones muscles, as shown in Figure 1. Thermal IR imaging measurements were performed in a controlled-climate room. Patients seated with both hands placed on a table covered with a black sheet; measurements were made on the dominant hand to minimize potential bias due to muscle hypertrophy and motor capabilities. Prior to starting the thermal IR imaging recordings, the patients observed a 20-minute acclimatization period in the recording room, which was set at a standardized temperature (23°C), humidity (50-60%), without any direct ventilation . The subjects were asked to abstain from assuming any vasomotor substance (e.g., alcohol, coffee, tea etc), nor undergo of physical activity during the 2 hours prior to evaluation. High-resolution digital thermal images of the hand were acquired at baseline and after a functional exercise. The exercise consisted of repeated isometric contractions through the compression of a calibrated digital dynamometer interfaced to an ADInstruments 8/30 PowerLab computerized system . Subjects first underwent 1.5 minutes of baseline thermal recording. Next, subjects were required to press the dynamometer handle every 2 seconds for a total of 2 minutes at 20% of their previously assessed maximal individual strength. Soon after the exercise, the subjects repositioned their hand in the starting position, undergoing 5 minutes of thermal recording. We used a 14-bit digital thermal camera (FLIR SC660 QWIP, Sweden), sensitive in the 7-14 μ m band and with 0.04 κ temperature resolution. The thermal imaging’s sampling rate frequency was set to 0.1 Hz. ROI temperature data were extracted by means of the FLIR ThermaCAM Researcher Professional 2.9. Software.
Parameter estimation procedure
The Time- domain parameter Identification based on graphical method [ ]
Process gain is determined by dividing the steady state output (t → ∞)
(assumed to be the final output value of y(t)) by the input set point value (T).
The lag time or dead time is the time interval between the input being applied to the system
and the output responding to this signal. The time delay from the onset
of the re-warming process and the end of the isometric exercise is often
referred to as lag time (LT) .
Open loop pole location
It is the inverse of system time constant.
The system time constant is the time taken for the output
to reach 63% of the final value.
Parameter search space
Lag Time LT
Open pole location a
Integral controller gain K
Disturbance gain d
For each subject, the model parameters were computed for each of the fourteen regions of interest. The statistical analysis was performed to search for the most significant joint regions that could differentiate between PsA patients and HCs based on the estimated model parameters. To this goal, we analyzed the estimated model parameters at each joint regions individually and at the fourteen ROIs all together.The distributions of the estimated model parameters for each group were tested for normality by visual inspection of the frequency distribution and Shapiro-Wilk test . All the parameters for each group were compared through Wilcoxon-Mann-Whitney test . The level of statistical significance was fixed at 0.05. A multiple logistic regression classification algorithm  was performed in order to evaluate which parameter better reproduces the probability to detect and classify the presence of PsA as clinically diagnosed, according to the CASPAR criteria . The clinical diagnosis was adopted as independent variable. The classification procedure was a region-based classification. The cut-off for the best classification was established by means of a receiver operating characteristic (ROC) analysis  applied to the multiple logistic regression model output. ROC analysis allows the evaluation of the optimal cut-off for a binary classification resulting from a compromise between the 1-specificity, i.e., the false-positive rate, and the sensitivity, i.e., the true positive rate .
Group average values
Parameter (Mean(Standard deviation))
ROI 1 : I MCP
ROI 2 : IP
ROI3 : II MCP
ROI4 : I IPP
ROI5 : I IPD
ROI6: III MCP
ROI7: II IPP
ROI8: II IPD
ROI9: IV MCP
ROI10 : III IPP
ROI11 : III IPD
ROI12 : V MCP
ROI13 : IV IPP
ROI14 : IV IPD
All 14 ROIs
MCP used for Metacapphalangeal, IP used for Interphalangeal,
IPP used for proximal interphalangeal,and IPD used for distal interphalangeal
Wilcoxon statistical result
Region of interest
Model parameter (Ranksum,Z statistics, p value)
All 14 ROIs
Discriminant parameters for thumb interphalangeal joint region classification
Standard error SE
The aim of the present study was to identify quantitative parameters, which describe the functional differences in the thermal recovery of the skin, overlying the proximal and distal interphalangeal joints, from a controlled mild isometric exercise shown by healthy controls and PsA patients . We hypothesized that the implementation of the functional thermoregulatory model proposed by Mariotti et al.  to model the skin thermoregulatory processes in response to isometric exercise could evaluate how the pathophysiological differences due to joint inflammatory characteristics corresponding to the PsA disorder affect these processes [9, 15, 17]. The thermoregulatory system was modeled through two hierarchical control units: a higher level unit (supervisor) and a lower feedback level (executor) driven by the supervisor. The implemented model is unequivocally identified by a set of four functional parameters (a, k, d, LT) . The statistical analysis was performed for all the Interphalangeal, Metacarpophalangeal, Proximal Interphalangeal and Distal Interphalangeal regions individually and for the fourteen regions all together, in order to check which of them is the most significantly discriminating region between PsA and HCs groups. Our analysis confirmed that PsA patients exhibit different thermoregulatory dynamic responses to the controlled isometric exercise compared to HCs. Delayed and prolonged re-warming processes characterized by an undershoot onset after the end of the isometric exercise was found . This finding is expressed by the PsAs’ higher values for model disturbance gain (d). Therefore, in the presence of the disease, the skin thermoregulatory recovery process could be mainly based on the passive heat exchange because of the withdrawal of the cutaneous vasodilation activity and the intact vasoconstrictor action in the affected joint region [15, 17]. The higher k values found for PsA with respect to HCs values reflect the higher active and systemic vasodilation after the end of the onset undershoot. This finding might be attributed to a higher emissivity of the PsA areas  in the presence of more arterioles or even chronic structure widening of the existing arterioles with higher basal flux . Moreover, PsA showed a faster temperature increase after the undershoot onset compared to the healthy. This finding is evident by the higher mean values of the model parameter of open loop location (a). Region classification on the basis of the model parameters seems to indicate that thumb’s interphalageal joint region is the most expressive region. However, the small sample size does not allow to draw any conclusion about, as further studies on larger samples are needed. The misclassified healthy regions were attributed mostly to those exhibiting very small undershoot recovery curves in response to the controlled exercise. That finding might be due to the little effect on blood flow in nonglobrous skin (finger skin) known to be in normothermic conditions after the end of isometric exercise [15, 16]. It should be pointed out that the implementation of such an approach is valid within two limits: i) the limitations of the model itself, which is the assumption of a step response and the adoption of a simple prototype second-order system, ii) the limit of the time period after the end of the isometric exercise selected to study the dynamics of the temperature recovery curves (i.e. in our case 5 min). The method specificity has to be tested by increasing the number of participants.
In this study, we identified four quantitative parameters to describe the functional differences in thermal recovery from a controlled isometric exercise shown by PsA and healthy subjects. A homeostatic negative feedback loop, characterized by the four parameters, describes how the control mechanisms are activated, maintained in healthy individuals and impaired in PsA patients. Region classification on the basis of the model parameters demonstrated that Thumb’s interphalageal joint region is the most indicative region for PsA joint inflammatory disease, while further studies on larger samples are needed. In fact, it provided 100% true-positive discrimination for PsA affected regions and 88.89 % of correct classification of healthy regions.
The authors would like to thank Luigino Di Donato and Daniela Cardone, ITAB, for their assistance with data acquisition.
- Boehncke WH, Merolal JF, Thaçi D, Krueger GG, Walsh J, Kim N, Gottlieb AB: Diagnosing and treating psoriatic arthritis-an update. Br J Dermatol 2014, 170: 772–286. 10.1111/bjd.12748View ArticleGoogle Scholar
- Abd El Baky AM, Waked IS: Non-steroidal anti-inflammatory phonophoresis versus topical application in improvement of hand grip strength in psoriatic arthritic patients. J Am Sci 2011, 7: 110–114.Google Scholar
- Hern S, Stanton AW, Mellor R, Levick JR, Mortimer PS: Control of cutaneous blood vessels in psoriatic plaques. J Investigat Dermatol 1999, 113: 127–132. 10.1046/j.1523-1747.1999.00638.xView ArticleGoogle Scholar
- Warshaw TG: Thermal studies in psoriasis. J Investigat Dermatol 1973, 60: 91–93. 10.1111/1523-1747.ep12724168View ArticleGoogle Scholar
- Zalewska A, Gralewicz G, Owczarek G, Wiecek B: Thermography in psoriasis vulgaris evaluation. Conf Proc IEEE Eng Med Biol Soc 2005, 1: 627–630.Google Scholar
- Mariotti A, Grossi G, Amerio P, Orlando G, Mattei PA, Tulli A, Romani GL, Merla A: Finger thermoregulatory model assessing functional impairment in raynaud’s phenomenon. Ann Biomed Eng 2009, 37: 2631–2639. 10.1007/s10439-009-9788-9View ArticleGoogle Scholar
- Mariotti A, Di Carlo L, Orlando G, Corradini ML, Di Donato L, Pompa P, Iezzi R, Cotroneo AR, Romani GL, Merla A: Scrotal thermoregulatory model and assessment of the impairment of scrotal temperature control in varicocele. Ann Biomed Eng 2011, 39: 664–673. 10.1007/s10439-010-0191-3View ArticleGoogle Scholar
- Spalding SJ, Kwoh CK, Boudreau R, Enama J, Lunich J, Huber D, Denes L, Hirsch R: Three-dimensional and thermal surface imaging produces reliable measures of joint shape and temperature: a potential tool for quantifying arthritis. Arthritis Res Ther 2008. 10: R10.doi: 10.1186/ar2360.Google Scholar
- Devereaux MD, Parr GR, Thomas DP, Hazleman BL: Disease activity indexes in rheumatoid arthritis; a prospective, comparative study with thermography. Ann Rheum Dis 1985, 44: 434–437. 10.1136/ard.44.7.434View ArticleGoogle Scholar
- Castillo-Martínez C, Valdes-Rodríguez R, Kolosovas-Machuca ES, Moncada B, González FJ: Use of digital infrared imaging in the assessment of childhood psoriasis. Skin Res Technol 2013, 19: 549–551. 10.1111/j.1600-0846.2011.00611.xView ArticleGoogle Scholar
- Capo A, Merla A, Mattei P, Auriemma M, Panarese F, Celletti E, Abate M, Romani GL, Amerio P: Assessment of psoriatic arthritis by means of functional infrared imaging: A pilot study. Clinc Drug Investig 2013.Google Scholar
- Ismail E, Orlando G, Corradini ML, Amerio P, Romani GL, Merla A: Differential diagnosis of raynaud’s phenomenon based on modeling of finger thermoregulation. Physiol Meas 2014, 35: 703–716. 10.1088/0967-3334/35/4/703View ArticleGoogle Scholar
- Ismail E, Orlando G, Pompa P, Gabrielli D, Di Donato L, Cardone D, Merla A: Time-domain analysis of scrotal thermoregulatory impairment in varicocele. Front Physiol 2014, 5: 342.View ArticleGoogle Scholar
- Sawasaki N, Iwase S, Mano T: Effect of skin sympathetic response to local or systemic cold exposure on thermoregulatory functions in humans. Auton Neurosci 2001, 87: 274–281. 10.1016/S1566-0702(00)00253-8View ArticleGoogle Scholar
- Johnson JM, Minson CT, Kellogg DL Jr: Cutaneous vasodilator and vasoconstrictor mechanisms in temperature regulation. Compr Physiol 2014, 4: 33–89.View ArticleGoogle Scholar
- Shibasaki M, Secher NH, Johnson JM, Crandall CG: Central command and the cutaneous vascular response to isometric exercise in heated humans. J Physiol 2005, 565: 667–673. 10.1113/jphysiol.2005.083535View ArticleGoogle Scholar
- Johnson JM: Exercise in a hot environment: the skin circulation. scand J Med Sci Sports 2010, 20: 29–39.View ArticleGoogle Scholar
- Charkoudian N: Skin blood flow in adult human thermoregulation: how it works, when it does not, and why. Mayo Clin Proc 2003, 78: 603–612. 10.4065/78.5.603View ArticleGoogle Scholar
- Sanial DC, Maji NK: Thermoregulation through cutaneous under variable atmospheric and physiological conditions. J Theor Biol 2001, 208: 451–456. 10.1006/jtbi.2000.2231View ArticleGoogle Scholar
- Merla A, Di Donato L, Di Luzio S, Romani GL: Quantifing the relevance and stage of disease with the tau image technique: a complementary diagnostic imaging technique based on infrared functional imaging. IEEE Eng Med Biol Mag 2002, 21: 86–91.View ArticleGoogle Scholar
- Oussar Y, Dreyfus G: How to be a gray box: dynamic semi-physical modelling. Neural Netw 2001, 14: 1161–1172. 10.1016/S0893-6080(01)00096-XView ArticleGoogle Scholar
- Rollins D, Bhabdar N, Hulting S: System identification of the human thermoregulatory system using continuous-time block-oriented predictive modelling. Chem Eng Sci 2006, 61: 1516–1527. 10.1016/j.ces.2005.08.036View ArticleGoogle Scholar
- Waterhouse: Homeostatic control mechanism. Anaesth Intensive Care 2004, 5: 236–240. 10.1383/anes.184.108.40.206706View ArticleGoogle Scholar
- Forssel U, Ljung L: Closed loop identification revisited. Automatica 1999, 35: 1215–1241. 10.1016/S0005-1098(99)00022-9View ArticleGoogle Scholar
- Nocedal J, Wright SJ: Numerical Optimization. 2nd ednNew York: John Wiley and Sons; 2006.Google Scholar
- Kealy T, O’Dwyer A: Comparison of open and closed loop process identification techniques in the time domain. In Proceedings of the 3nd Wismarer Automatisierungssymposium, Wismar, Germany, September, 2001, Paper 1.3–4. Edited by: Smith Y. Germany: Wismar; 2001.Google Scholar
- Luo Y, Wang Y, Kong L: System identification of thermal process based on chaos particle swarm optimization. Automation and Logistics, 2008. ICAL 2008. IEEE International Conference on 2008, 2598–2602. doi:10.1109/ICAL.2008.4636610Google Scholar
- Lagarias JC, Reeds JA, Wright MH, Wright PE: Convergence properties of the nelder-mead simplex method in low dimensions. SIAM J Optimizat 1998, 9: 112–147. 10.1137/S1052623496303470MathSciNetView ArticleGoogle Scholar
- Tarantola A, Valette B: Generalized nonlinear inverse problems solved using the least squares criterion. Rev Geophys Space Phys 1982, 20: 219–233. 10.1029/RG020i002p00219MathSciNetView ArticleGoogle Scholar
- Razali NM, Wah YB: Power comparisons of shaprio-wilk, kolmogorov-smirnov, lilliefors and anderson- darling tests. J Stat Model Analytics 2011, 2: 22–33.Google Scholar
- Agresti A: Categorical Data Analysis. 2nd ednHoboken, NJ: Wiley InterScience; 2002.View ArticleGoogle Scholar
- Westin LK: Receiver operating characteristic (roc) analysis:evaluating discriminance effects among decision support systems. Technical report, Department of Computing Science in Umeå University, Computer Science Department,Umeå, Sweden; 2001. [http://www8.cs.umu.se/research/reports/2001/018/part1.pdf]Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.